TSTP Solution File: COM148+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM148+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 18:06:16 EDT 2022
% Result : Theorem 3.63s 2.53s
% Output : Proof 4.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM148+1 : TPTP v8.1.0. Released v6.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 15:27:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 3.63/2.53 % SZS status Theorem
% 3.63/2.53 % SZS output start Proof
% 3.63/2.53 tff(visSomeExp_type, type, (
% 3.63/2.53 visSomeExp: $i > $o)).
% 3.63/2.53 tff(vsomeExp_type, type, (
% 3.63/2.53 vsomeExp: $i > $i)).
% 3.63/2.53 tff(tptp_fun_Veout_75_type, type, (
% 3.63/2.53 tptp_fun_Veout_75: $i)).
% 3.63/2.53 tff(vabs_type, type, (
% 3.63/2.53 vabs: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2_69_type, type, (
% 3.63/2.53 tptp_fun_Ve2_69: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(ve1_type, type, (
% 3.63/2.53 ve1: $i)).
% 3.63/2.53 tff(varrow_type, type, (
% 3.63/2.53 varrow: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_VT_76_type, type, (
% 3.63/2.53 tptp_fun_VT_76: $i)).
% 3.63/2.53 tff(tptp_fun_VS_71_type, type, (
% 3.63/2.53 tptp_fun_VS_71: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(vapp_type, type, (
% 3.63/2.53 vapp: ( $i * $i ) > $i)).
% 3.63/2.53 tff(ve2_type, type, (
% 3.63/2.53 ve2: $i)).
% 3.63/2.53 tff(vempty_type, type, (
% 3.63/2.53 vempty: $i)).
% 3.63/2.53 tff(tptp_fun_VT1_68_type, type, (
% 3.63/2.53 tptp_fun_VT1_68: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Vx_70_type, type, (
% 3.63/2.53 tptp_fun_Vx_70: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(vtcheck_type, type, (
% 3.63/2.53 vtcheck: ( $i * $i * $i ) > $o)).
% 3.63/2.53 tff(tptp_fun_VT2_67_type, type, (
% 3.63/2.53 tptp_fun_VT2_67: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(vbind_type, type, (
% 3.63/2.53 vbind: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2_72_type, type, (
% 3.63/2.53 tptp_fun_Ve2_72: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1_73_type, type, (
% 3.63/2.53 tptp_fun_Ve1_73: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1_64_type, type, (
% 3.63/2.53 tptp_fun_Ve1_64: ( $i * $i ) > $i)).
% 3.63/2.53 tff(vreduce_type, type, (
% 3.63/2.53 vreduce: $i > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1red_63_type, type, (
% 3.63/2.53 tptp_fun_Ve1red_63: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2_65_type, type, (
% 3.63/2.53 tptp_fun_Ve2_65: ( $i * $i ) > $i)).
% 3.63/2.53 tff(vnoExp_type, type, (
% 3.63/2.53 vnoExp: $i)).
% 3.63/2.53 tff(tptp_fun_Veout_74_type, type, (
% 3.63/2.53 tptp_fun_Veout_74: $i)).
% 3.63/2.53 tff(visValue_type, type, (
% 3.63/2.53 visValue: $i > $o)).
% 3.63/2.53 tff(vsomeType_type, type, (
% 3.63/2.53 vsomeType: $i > $i)).
% 3.63/2.53 tff(vlookup_type, type, (
% 3.63/2.53 vlookup: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Vx_66_type, type, (
% 3.63/2.53 tptp_fun_Vx_66: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(vvar_type, type, (
% 3.63/2.53 vvar: $i > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2_60_type, type, (
% 3.63/2.53 tptp_fun_Ve2_60: ( $i * $i ) > $i)).
% 3.63/2.53 tff(vgetSomeExp_type, type, (
% 3.63/2.53 vgetSomeExp: $i > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1red_61_type, type, (
% 3.63/2.53 tptp_fun_Ve1red_61: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1_62_type, type, (
% 3.63/2.53 tptp_fun_Ve1_62: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2red_56_type, type, (
% 3.63/2.53 tptp_fun_Ve2red_56: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2_55_type, type, (
% 3.63/2.53 tptp_fun_Ve2_55: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1_57_type, type, (
% 3.63/2.53 tptp_fun_Ve1_57: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_VS_58_type, type, (
% 3.63/2.53 tptp_fun_VS_58: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Vx_59_type, type, (
% 3.63/2.53 tptp_fun_Vx_59: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Vx_44_type, type, (
% 3.63/2.53 tptp_fun_Vx_44: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2red_45_type, type, (
% 3.63/2.53 tptp_fun_Ve2red_45: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1_46_type, type, (
% 3.63/2.53 tptp_fun_Ve1_46: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_VS_47_type, type, (
% 3.63/2.53 tptp_fun_VS_47: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Vx_48_type, type, (
% 3.63/2.53 tptp_fun_Vx_48: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2_49_type, type, (
% 3.63/2.53 tptp_fun_Ve2_49: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve_41_type, type, (
% 3.63/2.53 tptp_fun_Ve_41: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_VS_42_type, type, (
% 3.63/2.53 tptp_fun_VS_42: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Vx_43_type, type, (
% 3.63/2.53 tptp_fun_Vx_43: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2_51_type, type, (
% 3.63/2.53 tptp_fun_Ve2_51: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve2red_53_type, type, (
% 3.63/2.53 tptp_fun_Ve2red_53: ( $i * $i ) > $i)).
% 3.63/2.53 tff(vsubst_type, type, (
% 3.63/2.53 vsubst: ( $i * $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Ve1_50_type, type, (
% 3.63/2.53 tptp_fun_Ve1_50: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_Vx_52_type, type, (
% 3.63/2.53 tptp_fun_Vx_52: ( $i * $i ) > $i)).
% 3.63/2.53 tff(tptp_fun_VS_54_type, type, (
% 3.63/2.53 tptp_fun_VS_54: ( $i * $i ) > $i)).
% 3.63/2.53 tff(1,assumption,(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))), introduced(assumption)).
% 3.63/2.53 tff(2,plain,
% 3.63/2.53 (vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)) = ve1),
% 3.63/2.53 inference(symmetry,[status(thm)],[1])).
% 3.63/2.53 tff(3,assumption,((~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))))) | (~((vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)) | (~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))))), introduced(assumption)).
% 3.63/2.53 tff(4,plain,
% 3.63/2.53 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : refl((~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))))),
% 3.63/2.53 inference(bind,[status(th)],[])).
% 3.63/2.53 tff(5,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 3.63/2.53 inference(quant_intro,[status(thm)],[4])).
% 3.63/2.53 tff(6,plain,
% 3.63/2.53 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : trans(monotonicity(rewrite(((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), trans(monotonicity(trans(monotonicity(rewrite(((VExp0 = VExp2) & (VExp1 = VExp3)) <=> (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> (~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), rewrite((~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> (((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), rewrite((((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), rewrite((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))))),
% 3.63/2.53 inference(bind,[status(th)],[])).
% 3.63/2.53 tff(7,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 3.63/2.53 inference(quant_intro,[status(thm)],[6])).
% 3.63/2.53 tff(8,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 3.63/2.53 inference(rewrite,[status(thm)],[])).
% 3.63/2.53 tff(9,plain,
% 3.63/2.53 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : rewrite((((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))))),
% 3.63/2.53 inference(bind,[status(th)],[])).
% 3.63/2.53 tff(10,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 3.63/2.53 inference(quant_intro,[status(thm)],[9])).
% 3.63/2.53 tff(11,axiom,(![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-app'')).
% 3.63/2.53 tff(12,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 3.63/2.53 inference(modus_ponens,[status(thm)],[11, 10])).
% 3.63/2.53 tff(13,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 3.63/2.53 inference(modus_ponens,[status(thm)],[12, 8])).
% 3.63/2.53 tff(14,plain,(
% 3.63/2.53 ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 3.63/2.53 inference(skolemize,[status(sab)],[13])).
% 3.63/2.53 tff(15,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 3.63/2.53 inference(modus_ponens,[status(thm)],[14, 7])).
% 3.63/2.53 tff(16,plain,
% 3.63/2.53 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 3.63/2.53 inference(modus_ponens,[status(thm)],[15, 5])).
% 3.63/2.53 tff(17,plain,
% 3.63/2.53 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))))) | (~((vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)) | (~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))))))),
% 3.63/2.53 inference(quant_inst,[status(thm)],[])).
% 3.63/2.53 tff(18,plain,
% 3.63/2.53 ($false),
% 3.63/2.53 inference(unit_resolution,[status(thm)],[17, 16, 3])).
% 3.63/2.53 tff(19,plain,(~((~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))))) | (~((vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)) | (~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))))), inference(lemma,lemma(discharge,[]))).
% 3.63/2.53 tff(20,plain,
% 3.63/2.53 (((~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))))) | (~((vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)) | (~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))))) | ((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))))),
% 3.63/2.53 inference(tautology,[status(thm)],[])).
% 3.63/2.53 tff(21,plain,
% 3.63/2.53 ((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))))),
% 3.63/2.53 inference(unit_resolution,[status(thm)],[20, 19])).
% 3.63/2.53 tff(22,plain,
% 3.63/2.53 ((vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)) <=> (vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.53 inference(commutativity,[status(thm)],[])).
% 3.63/2.53 tff(23,plain,
% 3.63/2.53 ((~(vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) <=> (~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.63/2.53 inference(monotonicity,[status(thm)],[22])).
% 3.63/2.53 tff(24,assumption,(vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)), introduced(assumption)).
% 3.63/2.53 tff(25,plain,
% 3.63/2.53 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 3.63/2.53 inference(bind,[status(th)],[])).
% 3.63/2.53 tff(26,plain,
% 3.63/2.53 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 3.63/2.53 inference(quant_intro,[status(thm)],[25])).
% 3.63/2.53 tff(27,plain,
% 3.63/2.53 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 3.63/2.53 inference(rewrite,[status(thm)],[])).
% 3.63/2.53 tff(28,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 3.63/2.53 tff(29,plain,
% 3.63/2.53 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 3.63/2.53 inference(modus_ponens,[status(thm)],[28, 27])).
% 3.63/2.53 tff(30,plain,(
% 3.63/2.53 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 3.63/2.53 inference(skolemize,[status(sab)],[29])).
% 3.63/2.53 tff(31,plain,
% 3.63/2.53 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 3.63/2.53 inference(modus_ponens,[status(thm)],[30, 26])).
% 3.63/2.54 tff(32,plain,
% 3.63/2.54 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)))),
% 3.63/2.54 inference(quant_inst,[status(thm)],[])).
% 3.63/2.54 tff(33,plain,
% 3.63/2.54 ($false),
% 3.63/2.54 inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 3.63/2.54 tff(34,plain,(~(vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))), inference(lemma,lemma(discharge,[]))).
% 3.63/2.54 tff(35,plain,
% 3.63/2.54 (~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[34, 23])).
% 3.63/2.54 tff(36,plain,
% 3.63/2.54 (((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76)))) | (vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.54 inference(tautology,[status(thm)],[])).
% 3.63/2.54 tff(37,plain,
% 3.63/2.54 ((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76)))),
% 3.63/2.54 inference(unit_resolution,[status(thm)],[36, 35])).
% 3.63/2.54 tff(38,plain,
% 3.63/2.54 ((vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)) <=> (vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.54 inference(commutativity,[status(thm)],[])).
% 3.63/2.54 tff(39,plain,
% 3.63/2.54 ((~(vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) <=> (~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.63/2.54 inference(monotonicity,[status(thm)],[38])).
% 3.63/2.54 tff(40,assumption,(vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)), introduced(assumption)).
% 3.63/2.54 tff(41,plain,
% 3.63/2.54 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : refl((~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))))),
% 3.63/2.54 inference(bind,[status(th)],[])).
% 3.63/2.54 tff(42,plain,
% 3.63/2.54 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.63/2.54 inference(quant_intro,[status(thm)],[41])).
% 3.63/2.54 tff(43,plain,
% 3.63/2.54 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.63/2.54 inference(rewrite,[status(thm)],[])).
% 3.63/2.54 tff(44,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-abs-app'')).
% 3.63/2.54 tff(45,plain,
% 3.63/2.54 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[44, 43])).
% 3.63/2.54 tff(46,plain,(
% 3.63/2.54 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.63/2.54 inference(skolemize,[status(sab)],[45])).
% 3.63/2.54 tff(47,plain,
% 3.63/2.54 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[46, 42])).
% 3.63/2.54 tff(48,plain,
% 3.63/2.54 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)))),
% 3.63/2.54 inference(quant_inst,[status(thm)],[])).
% 3.63/2.54 tff(49,plain,
% 3.63/2.54 ($false),
% 3.63/2.54 inference(unit_resolution,[status(thm)],[48, 47, 40])).
% 3.63/2.54 tff(50,plain,(~(vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))), inference(lemma,lemma(discharge,[]))).
% 3.63/2.54 tff(51,plain,
% 3.63/2.54 (~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[50, 39])).
% 3.63/2.54 tff(52,plain,
% 3.63/2.54 (((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))) | (~(VT!76 = varrow(tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.54 inference(tautology,[status(thm)],[])).
% 3.63/2.54 tff(53,plain,
% 3.63/2.54 ((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))) | (~(VT!76 = varrow(tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.54 inference(unit_resolution,[status(thm)],[52, 51])).
% 3.63/2.54 tff(54,plain,
% 3.63/2.54 (((vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2)))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> (vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 3.63/2.54 inference(rewrite,[status(thm)],[])).
% 3.63/2.54 tff(55,plain,
% 3.63/2.54 ((~(~(vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2)))))) <=> (vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2))))),
% 3.63/2.54 inference(rewrite,[status(thm)],[])).
% 3.63/2.54 tff(56,plain,
% 3.63/2.54 (((~(~(vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2)))))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> ((vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2)))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 3.63/2.54 inference(monotonicity,[status(thm)],[55])).
% 3.63/2.54 tff(57,plain,
% 3.63/2.54 (((~(~(vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2)))))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> (vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 3.63/2.54 inference(transitivity,[status(thm)],[56, 54])).
% 3.63/2.54 tff(58,plain,
% 3.63/2.54 ((~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 3.63/2.54 inference(rewrite,[status(thm)],[])).
% 3.63/2.54 tff(59,plain,
% 3.63/2.54 ((~![VT: $i] : ((vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2)))) => ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 3.63/2.54 inference(rewrite,[status(thm)],[])).
% 3.63/2.54 tff(60,axiom,(~![VT: $i] : ((vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2)))) => ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Progress-T-app'')).
% 3.63/2.54 tff(61,plain,
% 3.63/2.54 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[60, 59])).
% 3.63/2.54 tff(62,plain,
% 3.63/2.54 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[61, 58])).
% 3.63/2.54 tff(63,plain,
% 3.63/2.54 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[62, 58])).
% 3.63/2.54 tff(64,plain,
% 3.63/2.54 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[63, 58])).
% 3.63/2.54 tff(65,plain,
% 3.63/2.54 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[64, 58])).
% 3.63/2.54 tff(66,plain,
% 3.63/2.54 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[65, 58])).
% 3.63/2.54 tff(67,plain,
% 3.63/2.54 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[66, 58])).
% 3.63/2.54 tff(68,plain,
% 3.63/2.54 (vtcheck(vempty, vapp(ve1, ve2), VT!76) & (~visValue(vapp(ve1, ve2))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.63/2.54 inference(modus_ponens,[status(thm)],[67, 57])).
% 3.63/2.54 tff(69,plain,
% 3.63/2.54 (vtcheck(vempty, vapp(ve1, ve2), VT!76)),
% 3.63/2.54 inference(and_elim,[status(thm)],[68])).
% 3.63/2.54 tff(70,plain,
% 3.63/2.54 (^[Ve: $i, VT: $i, VC: $i] : refl(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))))),
% 3.63/2.54 inference(bind,[status(th)],[])).
% 3.63/2.54 tff(71,plain,
% 3.63/2.54 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 3.63/2.54 inference(quant_intro,[status(thm)],[70])).
% 3.63/2.54 tff(72,plain,
% 3.63/2.54 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(rewrite(((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) <=> (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT)))))), rewrite(((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) <=> (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))))), rewrite(((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) <=> (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))))), rewrite(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))))),
% 3.63/2.54 inference(bind,[status(th)],[])).
% 3.63/2.54 tff(73,plain,
% 3.63/2.54 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 3.63/2.54 inference(quant_intro,[status(thm)],[72])).
% 3.63/2.54 tff(74,plain,
% 3.63/2.54 (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve)))))),
% 3.63/2.55 inference(bind,[status(th)],[])).
% 3.63/2.55 tff(75,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))),
% 3.63/2.55 inference(quant_intro,[status(thm)],[74])).
% 3.63/2.55 tff(76,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 3.63/2.55 inference(rewrite,[status(thm)],[])).
% 3.63/2.55 tff(77,plain,
% 3.63/2.55 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 3.63/2.55 inference(bind,[status(th)],[])).
% 3.63/2.55 tff(78,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 3.63/2.55 inference(quant_intro,[status(thm)],[77])).
% 3.63/2.55 tff(79,axiom,(![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 3.63/2.55 tff(80,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 3.63/2.55 inference(modus_ponens,[status(thm)],[79, 78])).
% 3.63/2.55 tff(81,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 3.63/2.55 inference(modus_ponens,[status(thm)],[80, 76])).
% 3.63/2.55 tff(82,plain,(
% 3.63/2.55 ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 3.63/2.55 inference(skolemize,[status(sab)],[81])).
% 3.63/2.55 tff(83,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))),
% 3.63/2.55 inference(modus_ponens,[status(thm)],[82, 75])).
% 3.63/2.55 tff(84,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 3.63/2.55 inference(modus_ponens,[status(thm)],[83, 73])).
% 3.63/2.55 tff(85,plain,
% 3.63/2.55 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))),
% 3.63/2.55 inference(modus_ponens,[status(thm)],[84, 71])).
% 3.63/2.55 tff(86,plain,
% 3.63/2.55 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, vapp(ve1, ve2), VT!76)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))) | (~(VT!76 = varrow(tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vempty, vapp(ve1, ve2), VT!76)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))) | (~(VT!76 = varrow(tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.63/2.56 inference(rewrite,[status(thm)],[])).
% 3.63/2.56 tff(87,plain,
% 3.63/2.56 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, vapp(ve1, ve2), VT!76)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))) | (~(VT!76 = varrow(tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.63/2.56 inference(quant_inst,[status(thm)],[])).
% 3.63/2.56 tff(88,plain,
% 3.63/2.56 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vempty, vapp(ve1, ve2), VT!76)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))) | (~(VT!76 = varrow(tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.63/2.56 inference(modus_ponens,[status(thm)],[87, 86])).
% 3.63/2.56 tff(89,plain,
% 3.63/2.56 ((~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2))))) | (~(VT!76 = varrow(tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT1_68(vempty, VT!76, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_69(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VT2_67(vempty, VT!76, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.63/2.56 inference(unit_resolution,[status(thm)],[88, 85, 69])).
% 3.63/2.56 tff(90,plain,
% 3.63/2.56 ((~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_66(vempty, VT!76, vapp(ve1, ve2)), vempty) = vsomeType(VT!76))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.63/2.56 inference(unit_resolution,[status(thm)],[89, 53])).
% 3.63/2.56 tff(91,plain,
% 3.63/2.56 (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.63/2.56 inference(unit_resolution,[status(thm)],[90, 37])).
% 3.63/2.56 tff(92,plain,
% 3.63/2.56 (((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.56 inference(tautology,[status(thm)],[])).
% 3.63/2.56 tff(93,plain,
% 3.63/2.56 (vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))),
% 3.63/2.56 inference(unit_resolution,[status(thm)],[92, 91])).
% 3.63/2.56 tff(94,plain,
% 3.63/2.56 ((vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)) <=> (vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.57 inference(commutativity,[status(thm)],[])).
% 3.63/2.57 tff(95,plain,
% 3.63/2.57 ((vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) <=> (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))),
% 3.63/2.57 inference(symmetry,[status(thm)],[94])).
% 3.63/2.57 tff(96,assumption,(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), introduced(assumption)).
% 3.63/2.57 tff(97,plain,
% 3.63/2.57 (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)),
% 3.63/2.57 inference(modus_ponens,[status(thm)],[96, 95])).
% 3.63/2.57 tff(98,assumption,(~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))), introduced(assumption)).
% 3.63/2.57 tff(99,plain,
% 3.63/2.57 ($false),
% 3.63/2.57 inference(unit_resolution,[status(thm)],[98, 97])).
% 3.63/2.57 tff(100,plain,((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))), inference(lemma,lemma(discharge,[]))).
% 3.63/2.57 tff(101,plain,
% 3.63/2.57 (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)),
% 3.63/2.57 inference(unit_resolution,[status(thm)],[100, 93])).
% 3.63/2.57 tff(102,plain,
% 3.63/2.57 ((~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))))),
% 3.63/2.57 inference(tautology,[status(thm)],[])).
% 3.63/2.57 tff(103,plain,
% 3.63/2.57 (~((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)))),
% 3.63/2.57 inference(unit_resolution,[status(thm)],[102, 101, 21])).
% 3.63/2.57 tff(104,plain,
% 3.63/2.57 (((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))) | (tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)),
% 3.63/2.57 inference(tautology,[status(thm)],[])).
% 3.63/2.57 tff(105,plain,
% 3.63/2.57 (tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1),
% 3.63/2.57 inference(unit_resolution,[status(thm)],[104, 103])).
% 3.63/2.57 tff(106,plain,
% 3.63/2.57 (ve1 = tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))),
% 3.63/2.57 inference(symmetry,[status(thm)],[105])).
% 3.63/2.57 tff(107,plain,
% 3.63/2.57 (tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1) = tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))),
% 3.63/2.57 inference(monotonicity,[status(thm)],[106])).
% 3.63/2.57 tff(108,plain,
% 3.63/2.57 (tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1) = tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))),
% 3.63/2.57 inference(monotonicity,[status(thm)],[106])).
% 3.63/2.57 tff(109,plain,
% 3.63/2.57 (vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))),
% 3.63/2.57 inference(monotonicity,[status(thm)],[108, 107])).
% 3.63/2.57 tff(110,plain,
% 3.63/2.57 (vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))),
% 3.63/2.57 inference(symmetry,[status(thm)],[109])).
% 3.63/2.57 tff(111,plain,
% 3.63/2.57 (vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = ve1),
% 3.63/2.57 inference(transitivity,[status(thm)],[110, 2])).
% 3.63/2.57 tff(112,plain,
% 3.63/2.57 (visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))) <=> visValue(ve1)),
% 3.63/2.57 inference(monotonicity,[status(thm)],[111])).
% 3.63/2.57 tff(113,plain,
% 3.63/2.57 (visValue(ve1) <=> visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.63/2.57 inference(symmetry,[status(thm)],[112])).
% 3.63/2.57 tff(114,assumption,(visValue(ve1)), introduced(assumption)).
% 3.63/2.57 tff(115,plain,
% 3.63/2.57 (visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.63/2.57 inference(modus_ponens,[status(thm)],[114, 113])).
% 3.63/2.57 tff(116,plain,
% 3.63/2.57 (^[Ve1: $i, Ve2: $i, VExp0: $i] : refl(((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))) <=> ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))))),
% 3.63/2.57 inference(bind,[status(th)],[])).
% 3.63/2.57 tff(117,plain,
% 3.63/2.57 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))) <=> ![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 3.63/2.57 inference(quant_intro,[status(thm)],[116])).
% 3.63/2.57 tff(118,plain,
% 3.63/2.57 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))) <=> ![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 3.63/2.57 inference(rewrite,[status(thm)],[])).
% 3.63/2.57 tff(119,plain,
% 3.63/2.57 (^[Ve1: $i, Ve2: $i, VExp0: $i] : rewrite(((VExp0 = vapp(Ve1, Ve2)) => (~visValue(VExp0))) <=> ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))))),
% 3.63/2.57 inference(bind,[status(th)],[])).
% 3.63/2.57 tff(120,plain,
% 3.63/2.57 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((VExp0 = vapp(Ve1, Ve2)) => (~visValue(VExp0))) <=> ![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 3.63/2.57 inference(quant_intro,[status(thm)],[119])).
% 3.63/2.57 tff(121,axiom,(![Ve1: $i, Ve2: $i, VExp0: $i] : ((VExp0 = vapp(Ve1, Ve2)) => (~visValue(VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isValue2')).
% 3.63/2.57 tff(122,plain,
% 3.63/2.57 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 3.63/2.57 inference(modus_ponens,[status(thm)],[121, 120])).
% 3.63/2.57 tff(123,plain,
% 3.63/2.57 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 3.63/2.57 inference(modus_ponens,[status(thm)],[122, 118])).
% 3.63/2.57 tff(124,plain,(
% 3.63/2.57 ![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 3.63/2.57 inference(skolemize,[status(sab)],[123])).
% 3.63/2.57 tff(125,plain,
% 3.63/2.57 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 3.63/2.57 inference(modus_ponens,[status(thm)],[124, 117])).
% 3.63/2.57 tff(126,plain,
% 3.63/2.57 (((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))) <=> ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.63/2.57 inference(rewrite,[status(thm)],[])).
% 3.63/2.57 tff(127,plain,
% 3.63/2.57 (((~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | $false) <=> (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.63/2.57 inference(rewrite,[status(thm)],[])).
% 3.63/2.57 tff(128,plain,
% 3.63/2.57 ((~$true) <=> $false),
% 3.63/2.57 inference(rewrite,[status(thm)],[])).
% 3.63/2.57 tff(129,plain,
% 3.63/2.57 ((vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))) <=> $true),
% 3.63/2.57 inference(rewrite,[status(thm)],[])).
% 3.63/2.57 tff(130,plain,
% 3.63/2.57 ((~(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) <=> (~$true)),
% 3.63/2.57 inference(monotonicity,[status(thm)],[129])).
% 3.63/2.57 tff(131,plain,
% 3.63/2.57 ((~(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) <=> $false),
% 3.63/2.57 inference(transitivity,[status(thm)],[130, 128])).
% 3.63/2.57 tff(132,plain,
% 3.63/2.57 (((~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))) <=> ((~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | $false)),
% 3.63/2.57 inference(monotonicity,[status(thm)],[131])).
% 3.63/2.57 tff(133,plain,
% 3.63/2.57 (((~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))) <=> (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.63/2.57 inference(transitivity,[status(thm)],[132, 127])).
% 3.63/2.57 tff(134,plain,
% 3.63/2.57 (((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | ((~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.63/2.57 inference(monotonicity,[status(thm)],[133])).
% 3.63/2.57 tff(135,plain,
% 3.63/2.57 (((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | ((~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.63/2.57 inference(transitivity,[status(thm)],[134, 126])).
% 3.63/2.57 tff(136,plain,
% 3.63/2.57 ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | ((~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.63/2.58 inference(quant_inst,[status(thm)],[])).
% 3.63/2.58 tff(137,plain,
% 3.63/2.58 ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.63/2.58 inference(modus_ponens,[status(thm)],[136, 135])).
% 3.63/2.58 tff(138,plain,
% 3.63/2.58 (~visValue(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.63/2.58 inference(unit_resolution,[status(thm)],[137, 125])).
% 3.63/2.58 tff(139,plain,
% 3.63/2.58 ($false),
% 3.63/2.58 inference(unit_resolution,[status(thm)],[138, 115])).
% 3.63/2.58 tff(140,plain,((~visValue(ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))), inference(lemma,lemma(discharge,[]))).
% 3.63/2.58 tff(141,plain,
% 3.63/2.58 (~visValue(ve1)),
% 3.63/2.58 inference(unit_resolution,[status(thm)],[140, 1])).
% 3.63/2.58 tff(142,plain,
% 3.63/2.58 (vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)) <=> vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))),
% 3.63/2.58 inference(monotonicity,[status(thm)],[105])).
% 3.63/2.58 tff(143,plain,
% 3.63/2.58 (((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))),
% 3.63/2.58 inference(tautology,[status(thm)],[])).
% 3.63/2.58 tff(144,plain,
% 3.63/2.58 (vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))),
% 3.63/2.58 inference(unit_resolution,[status(thm)],[143, 91])).
% 3.63/2.58 tff(145,plain,
% 3.63/2.58 (vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))),
% 3.63/2.58 inference(modus_ponens,[status(thm)],[144, 142])).
% 3.63/2.58 tff(146,plain,
% 3.63/2.58 (^[VT: $i] : refl((visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT))) <=> (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT))))),
% 3.63/2.58 inference(bind,[status(th)],[])).
% 3.63/2.58 tff(147,plain,
% 3.63/2.58 (![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT))) <=> ![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))),
% 3.63/2.58 inference(quant_intro,[status(thm)],[146])).
% 3.63/2.58 tff(148,plain,
% 3.63/2.58 (^[VT: $i] : trans(monotonicity(trans(monotonicity(rewrite((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) <=> (~(visValue(ve1) | (~vtcheck(vempty, ve1, VT))))), ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) <=> (~(~(visValue(ve1) | (~vtcheck(vempty, ve1, VT))))))), rewrite((~(~(visValue(ve1) | (~vtcheck(vempty, ve1, VT))))) <=> (visValue(ve1) | (~vtcheck(vempty, ve1, VT)))), ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) <=> (visValue(ve1) | (~vtcheck(vempty, ve1, VT))))), (((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!74))) <=> ((visValue(ve1) | (~vtcheck(vempty, ve1, VT))) | (vreduce(ve1) = vsomeExp(Veout!74))))), rewrite(((visValue(ve1) | (~vtcheck(vempty, ve1, VT))) | (vreduce(ve1) = vsomeExp(Veout!74))) <=> (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))), (((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!74))) <=> (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))))),
% 3.63/2.58 inference(bind,[status(th)],[])).
% 3.63/2.58 tff(149,plain,
% 3.63/2.58 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!74))) <=> ![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))),
% 3.63/2.58 inference(quant_intro,[status(thm)],[148])).
% 3.63/2.58 tff(150,plain,
% 3.63/2.58 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 3.63/2.58 inference(rewrite,[status(thm)],[])).
% 3.63/2.58 tff(151,plain,
% 3.63/2.58 (^[VT: $i] : rewrite(((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) => ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))) <=> ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))))),
% 3.63/2.58 inference(bind,[status(th)],[])).
% 3.63/2.58 tff(152,plain,
% 3.63/2.58 (![VT: $i] : ((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) => ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 3.63/2.58 inference(quant_intro,[status(thm)],[151])).
% 3.63/2.58 tff(153,axiom,(![VT: $i] : ((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) => ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Progress-T-app-IH1'')).
% 3.63/2.58 tff(154,plain,
% 3.63/2.58 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 3.63/2.58 inference(modus_ponens,[status(thm)],[153, 152])).
% 3.63/2.58 tff(155,plain,
% 3.63/2.58 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 3.63/2.58 inference(modus_ponens,[status(thm)],[154, 150])).
% 3.63/2.58 tff(156,plain,(
% 3.63/2.58 ![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!74)))),
% 3.63/2.58 inference(skolemize,[status(sab)],[155])).
% 3.63/2.58 tff(157,plain,
% 3.63/2.58 (![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))),
% 3.63/2.58 inference(modus_ponens,[status(thm)],[156, 149])).
% 3.63/2.58 tff(158,plain,
% 3.63/2.58 (![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))),
% 3.63/2.58 inference(modus_ponens,[status(thm)],[157, 147])).
% 3.63/2.58 tff(159,plain,
% 3.63/2.58 (((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))) | (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))))) <=> ((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))) | visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))))),
% 3.63/2.58 inference(rewrite,[status(thm)],[])).
% 3.63/2.58 tff(160,plain,
% 3.63/2.58 ((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))) | (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))))),
% 3.63/2.58 inference(quant_inst,[status(thm)],[])).
% 3.63/2.58 tff(161,plain,
% 3.63/2.58 ((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, VT)))) | visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))),
% 3.63/2.58 inference(modus_ponens,[status(thm)],[160, 159])).
% 3.63/2.58 tff(162,plain,
% 3.63/2.58 (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!74))),
% 3.63/2.58 inference(unit_resolution,[status(thm)],[161, 158, 145])).
% 3.63/2.58 tff(163,plain,
% 3.63/2.58 (vreduce(ve1) = vsomeExp(Veout!74)),
% 3.63/2.58 inference(unit_resolution,[status(thm)],[162, 141])).
% 3.63/2.58 tff(164,plain,
% 3.63/2.58 (((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))))) <=> ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))))))),
% 3.63/2.58 inference(rewrite,[status(thm)],[])).
% 3.63/2.58 tff(165,plain,
% 3.63/2.58 ((~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) <=> (~((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))))),
% 3.63/2.58 inference(rewrite,[status(thm)],[])).
% 3.63/2.58 tff(166,plain,
% 3.63/2.58 (((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))) <=> ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))))))),
% 3.63/2.59 inference(monotonicity,[status(thm)],[165])).
% 3.63/2.59 tff(167,plain,
% 3.63/2.59 (((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))) <=> ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))))))),
% 3.63/2.59 inference(transitivity,[status(thm)],[166, 164])).
% 3.63/2.59 tff(168,plain,
% 3.63/2.59 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))),
% 3.63/2.59 inference(quant_inst,[status(thm)],[])).
% 3.63/2.59 tff(169,plain,
% 3.63/2.59 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))))),
% 3.63/2.60 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.63/2.60 tff(170,plain,
% 3.63/2.60 (~((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))))),
% 3.63/2.60 inference(unit_resolution,[status(thm)],[169, 16])).
% 3.63/2.60 tff(171,plain,
% 3.63/2.60 (((~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))) | (~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))) | ((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))),
% 3.71/2.60 inference(tautology,[status(thm)],[])).
% 3.71/2.60 tff(172,plain,
% 3.71/2.60 ((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.71/2.60 inference(unit_resolution,[status(thm)],[171, 170])).
% 3.71/2.60 tff(173,plain,
% 3.71/2.60 (vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(ve1, ve2)),
% 3.71/2.60 inference(monotonicity,[status(thm)],[111])).
% 3.71/2.60 tff(174,plain,
% 3.71/2.60 (vapp(ve1, ve2) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)),
% 3.71/2.60 inference(symmetry,[status(thm)],[173])).
% 3.71/2.60 tff(175,plain,
% 3.71/2.60 (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(ve1, ve2)),
% 3.71/2.60 inference(symmetry,[status(thm)],[93])).
% 3.71/2.60 tff(176,assumption,(~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))), introduced(assumption)).
% 3.71/2.60 tff(177,plain,
% 3.71/2.60 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))) | (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.60 inference(tautology,[status(thm)],[])).
% 3.71/2.60 tff(178,plain,
% 3.71/2.60 (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.60 inference(unit_resolution,[status(thm)],[177, 176])).
% 3.71/2.60 tff(179,plain,
% 3.71/2.60 (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))),
% 3.71/2.60 inference(symmetry,[status(thm)],[178])).
% 3.71/2.60 tff(180,plain,
% 3.71/2.60 (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)),
% 3.71/2.60 inference(transitivity,[status(thm)],[179, 175, 174])).
% 3.71/2.60 tff(181,plain,
% 3.71/2.60 ((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.71/2.61 inference(tautology,[status(thm)],[])).
% 3.71/2.61 tff(182,plain,
% 3.71/2.61 ((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[181, 180])).
% 3.71/2.61 tff(183,plain,
% 3.71/2.61 (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[182, 172])).
% 3.71/2.61 tff(184,plain,
% 3.71/2.61 (((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))) | (tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.61 inference(tautology,[status(thm)],[])).
% 3.71/2.61 tff(185,plain,
% 3.71/2.61 (tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[184, 183])).
% 3.71/2.61 tff(186,plain,
% 3.71/2.61 (tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve1),
% 3.71/2.61 inference(transitivity,[status(thm)],[185, 110, 2])).
% 3.71/2.61 tff(187,plain,
% 3.71/2.61 (vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vreduce(ve1)),
% 3.71/2.61 inference(monotonicity,[status(thm)],[186])).
% 3.71/2.61 tff(188,plain,
% 3.71/2.61 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))) | (tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.61 inference(tautology,[status(thm)],[])).
% 3.71/2.61 tff(189,plain,
% 3.71/2.61 (tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[188, 176])).
% 3.71/2.61 tff(190,plain,
% 3.71/2.61 (tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vsomeExp(Veout!74)),
% 3.71/2.61 inference(transitivity,[status(thm)],[189, 187, 163])).
% 3.71/2.61 tff(191,plain,
% 3.71/2.61 (visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) <=> visSomeExp(vsomeExp(Veout!74))),
% 3.71/2.61 inference(monotonicity,[status(thm)],[190])).
% 3.71/2.61 tff(192,plain,
% 3.71/2.61 (visSomeExp(vsomeExp(Veout!74)) <=> visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.61 inference(symmetry,[status(thm)],[191])).
% 3.71/2.61 tff(193,plain,
% 3.71/2.61 (^[Ve: $i, VOptExp0: $i] : refl((visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))) <=> (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))))),
% 3.71/2.61 inference(bind,[status(th)],[])).
% 3.71/2.61 tff(194,plain,
% 3.71/2.61 (![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))) <=> ![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 3.71/2.61 inference(quant_intro,[status(thm)],[193])).
% 3.71/2.61 tff(195,plain,
% 3.71/2.61 (![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))) <=> ![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 3.71/2.61 inference(rewrite,[status(thm)],[])).
% 3.71/2.61 tff(196,plain,
% 3.71/2.61 (^[Ve: $i, VOptExp0: $i] : rewrite(((VOptExp0 = vsomeExp(Ve)) => visSomeExp(VOptExp0)) <=> (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))))),
% 3.71/2.61 inference(bind,[status(th)],[])).
% 3.71/2.61 tff(197,plain,
% 3.71/2.61 (![Ve: $i, VOptExp0: $i] : ((VOptExp0 = vsomeExp(Ve)) => visSomeExp(VOptExp0)) <=> ![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 3.71/2.61 inference(quant_intro,[status(thm)],[196])).
% 3.71/2.61 tff(198,axiom,(![Ve: $i, VOptExp0: $i] : ((VOptExp0 = vsomeExp(Ve)) => visSomeExp(VOptExp0))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isSomeExp1')).
% 3.71/2.61 tff(199,plain,
% 3.71/2.61 (![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 3.71/2.61 inference(modus_ponens,[status(thm)],[198, 197])).
% 3.71/2.61 tff(200,plain,
% 3.71/2.61 (![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 3.71/2.61 inference(modus_ponens,[status(thm)],[199, 195])).
% 3.71/2.61 tff(201,plain,(
% 3.71/2.61 ![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 3.71/2.61 inference(skolemize,[status(sab)],[200])).
% 3.71/2.61 tff(202,plain,
% 3.71/2.61 (![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 3.71/2.61 inference(modus_ponens,[status(thm)],[201, 194])).
% 3.71/2.61 tff(203,plain,
% 3.71/2.61 (((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!74))) <=> ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!74)))),
% 3.71/2.61 inference(rewrite,[status(thm)],[])).
% 3.71/2.61 tff(204,plain,
% 3.71/2.61 ((visSomeExp(vsomeExp(Veout!74)) | $false) <=> visSomeExp(vsomeExp(Veout!74))),
% 3.71/2.61 inference(rewrite,[status(thm)],[])).
% 3.71/2.61 tff(205,plain,
% 3.71/2.61 ((vsomeExp(Veout!74) = vsomeExp(Veout!74)) <=> $true),
% 3.71/2.61 inference(rewrite,[status(thm)],[])).
% 3.71/2.61 tff(206,plain,
% 3.71/2.61 ((~(vsomeExp(Veout!74) = vsomeExp(Veout!74))) <=> (~$true)),
% 3.71/2.61 inference(monotonicity,[status(thm)],[205])).
% 3.71/2.61 tff(207,plain,
% 3.71/2.61 ((~(vsomeExp(Veout!74) = vsomeExp(Veout!74))) <=> $false),
% 3.71/2.61 inference(transitivity,[status(thm)],[206, 128])).
% 3.71/2.61 tff(208,plain,
% 3.71/2.61 ((visSomeExp(vsomeExp(Veout!74)) | (~(vsomeExp(Veout!74) = vsomeExp(Veout!74)))) <=> (visSomeExp(vsomeExp(Veout!74)) | $false)),
% 3.71/2.61 inference(monotonicity,[status(thm)],[207])).
% 3.71/2.61 tff(209,plain,
% 3.71/2.61 ((visSomeExp(vsomeExp(Veout!74)) | (~(vsomeExp(Veout!74) = vsomeExp(Veout!74)))) <=> visSomeExp(vsomeExp(Veout!74))),
% 3.71/2.61 inference(transitivity,[status(thm)],[208, 204])).
% 3.71/2.61 tff(210,plain,
% 3.71/2.61 (((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | (visSomeExp(vsomeExp(Veout!74)) | (~(vsomeExp(Veout!74) = vsomeExp(Veout!74))))) <=> ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!74)))),
% 3.71/2.61 inference(monotonicity,[status(thm)],[209])).
% 3.71/2.61 tff(211,plain,
% 3.71/2.61 (((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | (visSomeExp(vsomeExp(Veout!74)) | (~(vsomeExp(Veout!74) = vsomeExp(Veout!74))))) <=> ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!74)))),
% 3.71/2.61 inference(transitivity,[status(thm)],[210, 203])).
% 3.71/2.61 tff(212,plain,
% 3.71/2.61 ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | (visSomeExp(vsomeExp(Veout!74)) | (~(vsomeExp(Veout!74) = vsomeExp(Veout!74))))),
% 3.71/2.61 inference(quant_inst,[status(thm)],[])).
% 3.71/2.61 tff(213,plain,
% 3.71/2.61 ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!74))),
% 3.71/2.61 inference(modus_ponens,[status(thm)],[212, 211])).
% 3.71/2.61 tff(214,plain,
% 3.71/2.61 (visSomeExp(vsomeExp(Veout!74))),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[213, 202])).
% 3.71/2.61 tff(215,plain,
% 3.71/2.61 (visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.61 inference(modus_ponens,[status(thm)],[214, 192])).
% 3.71/2.61 tff(216,plain,
% 3.71/2.61 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))) | (~visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.61 inference(tautology,[status(thm)],[])).
% 3.71/2.61 tff(217,plain,
% 3.71/2.61 (~visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[216, 176])).
% 3.71/2.61 tff(218,plain,
% 3.71/2.61 ($false),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[217, 215])).
% 3.71/2.61 tff(219,plain,(((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))) | (~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.61 tff(220,plain,
% 3.71/2.61 ((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[219, 1])).
% 3.71/2.61 tff(221,assumption,(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))), introduced(assumption)).
% 3.71/2.61 tff(222,plain,
% 3.71/2.61 (^[Veout: $i] : refl((~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))) <=> (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 3.71/2.61 inference(bind,[status(th)],[])).
% 3.71/2.61 tff(223,plain,
% 3.71/2.61 (![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))) <=> ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.71/2.61 inference(quant_intro,[status(thm)],[222])).
% 3.71/2.61 tff(224,plain,
% 3.71/2.61 (![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.71/2.61 inference(and_elim,[status(thm)],[68])).
% 3.71/2.61 tff(225,plain,
% 3.71/2.61 (![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 3.71/2.61 inference(modus_ponens,[status(thm)],[224, 223])).
% 3.71/2.61 tff(226,plain,
% 3.71/2.61 ((~![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 3.71/2.61 inference(quant_inst,[status(thm)],[])).
% 3.71/2.61 tff(227,plain,
% 3.71/2.61 ($false),
% 3.71/2.61 inference(unit_resolution,[status(thm)],[226, 225, 221])).
% 3.71/2.61 tff(228,plain,(~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.61 tff(229,plain,
% 3.71/2.61 (((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.62 inference(tautology,[status(thm)],[])).
% 3.71/2.62 tff(230,plain,
% 3.71/2.62 ((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 3.71/2.62 inference(unit_resolution,[status(thm)],[229, 228])).
% 3.71/2.62 tff(231,plain,
% 3.71/2.62 ((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) <=> (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.62 inference(commutativity,[status(thm)],[])).
% 3.71/2.62 tff(232,plain,
% 3.71/2.62 (vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))),
% 3.71/2.62 inference(transitivity,[status(thm)],[173, 93])).
% 3.71/2.62 tff(233,plain,
% 3.71/2.62 ((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) <=> (vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.71/2.62 inference(monotonicity,[status(thm)],[232])).
% 3.71/2.62 tff(234,plain,
% 3.71/2.62 ((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) <=> (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.62 inference(transitivity,[status(thm)],[233, 231])).
% 3.71/2.62 tff(235,plain,
% 3.71/2.62 ((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) <=> (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.62 inference(monotonicity,[status(thm)],[234])).
% 3.71/2.62 tff(236,plain,
% 3.71/2.62 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))),
% 3.71/2.62 inference(quant_inst,[status(thm)],[])).
% 3.71/2.62 tff(237,plain,
% 3.71/2.62 (~((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))),
% 3.71/2.62 inference(unit_resolution,[status(thm)],[236, 16])).
% 3.71/2.62 tff(238,plain,
% 3.71/2.62 (((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))) | ((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))),
% 3.71/2.63 inference(tautology,[status(thm)],[])).
% 3.71/2.63 tff(239,plain,
% 3.71/2.63 ((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.71/2.63 inference(unit_resolution,[status(thm)],[238, 237])).
% 3.71/2.63 tff(240,plain,
% 3.71/2.63 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.63 inference(quant_inst,[status(thm)],[])).
% 3.71/2.63 tff(241,plain,
% 3.71/2.63 (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.63 inference(unit_resolution,[status(thm)],[240, 47])).
% 3.71/2.63 tff(242,plain,
% 3.71/2.63 (((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))) | (vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.63 inference(tautology,[status(thm)],[])).
% 3.71/2.63 tff(243,plain,
% 3.71/2.63 ((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))),
% 3.71/2.63 inference(unit_resolution,[status(thm)],[242, 241])).
% 3.71/2.63 tff(244,assumption,(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)), introduced(assumption)).
% 3.71/2.63 tff(245,plain,
% 3.71/2.63 ((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.71/2.64 inference(tautology,[status(thm)],[])).
% 3.71/2.64 tff(246,plain,
% 3.71/2.64 ((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.71/2.64 inference(unit_resolution,[status(thm)],[245, 244])).
% 3.71/2.64 tff(247,plain,
% 3.71/2.64 ($false),
% 3.71/2.64 inference(unit_resolution,[status(thm)],[246, 243, 239])).
% 3.71/2.64 tff(248,plain,(~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.64 tff(249,plain,
% 3.71/2.64 (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.64 inference(modus_ponens,[status(thm)],[248, 235])).
% 3.71/2.64 tff(250,plain,
% 3.71/2.64 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.64 inference(tautology,[status(thm)],[])).
% 3.71/2.64 tff(251,plain,
% 3.71/2.64 ((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.64 inference(unit_resolution,[status(thm)],[250, 249])).
% 3.71/2.64 tff(252,plain,
% 3.71/2.64 ((vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) <=> (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.64 inference(commutativity,[status(thm)],[])).
% 3.71/2.64 tff(253,plain,
% 3.71/2.64 ((vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) <=> (vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.71/2.64 inference(monotonicity,[status(thm)],[232])).
% 3.71/2.64 tff(254,plain,
% 3.71/2.64 ((vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) <=> (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.64 inference(transitivity,[status(thm)],[253, 252])).
% 3.71/2.64 tff(255,plain,
% 3.71/2.64 ((~(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) <=> (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.64 inference(monotonicity,[status(thm)],[254])).
% 3.71/2.64 tff(256,assumption,(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)), introduced(assumption)).
% 3.71/2.64 tff(257,plain,
% 3.71/2.64 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)))),
% 3.71/2.64 inference(quant_inst,[status(thm)],[])).
% 3.71/2.64 tff(258,plain,
% 3.71/2.64 ($false),
% 3.71/2.64 inference(unit_resolution,[status(thm)],[257, 31, 256])).
% 3.71/2.64 tff(259,plain,(~(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.64 tff(260,plain,
% 3.71/2.64 (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.64 inference(modus_ponens,[status(thm)],[259, 255])).
% 3.71/2.65 tff(261,plain,
% 3.71/2.65 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.65 inference(tautology,[status(thm)],[])).
% 3.71/2.65 tff(262,plain,
% 3.71/2.65 ((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.65 inference(unit_resolution,[status(thm)],[261, 260])).
% 3.71/2.65 tff(263,assumption,(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))), introduced(assumption)).
% 3.71/2.65 tff(264,plain,
% 3.71/2.65 ((~![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.71/2.65 inference(quant_inst,[status(thm)],[])).
% 3.71/2.65 tff(265,plain,
% 3.71/2.65 ($false),
% 3.71/2.65 inference(unit_resolution,[status(thm)],[264, 225, 263])).
% 3.71/2.65 tff(266,plain,(~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.65 tff(267,plain,
% 3.71/2.65 (((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 3.71/2.65 inference(tautology,[status(thm)],[])).
% 3.71/2.65 tff(268,plain,
% 3.71/2.65 ((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.71/2.65 inference(unit_resolution,[status(thm)],[267, 266])).
% 3.71/2.65 tff(269,assumption,(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))), introduced(assumption)).
% 3.71/2.65 tff(270,plain,
% 3.71/2.65 (visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) <=> visValue(vapp(ve1, ve2))),
% 3.71/2.65 inference(monotonicity,[status(thm)],[175])).
% 3.71/2.65 tff(271,plain,
% 3.71/2.65 (visValue(vapp(ve1, ve2)) <=> visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.71/2.65 inference(symmetry,[status(thm)],[270])).
% 3.71/2.65 tff(272,plain,
% 3.71/2.65 ((~visValue(vapp(ve1, ve2))) <=> (~visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.65 inference(monotonicity,[status(thm)],[271])).
% 3.71/2.65 tff(273,plain,
% 3.71/2.65 (~visValue(vapp(ve1, ve2))),
% 3.71/2.65 inference(and_elim,[status(thm)],[68])).
% 3.71/2.65 tff(274,plain,
% 3.71/2.65 (~visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.71/2.65 inference(modus_ponens,[status(thm)],[273, 272])).
% 3.71/2.65 tff(275,plain,
% 3.71/2.65 (^[Vx: $i, VS: $i, Ve: $i, VExp0: $i] : refl((visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve)))) <=> (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve)))))),
% 3.71/2.65 inference(bind,[status(th)],[])).
% 3.71/2.65 tff(276,plain,
% 3.71/2.65 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve)))) <=> ![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 3.71/2.65 inference(quant_intro,[status(thm)],[275])).
% 3.71/2.65 tff(277,plain,
% 3.71/2.65 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve)))) <=> ![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 3.71/2.65 inference(rewrite,[status(thm)],[])).
% 3.71/2.65 tff(278,plain,
% 3.71/2.65 (^[Vx: $i, VS: $i, Ve: $i, VExp0: $i] : rewrite(((VExp0 = vabs(Vx, VS, Ve)) => visValue(VExp0)) <=> (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve)))))),
% 3.71/2.65 inference(bind,[status(th)],[])).
% 3.71/2.65 tff(279,plain,
% 3.71/2.65 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : ((VExp0 = vabs(Vx, VS, Ve)) => visValue(VExp0)) <=> ![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 3.71/2.65 inference(quant_intro,[status(thm)],[278])).
% 3.71/2.65 tff(280,axiom,(![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : ((VExp0 = vabs(Vx, VS, Ve)) => visValue(VExp0))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isValue0')).
% 3.71/2.65 tff(281,plain,
% 3.71/2.65 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 3.71/2.65 inference(modus_ponens,[status(thm)],[280, 279])).
% 3.71/2.65 tff(282,plain,
% 3.71/2.65 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 3.71/2.65 inference(modus_ponens,[status(thm)],[281, 277])).
% 3.71/2.65 tff(283,plain,(
% 3.71/2.65 ![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 3.71/2.65 inference(skolemize,[status(sab)],[282])).
% 3.71/2.65 tff(284,plain,
% 3.71/2.65 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 3.71/2.65 inference(modus_ponens,[status(thm)],[283, 276])).
% 3.71/2.65 tff(285,plain,
% 3.71/2.65 (((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | (visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) <=> ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 3.71/2.65 inference(rewrite,[status(thm)],[])).
% 3.71/2.65 tff(286,plain,
% 3.71/2.65 ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | (visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 3.71/2.65 inference(quant_inst,[status(thm)],[])).
% 3.71/2.65 tff(287,plain,
% 3.71/2.65 ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | visValue(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.65 inference(modus_ponens,[status(thm)],[286, 285])).
% 3.71/2.65 tff(288,plain,
% 3.71/2.65 ($false),
% 3.71/2.65 inference(unit_resolution,[status(thm)],[287, 284, 274, 269])).
% 3.71/2.65 tff(289,plain,(~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.65 tff(290,plain,
% 3.71/2.65 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.71/2.65 inference(tautology,[status(thm)],[])).
% 3.71/2.65 tff(291,plain,
% 3.71/2.65 ((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.66 inference(unit_resolution,[status(thm)],[290, 289])).
% 3.71/2.66 tff(292,assumption,(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))), introduced(assumption)).
% 3.71/2.66 tff(293,plain,
% 3.71/2.66 ((~![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 3.71/2.66 inference(quant_inst,[status(thm)],[])).
% 3.71/2.66 tff(294,plain,
% 3.71/2.66 ($false),
% 3.71/2.66 inference(unit_resolution,[status(thm)],[293, 225, 292])).
% 3.71/2.66 tff(295,plain,(~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))), inference(lemma,lemma(discharge,[]))).
% 3.71/2.66 tff(296,plain,
% 3.71/2.66 (((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.66 inference(tautology,[status(thm)],[])).
% 3.71/2.66 tff(297,plain,
% 3.71/2.66 ((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.71/2.66 inference(unit_resolution,[status(thm)],[296, 295])).
% 3.71/2.66 tff(298,plain,
% 3.71/2.66 ((vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2))) <=> (vreduce(vapp(ve1, ve2)) = vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.71/2.66 inference(commutativity,[status(thm)],[])).
% 3.71/2.66 tff(299,plain,
% 3.71/2.66 ((vreduce(vapp(ve1, ve2)) = vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) <=> (vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))),
% 3.71/2.66 inference(symmetry,[status(thm)],[298])).
% 3.71/2.66 tff(300,plain,
% 3.71/2.66 (vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2))),
% 3.71/2.66 inference(monotonicity,[status(thm)],[175])).
% 3.71/2.66 tff(301,plain,
% 3.71/2.66 (vreduce(vapp(ve1, ve2)) = vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.71/2.66 inference(symmetry,[status(thm)],[300])).
% 3.71/2.66 tff(302,plain,
% 3.71/2.66 (vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2))),
% 3.71/2.66 inference(modus_ponens,[status(thm)],[301, 299])).
% 3.71/2.66 tff(303,plain,
% 3.71/2.66 (^[VExp0: $i, RESULT: $i] : trans(monotonicity(rewrite((~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) <=> (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))))))))), rewrite((~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) <=> (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)))))))), rewrite((~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) <=> (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))))))), rewrite((~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) <=> (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))))))), rewrite((~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))))) <=> (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))))))), (((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))) <=> ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))))))))), rewrite(((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))))))) <=> ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))), (((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))) <=> ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))))),
% 3.71/2.66 inference(bind,[status(th)],[])).
% 3.71/2.66 tff(304,plain,
% 3.71/2.66 (![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))) <=> ![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))),
% 3.71/2.66 inference(quant_intro,[status(thm)],[303])).
% 3.71/2.66 tff(305,plain,
% 3.71/2.66 (^[VExp0: $i, RESULT: $i] : rewrite(((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))) <=> ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))))),
% 3.71/2.66 inference(bind,[status(th)],[])).
% 3.71/2.66 tff(306,plain,
% 3.71/2.66 (![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))) <=> ![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))))))),
% 3.71/2.66 inference(quant_intro,[status(thm)],[305])).
% 3.71/2.66 tff(307,plain,
% 3.71/2.66 (^[VExp0: $i, RESULT: $i] : trans(monotonicity(rewrite(((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) <=> (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))))))), rewrite(((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) <=> (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))))))), rewrite(((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) <=> (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))))))))), rewrite(((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) <=> (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)))))))), rewrite(((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) <=> (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))))))), rewrite(((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) <=> (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0)))))))), rewrite(((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) <=> (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))), (((~(vreduce(VExp0) = RESULT)) | ((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp))) <=> ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))))), rewrite(((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))))))) <=> ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))))))), (((~(vreduce(VExp0) = RESULT)) | ((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp))) <=> ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))))))))),
% 3.71/2.66 inference(bind,[status(th)],[])).
% 3.71/2.66 tff(308,plain,
% 3.71/2.66 (![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | ((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp))) <=> ![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))))))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[307])).
% 3.71/2.67 tff(309,plain,
% 3.71/2.67 (^[VExp0: $i, RESULT: $i] : trans(monotonicity(rewrite(((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) <=> ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0)))))), rewrite(((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) <=> ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp))), ((((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT))) <=> (((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT))))), rewrite((((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT))) <=> ((~(vreduce(VExp0) = RESULT)) | ((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)))), ((((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT))) <=> ((~(vreduce(VExp0) = RESULT)) | ((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)))))),
% 3.71/2.67 inference(bind,[status(th)],[])).
% 3.71/2.67 tff(310,plain,
% 3.71/2.67 (![VExp0: $i, RESULT: $i] : (((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT))) <=> ![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | ((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)))),
% 3.71/2.67 inference(quant_intro,[status(thm)],[309])).
% 3.71/2.67 tff(311,plain,
% 3.71/2.67 (![VExp0: $i, RESULT: $i] : (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT))) <=> ![VExp0: $i, RESULT: $i] : (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT)))),
% 3.71/2.67 inference(rewrite,[status(thm)],[])).
% 3.71/2.67 tff(312,plain,
% 3.71/2.67 (^[VExp0: $i, RESULT: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) <=> (?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)))), quant_intro(proof_bind(^[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : trans(monotonicity(rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))), (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) <=> (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))))), rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))), (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))))), (?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) <=> ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))))), (((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) <=> ((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))))), rewrite(((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))))), (((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))))), quant_intro(proof_bind(^[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)))), (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) <=> (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)))), rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))), (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2)))), ((((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))))), rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))), ((((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))))), (?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))))), ((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) <=> ((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))))), rewrite(((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))))), ((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))))), quant_intro(proof_bind(^[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : trans(monotonicity(trans(monotonicity(rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)))), (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) <=> (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))))), rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)))), (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2))))), ((((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp)) <=> (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2))) & (RESULT = vnoExp)))), rewrite((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2))) & (RESULT = vnoExp)) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp))), ((((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp)) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp))))), (?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp)) <=> ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)))), (((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) <=> ((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp))))), rewrite(((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)))), (((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp))))), quant_intro(proof_bind(^[Ve1: $i, Ve1red: $i, Ve2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))), ((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) <=> (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))))), rewrite((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)))), ((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1))))), (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) <=> (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)))), rewrite((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))), (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)))), ((((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) <=> (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))))), rewrite((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))), ((((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))))), (?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) <=> ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))))), ((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) <=> ((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))))), rewrite(((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))))), ((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))))), quant_intro(proof_bind(^[Ve2: $i, Ve1: $i, Ve1red: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))), ((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) <=> (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))))), rewrite((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)))), ((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1))))), (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) <=> (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))))), rewrite((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)))), (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red))))), ((((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)) <=> (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)))), rewrite((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp))), ((((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp))))), (?[Ve2: $i, Ve1: $i, Ve1red: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)) <=> ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)))), (((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp))) <=> ((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp))))), rewrite(((?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)))), (((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp))))), (((vreduce(VExp0) = RESULT) => ((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)))) <=> ((vreduce(VExp0) = RESULT) => (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)))))), rewrite(((vreduce(VExp0) = RESULT) => (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT)))), (((vreduce(VExp0) = RESULT) => ((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)))) <=> (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT)))))),
% 3.80/2.68 inference(bind,[status(th)],[])).
% 3.80/2.68 tff(313,plain,
% 3.80/2.68 (![VExp0: $i, RESULT: $i] : ((vreduce(VExp0) = RESULT) => ((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp)))) <=> ![VExp0: $i, RESULT: $i] : (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT)))),
% 3.80/2.68 inference(quant_intro,[status(thm)],[312])).
% 3.80/2.68 tff(314,axiom,(![VExp0: $i, RESULT: $i] : ((vreduce(VExp0) = RESULT) => ((((((?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp))) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & visSomeExp(Ve2red)) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & visValue(Ve2)) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : (((((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2))) & (~visSomeExp(Ve2red))) & (~visValue(Ve2))) & (RESULT = vnoExp))) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & visSomeExp(Ve1red)) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : (((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) & (Ve1red = vreduce(Ve1))) & (~visSomeExp(Ve1red))) & (RESULT = vnoExp))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''reduce-INV'')).
% 3.80/2.68 tff(315,plain,
% 3.80/2.68 (![VExp0: $i, RESULT: $i] : (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT)))),
% 3.80/2.68 inference(modus_ponens,[status(thm)],[314, 313])).
% 3.80/2.68 tff(316,plain,
% 3.80/2.68 (![VExp0: $i, RESULT: $i] : (?[Vx: $i, VS: $i, Ve: $i] : ((VExp0 = vabs(Vx, VS, Ve)) & (RESULT = vnoExp)) | ?[Vx: $i] : ((VExp0 = vvar(Vx)) & (RESULT = vnoExp)) | ?[Ve2: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red) & (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) | ?[VS: $i, Ve2red: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2) & (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) | ?[Vx: $i, VS: $i, Ve1: $i, Ve2red: $i, Ve2: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) & (Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & (~visValue(Ve2)) & (RESULT = vnoExp)) | ?[Ve1: $i, Ve1red: $i, Ve2: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red) & (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) | ?[Ve2: $i, Ve1: $i, Ve1red: $i] : ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))) & (Ve1red = vreduce(Ve1)) & (~visSomeExp(Ve1red)) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT)))),
% 3.80/2.69 inference(modus_ponens,[status(thm)],[315, 311])).
% 3.80/2.69 tff(317,plain,(
% 3.80/2.69 ![VExp0: $i, RESULT: $i] : (((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)) | (~(vreduce(VExp0) = RESULT)))),
% 3.80/2.69 inference(skolemize,[status(sab)],[316])).
% 3.80/2.69 tff(318,plain,
% 3.80/2.69 (![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | ((VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0))) & (tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0))) & (tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0))) & visValue(tptp_fun_Ve2_51(RESULT, VExp0)) & (RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))) | ((VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0))) & (tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0))) & (~visValue(tptp_fun_Ve2_55(RESULT, VExp0))) & (RESULT = vnoExp)) | ((VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0))) & visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)) & (RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | ((VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0))) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10))) & (tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0))) & (~visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0))) & (RESULT = vnoExp)))),
% 3.80/2.69 inference(modus_ponens,[status(thm)],[317, 310])).
% 3.80/2.69 tff(319,plain,
% 3.80/2.69 (![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))))))),
% 3.80/2.69 inference(modus_ponens,[status(thm)],[318, 308])).
% 3.80/2.69 tff(320,plain,
% 3.80/2.69 (![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))))))),
% 3.80/2.69 inference(modus_ponens,[status(thm)],[319, 306])).
% 3.80/2.69 tff(321,plain,
% 3.80/2.69 (![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))),
% 3.80/2.69 inference(modus_ponens,[status(thm)],[320, 304])).
% 3.80/2.69 tff(322,plain,
% 3.80/2.69 (((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) <=> ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))),
% 3.80/2.70 inference(rewrite,[status(thm)],[])).
% 3.80/2.70 tff(323,plain,
% 3.80/2.70 (((~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))))) <=> ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))),
% 3.80/2.71 inference(rewrite,[status(thm)],[])).
% 3.80/2.71 tff(324,plain,
% 3.80/2.71 ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) <=> (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))),
% 3.80/2.71 inference(rewrite,[status(thm)],[])).
% 3.80/2.71 tff(325,plain,
% 3.80/2.71 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))) <=> ((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))),
% 3.80/2.71 inference(monotonicity,[status(thm)],[324])).
% 3.80/2.71 tff(326,plain,
% 3.80/2.71 ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) <=> (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))))),
% 3.80/2.72 inference(monotonicity,[status(thm)],[325])).
% 3.80/2.72 tff(327,plain,
% 3.80/2.72 ((~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) <=> (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(328,plain,
% 3.80/2.72 ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) <=> (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(329,plain,
% 3.80/2.72 ((~(visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) <=> (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(330,plain,
% 3.80/2.72 ((~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) <=> (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))))),
% 3.80/2.72 inference(rewrite,[status(thm)],[])).
% 3.80/2.72 tff(331,plain,
% 3.80/2.72 (((~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))))) <=> ((~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))))),
% 3.80/2.74 inference(monotonicity,[status(thm)],[330, 329, 328, 327, 326])).
% 3.80/2.74 tff(332,plain,
% 3.80/2.74 (((~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))))) <=> ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))),
% 3.80/2.75 inference(transitivity,[status(thm)],[331, 323])).
% 3.80/2.75 tff(333,plain,
% 3.80/2.75 (((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))))) <=> ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))))),
% 3.80/2.76 inference(monotonicity,[status(thm)],[332])).
% 3.80/2.76 tff(334,plain,
% 3.80/2.76 (((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))))) <=> ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))),
% 3.80/2.77 inference(transitivity,[status(thm)],[333, 322])).
% 3.80/2.77 tff(335,plain,
% 3.80/2.77 ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))))),
% 3.89/2.78 inference(quant_inst,[status(thm)],[])).
% 3.89/2.78 tff(336,plain,
% 3.89/2.78 ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.89/2.78 inference(modus_ponens,[status(thm)],[335, 334])).
% 3.89/2.78 tff(337,plain,
% 3.89/2.78 ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~(vreduce(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(vapp(ve1, ve2)))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.89/2.79 inference(unit_resolution,[status(thm)],[336, 321])).
% 3.89/2.79 tff(338,plain,
% 3.89/2.79 ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~visValue(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | visSomeExp(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_54(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_52(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_50(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~(tptp_fun_Ve2red_53(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_51(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.89/2.79 inference(unit_resolution,[status(thm)],[337, 302])).
% 3.89/2.79 tff(339,plain,
% 3.89/2.79 ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vabs(tptp_fun_Vx_43(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_42(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve_41(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.89/2.80 inference(unit_resolution,[status(thm)],[338, 297])).
% 3.89/2.80 tff(340,plain,
% 3.89/2.80 ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_49(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~visSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_47(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_46(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), vgetSomeExp(tptp_fun_Ve2red_45(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.89/2.81 inference(unit_resolution,[status(thm)],[339, 291])).
% 3.89/2.81 tff(341,plain,
% 3.89/2.81 ((~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~visSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_60(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 3.89/2.81 inference(unit_resolution,[status(thm)],[340, 268])).
% 3.89/2.81 tff(342,plain,
% 3.89/2.81 ($false),
% 3.89/2.81 inference(unit_resolution,[status(thm)],[341, 262, 251, 230, 220])).
% 3.89/2.81 tff(343,plain,(~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))), inference(lemma,lemma(discharge,[]))).
% 3.89/2.81 tff(344,plain,
% 3.89/2.81 (((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))),
% 3.89/2.81 inference(tautology,[status(thm)],[])).
% 3.89/2.81 tff(345,plain,
% 3.89/2.81 ((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))),
% 3.89/2.81 inference(unit_resolution,[status(thm)],[344, 343])).
% 3.89/2.81 tff(346,plain,
% 3.89/2.81 (tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1) = tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))),
% 3.89/2.81 inference(monotonicity,[status(thm)],[106])).
% 3.89/2.81 tff(347,plain,
% 3.89/2.81 (vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)) = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))),
% 3.89/2.81 inference(monotonicity,[status(thm)],[346])).
% 3.89/2.81 tff(348,plain,
% 3.89/2.81 ((ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))) <=> (ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.89/2.81 inference(monotonicity,[status(thm)],[347])).
% 3.89/2.81 tff(349,assumption,(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))), introduced(assumption)).
% 3.89/2.81 tff(350,plain,
% 3.89/2.81 (ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[349, 348])).
% 3.89/2.81 tff(351,assumption,(vreduce(ve1) = vsomeExp(Veout!74)), introduced(assumption)).
% 3.92/2.81 tff(352,plain,
% 3.92/2.81 (ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))),
% 3.92/2.81 inference(transitivity,[status(thm)],[349, 347])).
% 3.92/2.81 tff(353,plain,
% 3.92/2.81 ((ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1))) <=> (vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(monotonicity,[status(thm)],[352])).
% 3.92/2.81 tff(354,plain,
% 3.92/2.81 ((vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1))) <=> (ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(symmetry,[status(thm)],[353])).
% 3.92/2.81 tff(355,plain,
% 3.92/2.81 ((~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) <=> (~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1))))),
% 3.92/2.81 inference(monotonicity,[status(thm)],[354])).
% 3.92/2.81 tff(356,assumption,(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1))), introduced(assumption)).
% 3.92/2.81 tff(357,plain,
% 3.92/2.81 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1))))),
% 3.92/2.81 inference(quant_inst,[status(thm)],[])).
% 3.92/2.81 tff(358,plain,
% 3.92/2.81 ($false),
% 3.92/2.81 inference(unit_resolution,[status(thm)],[357, 31, 356])).
% 3.92/2.81 tff(359,plain,(~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.81 tff(360,plain,
% 3.92/2.81 (~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(modus_ponens,[status(thm)],[359, 355])).
% 3.92/2.81 tff(361,plain,
% 3.92/2.81 (((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))))))) | (ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(tautology,[status(thm)],[])).
% 3.92/2.81 tff(362,plain,
% 3.92/2.81 ((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))))))),
% 3.92/2.81 inference(unit_resolution,[status(thm)],[361, 360])).
% 3.92/2.81 tff(363,plain,
% 3.92/2.81 ((ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) <=> (vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(monotonicity,[status(thm)],[352])).
% 3.92/2.81 tff(364,plain,
% 3.92/2.81 ((vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) <=> (ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(symmetry,[status(thm)],[363])).
% 3.92/2.81 tff(365,plain,
% 3.92/2.81 ((~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) <=> (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))))),
% 3.92/2.81 inference(monotonicity,[status(thm)],[364])).
% 3.92/2.81 tff(366,assumption,(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))), introduced(assumption)).
% 3.92/2.81 tff(367,plain,
% 3.92/2.81 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))))),
% 3.92/2.81 inference(quant_inst,[status(thm)],[])).
% 3.92/2.81 tff(368,plain,
% 3.92/2.81 ($false),
% 3.92/2.81 inference(unit_resolution,[status(thm)],[367, 31, 366])).
% 3.92/2.81 tff(369,plain,(~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.81 tff(370,plain,
% 3.92/2.81 (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(modus_ponens,[status(thm)],[369, 365])).
% 3.92/2.81 tff(371,plain,
% 3.92/2.81 ((visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))))) | (ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(tautology,[status(thm)],[])).
% 3.92/2.81 tff(372,plain,
% 3.92/2.81 (visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))))),
% 3.92/2.81 inference(unit_resolution,[status(thm)],[371, 370])).
% 3.92/2.81 tff(373,plain,
% 3.92/2.81 ((ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))) <=> (vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(monotonicity,[status(thm)],[352])).
% 3.92/2.81 tff(374,plain,
% 3.92/2.81 ((vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))) <=> (ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(symmetry,[status(thm)],[373])).
% 3.92/2.81 tff(375,plain,
% 3.92/2.81 ((~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) <=> (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))),
% 3.92/2.81 inference(monotonicity,[status(thm)],[374])).
% 3.92/2.81 tff(376,assumption,(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))), introduced(assumption)).
% 3.92/2.81 tff(377,plain,
% 3.92/2.81 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))),
% 3.92/2.81 inference(quant_inst,[status(thm)],[])).
% 3.92/2.81 tff(378,plain,
% 3.92/2.81 ($false),
% 3.92/2.81 inference(unit_resolution,[status(thm)],[377, 31, 376])).
% 3.92/2.81 tff(379,plain,(~(vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.81 tff(380,plain,
% 3.92/2.81 (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))),
% 3.92/2.81 inference(modus_ponens,[status(thm)],[379, 375])).
% 3.92/2.82 tff(381,plain,
% 3.92/2.82 (((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))))) | (ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))),
% 3.92/2.82 inference(tautology,[status(thm)],[])).
% 3.92/2.82 tff(382,plain,
% 3.92/2.82 ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))))),
% 3.92/2.82 inference(unit_resolution,[status(thm)],[381, 380])).
% 3.92/2.82 tff(383,plain,
% 3.92/2.82 (^[VOptExp0: $i] : refl(((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp))) <=> ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp))))),
% 3.92/2.82 inference(bind,[status(th)],[])).
% 3.92/2.82 tff(384,plain,
% 3.92/2.82 (![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp))) <=> ![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))),
% 3.92/2.82 inference(quant_intro,[status(thm)],[383])).
% 3.92/2.82 tff(385,plain,
% 3.92/2.82 (![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp))) <=> ![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))),
% 3.92/2.82 inference(rewrite,[status(thm)],[])).
% 3.92/2.82 tff(386,plain,
% 3.92/2.82 (^[VOptExp0: $i] : rewrite(((VOptExp0 = vnoExp) => (~visSomeExp(VOptExp0))) <=> ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp))))),
% 3.92/2.82 inference(bind,[status(th)],[])).
% 3.92/2.82 tff(387,plain,
% 3.92/2.82 (![VOptExp0: $i] : ((VOptExp0 = vnoExp) => (~visSomeExp(VOptExp0))) <=> ![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))),
% 3.92/2.82 inference(quant_intro,[status(thm)],[386])).
% 3.92/2.82 tff(388,axiom,(![VOptExp0: $i] : ((VOptExp0 = vnoExp) => (~visSomeExp(VOptExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isSomeExp0')).
% 3.92/2.82 tff(389,plain,
% 3.92/2.82 (![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))),
% 3.92/2.82 inference(modus_ponens,[status(thm)],[388, 387])).
% 3.92/2.82 tff(390,plain,
% 3.92/2.82 (![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))),
% 3.92/2.82 inference(modus_ponens,[status(thm)],[389, 385])).
% 3.92/2.82 tff(391,plain,(
% 3.92/2.82 ![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))),
% 3.92/2.82 inference(skolemize,[status(sab)],[390])).
% 3.92/2.82 tff(392,plain,
% 3.92/2.82 (![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))),
% 3.92/2.82 inference(modus_ponens,[status(thm)],[391, 384])).
% 3.92/2.82 tff(393,plain,
% 3.92/2.82 (((~![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))) | ((~visSomeExp(vsomeExp(Veout!74))) | (~(vsomeExp(Veout!74) = vnoExp)))) <=> ((~![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))) | (~visSomeExp(vsomeExp(Veout!74))) | (~(vsomeExp(Veout!74) = vnoExp)))),
% 3.92/2.82 inference(rewrite,[status(thm)],[])).
% 3.92/2.82 tff(394,plain,
% 3.92/2.82 ((~![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))) | ((~visSomeExp(vsomeExp(Veout!74))) | (~(vsomeExp(Veout!74) = vnoExp)))),
% 3.92/2.82 inference(quant_inst,[status(thm)],[])).
% 3.92/2.82 tff(395,plain,
% 3.92/2.82 ((~![VOptExp0: $i] : ((~visSomeExp(VOptExp0)) | (~(VOptExp0 = vnoExp)))) | (~visSomeExp(vsomeExp(Veout!74))) | (~(vsomeExp(Veout!74) = vnoExp))),
% 3.92/2.82 inference(modus_ponens,[status(thm)],[394, 393])).
% 3.92/2.82 tff(396,plain,
% 3.92/2.82 (~(vsomeExp(Veout!74) = vnoExp)),
% 3.92/2.82 inference(unit_resolution,[status(thm)],[395, 392, 214])).
% 3.92/2.82 tff(397,plain,
% 3.92/2.82 (((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1))))) | (vsomeExp(Veout!74) = vnoExp)),
% 3.92/2.82 inference(tautology,[status(thm)],[])).
% 3.92/2.82 tff(398,plain,
% 3.92/2.82 ((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1))))),
% 3.92/2.82 inference(unit_resolution,[status(thm)],[397, 396])).
% 3.92/2.82 tff(399,plain,
% 3.92/2.82 (((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1))))) | (vsomeExp(Veout!74) = vnoExp)),
% 3.92/2.82 inference(tautology,[status(thm)],[])).
% 3.92/2.82 tff(400,plain,
% 3.92/2.82 ((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1))))),
% 3.92/2.82 inference(unit_resolution,[status(thm)],[399, 396])).
% 3.92/2.82 tff(401,plain,
% 3.92/2.82 (((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))) | (vsomeExp(Veout!74) = vnoExp)),
% 3.92/2.82 inference(tautology,[status(thm)],[])).
% 3.92/2.82 tff(402,plain,
% 3.92/2.82 ((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))),
% 3.92/2.82 inference(unit_resolution,[status(thm)],[401, 396])).
% 3.92/2.82 tff(403,plain,
% 3.92/2.82 (((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1))))) | (vsomeExp(Veout!74) = vnoExp)),
% 3.92/2.82 inference(tautology,[status(thm)],[])).
% 3.92/2.82 tff(404,plain,
% 3.92/2.82 ((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1))))),
% 3.92/2.82 inference(unit_resolution,[status(thm)],[403, 396])).
% 3.92/2.82 tff(405,plain,
% 3.92/2.82 (((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74))))) <=> ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74))))),
% 3.92/2.82 inference(rewrite,[status(thm)],[])).
% 3.92/2.82 tff(406,plain,
% 3.92/2.82 (((~(vreduce(ve1) = vsomeExp(Veout!74))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))))) <=> ((~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74))))),
% 3.92/2.82 inference(rewrite,[status(thm)],[])).
% 3.92/2.82 tff(407,plain,
% 3.92/2.82 ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) <=> (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))),
% 3.92/2.82 inference(rewrite,[status(thm)],[])).
% 3.92/2.82 tff(408,plain,
% 3.92/2.82 (((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))) <=> ((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))),
% 3.92/2.82 inference(monotonicity,[status(thm)],[407])).
% 3.92/2.82 tff(409,plain,
% 3.92/2.82 ((~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) <=> (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))))),
% 3.92/2.83 inference(monotonicity,[status(thm)],[408])).
% 3.92/2.83 tff(410,plain,
% 3.92/2.83 ((~((~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) <=> (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))))))),
% 3.92/2.83 inference(rewrite,[status(thm)],[])).
% 3.92/2.83 tff(411,plain,
% 3.92/2.83 ((~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) <=> (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1))))))),
% 3.92/2.83 inference(rewrite,[status(thm)],[])).
% 3.92/2.83 tff(412,plain,
% 3.92/2.83 ((~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))))) <=> (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))))))),
% 3.92/2.83 inference(rewrite,[status(thm)],[])).
% 3.92/2.83 tff(413,plain,
% 3.92/2.83 ((~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) <=> (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))))))))),
% 3.94/2.83 inference(rewrite,[status(thm)],[])).
% 3.94/2.83 tff(414,plain,
% 3.94/2.83 (((~(vreduce(ve1) = vsomeExp(Veout!74))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))))) <=> ((~(vreduce(ve1) = vsomeExp(Veout!74))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))))),
% 3.94/2.83 inference(monotonicity,[status(thm)],[413, 412, 411, 410, 409])).
% 3.94/2.83 tff(415,plain,
% 3.94/2.83 (((~(vreduce(ve1) = vsomeExp(Veout!74))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10))))))) <=> ((~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74))))),
% 3.94/2.83 inference(transitivity,[status(thm)],[414, 406])).
% 3.94/2.83 tff(416,plain,
% 3.94/2.83 (((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~(vreduce(ve1) = vsomeExp(Veout!74))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))))) <=> ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74)))))),
% 3.94/2.83 inference(monotonicity,[status(thm)],[415])).
% 3.94/2.83 tff(417,plain,
% 3.94/2.83 (((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~(vreduce(ve1) = vsomeExp(Veout!74))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))))) <=> ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74))))),
% 3.94/2.84 inference(transitivity,[status(thm)],[416, 405])).
% 3.94/2.84 tff(418,plain,
% 3.94/2.84 ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | ((~(vreduce(ve1) = vsomeExp(Veout!74))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))))),
% 3.94/2.84 inference(quant_inst,[status(thm)],[])).
% 3.94/2.84 tff(419,plain,
% 3.94/2.84 ((~![VExp0: $i, RESULT: $i] : ((~(vreduce(VExp0) = RESULT)) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vabs(tptp_fun_Vx_43(RESULT, VExp0), tptp_fun_VS_42(RESULT, VExp0), tptp_fun_Ve_41(RESULT, VExp0)))))) | (~((~(RESULT = vnoExp)) | (~(VExp0 = vvar(tptp_fun_Vx_44(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), tptp_fun_Ve2_49(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_45(RESULT, VExp0) = vreduce(tptp_fun_Ve2_49(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vabs(tptp_fun_Vx_48(RESULT, VExp0), tptp_fun_VS_47(RESULT, VExp0), tptp_fun_Ve1_46(RESULT, VExp0)), vgetSomeExp(tptp_fun_Ve2red_45(RESULT, VExp0)))))))) | (~(visSomeExp(tptp_fun_Ve2red_53(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_VS_54(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0)), tptp_fun_Ve2_51(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_53(RESULT, VExp0) = vreduce(tptp_fun_Ve2_51(RESULT, VExp0)))) | (~visValue(tptp_fun_Ve2_51(RESULT, VExp0))) | (~(RESULT = vsomeExp(vsubst(tptp_fun_Vx_52(RESULT, VExp0), tptp_fun_Ve2_51(RESULT, VExp0), tptp_fun_Ve1_50(RESULT, VExp0))))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(RESULT, VExp0)) | visValue(tptp_fun_Ve2_55(RESULT, VExp0)) | (~(VExp0 = vapp(vabs(tptp_fun_Vx_59(RESULT, VExp0), tptp_fun_VS_58(RESULT, VExp0), tptp_fun_Ve1_57(RESULT, VExp0)), tptp_fun_Ve2_55(RESULT, VExp0)))) | (~(tptp_fun_Ve2red_56(RESULT, VExp0) = vreduce(tptp_fun_Ve2_55(RESULT, VExp0)))))) | (~((~(VExp0 = vapp(tptp_fun_Ve1_62(RESULT, VExp0), tptp_fun_Ve2_60(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_61(RESULT, VExp0) = vreduce(tptp_fun_Ve1_62(RESULT, VExp0)))) | (~visSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0))) | (~(RESULT = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(RESULT, VExp0)), tptp_fun_Ve2_60(RESULT, VExp0))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))) | (~((~(RESULT = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(RESULT, VExp0)) | (~(VExp0 = vapp(tptp_fun_Ve1_64(RESULT, VExp0), tptp_fun_Ve2_65(RESULT, VExp0)))) | (~(tptp_fun_Ve1red_63(RESULT, VExp0) = vreduce(tptp_fun_Ve1_64(RESULT, VExp0)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(RESULT, VExp0) = vabs(VVx0, VVS0, VVe10)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74)))),
% 3.94/2.84 inference(modus_ponens,[status(thm)],[418, 417])).
% 3.94/2.84 tff(420,plain,
% 3.94/2.84 ((~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vvar(tptp_fun_Vx_44(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_65(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_63(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1)))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))))) | (~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | (~(ve1 = vabs(tptp_fun_Vx_43(vsomeExp(Veout!74), ve1), tptp_fun_VS_42(vsomeExp(Veout!74), ve1), tptp_fun_Ve_41(vsomeExp(Veout!74), ve1)))))) | (~((~(vsomeExp(Veout!74) = vnoExp)) | visSomeExp(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1)) | visValue(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)) | (~(ve1 = vapp(vabs(tptp_fun_Vx_59(vsomeExp(Veout!74), ve1), tptp_fun_VS_58(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_57(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_56(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_55(vsomeExp(Veout!74), ve1)))))) | (~(vreduce(ve1) = vsomeExp(Veout!74)))),
% 3.94/2.84 inference(unit_resolution,[status(thm)],[419, 321])).
% 3.94/2.84 tff(421,plain,
% 3.94/2.84 ((~(visSomeExp(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1)) | (~(vsomeExp(Veout!74) = vsomeExp(vsubst(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1))))) | (~visValue(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1))) | (~(ve1 = vapp(vabs(tptp_fun_Vx_52(vsomeExp(Veout!74), ve1), tptp_fun_VS_54(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_50(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_53(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_51(vsomeExp(Veout!74), ve1)))))) | (~((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1) = vabs(VVx0, VVS0, VVe10)))) | (~(ve1 = vapp(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve1_62(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vgetSomeExp(tptp_fun_Ve1red_61(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_60(vsomeExp(Veout!74), ve1))))))) | (~((~(ve1 = vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1) = vreduce(tptp_fun_Ve2_49(vsomeExp(Veout!74), ve1)))) | (~visSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1))) | (~(vsomeExp(Veout!74) = vsomeExp(vapp(vabs(tptp_fun_Vx_48(vsomeExp(Veout!74), ve1), tptp_fun_VS_47(vsomeExp(Veout!74), ve1), tptp_fun_Ve1_46(vsomeExp(Veout!74), ve1)), vgetSomeExp(tptp_fun_Ve2red_45(vsomeExp(Veout!74), ve1)))))))) | (~(vreduce(ve1) = vsomeExp(Veout!74)))),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[420, 404, 402, 400, 398])).
% 3.94/2.85 tff(422,plain,
% 3.94/2.85 ($false),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[421, 382, 372, 362, 351])).
% 3.94/2.85 tff(423,plain,((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vreduce(ve1) = vsomeExp(Veout!74)))), inference(lemma,lemma(discharge,[]))).
% 3.94/2.85 tff(424,plain,
% 3.94/2.85 (~(vreduce(ve1) = vsomeExp(Veout!74))),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[423, 349])).
% 3.94/2.85 tff(425,plain,
% 3.94/2.85 (visValue(ve1)),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[162, 424])).
% 3.94/2.85 tff(426,assumption,(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))), introduced(assumption)).
% 3.94/2.85 tff(427,plain,
% 3.94/2.85 (^[Vx: $i, VExp0: $i] : refl(((~visValue(VExp0)) | (~(VExp0 = vvar(Vx)))) <=> ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx)))))),
% 3.94/2.85 inference(bind,[status(th)],[])).
% 3.94/2.85 tff(428,plain,
% 3.94/2.85 (![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx)))) <=> ![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))),
% 3.94/2.85 inference(quant_intro,[status(thm)],[427])).
% 3.94/2.85 tff(429,plain,
% 3.94/2.85 (![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx)))) <=> ![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))),
% 3.94/2.85 inference(rewrite,[status(thm)],[])).
% 3.94/2.85 tff(430,plain,
% 3.94/2.85 (^[Vx: $i, VExp0: $i] : rewrite(((VExp0 = vvar(Vx)) => (~visValue(VExp0))) <=> ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx)))))),
% 3.94/2.85 inference(bind,[status(th)],[])).
% 3.94/2.85 tff(431,plain,
% 3.94/2.85 (![Vx: $i, VExp0: $i] : ((VExp0 = vvar(Vx)) => (~visValue(VExp0))) <=> ![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))),
% 3.94/2.85 inference(quant_intro,[status(thm)],[430])).
% 3.94/2.85 tff(432,axiom,(![Vx: $i, VExp0: $i] : ((VExp0 = vvar(Vx)) => (~visValue(VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isValue1')).
% 3.94/2.85 tff(433,plain,
% 3.94/2.85 (![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))),
% 3.94/2.85 inference(modus_ponens,[status(thm)],[432, 431])).
% 3.94/2.85 tff(434,plain,
% 3.94/2.85 (![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))),
% 3.94/2.85 inference(modus_ponens,[status(thm)],[433, 429])).
% 3.94/2.85 tff(435,plain,(
% 3.94/2.85 ![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))),
% 3.94/2.85 inference(skolemize,[status(sab)],[434])).
% 3.94/2.85 tff(436,plain,
% 3.94/2.85 (![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))),
% 3.94/2.85 inference(modus_ponens,[status(thm)],[435, 428])).
% 3.94/2.85 tff(437,plain,
% 3.94/2.85 (((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | ((~visValue(ve1)) | (~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | (~visValue(ve1)) | (~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.94/2.85 inference(rewrite,[status(thm)],[])).
% 3.94/2.85 tff(438,plain,
% 3.94/2.85 ((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | ((~visValue(ve1)) | (~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))))),
% 3.94/2.85 inference(quant_inst,[status(thm)],[])).
% 3.94/2.85 tff(439,plain,
% 3.94/2.85 ((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | (~visValue(ve1)) | (~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.94/2.85 inference(modus_ponens,[status(thm)],[438, 437])).
% 3.94/2.85 tff(440,plain,
% 3.94/2.85 ($false),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[439, 436, 114, 426])).
% 3.94/2.85 tff(441,plain,((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~visValue(ve1))), inference(lemma,lemma(discharge,[]))).
% 3.94/2.85 tff(442,plain,
% 3.94/2.85 (~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[441, 425])).
% 3.94/2.85 tff(443,plain,
% 3.94/2.85 ($false),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[442, 350])).
% 3.94/2.85 tff(444,plain,(~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))), inference(lemma,lemma(discharge,[]))).
% 3.94/2.85 tff(445,plain,
% 3.94/2.85 (((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vlookup(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty) = vsomeType(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))))) | (ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))),
% 3.94/2.85 inference(tautology,[status(thm)],[])).
% 3.94/2.85 tff(446,plain,
% 3.94/2.85 ((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vlookup(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty) = vsomeType(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))))),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[445, 444])).
% 3.94/2.85 tff(447,plain,
% 3.94/2.85 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vlookup(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty) = vsomeType(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))))) | (~((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vlookup(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty) = vsomeType(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))))) | (~((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))))),
% 3.94/2.85 inference(rewrite,[status(thm)],[])).
% 3.94/2.85 tff(448,plain,
% 3.94/2.85 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vlookup(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty) = vsomeType(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))))) | (~((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))))),
% 3.94/2.85 inference(quant_inst,[status(thm)],[])).
% 3.94/2.85 tff(449,plain,
% 3.94/2.85 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vlookup(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty) = vsomeType(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))))) | (~((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))))),
% 3.94/2.85 inference(modus_ponens,[status(thm)],[448, 447])).
% 3.94/2.85 tff(450,plain,
% 3.94/2.85 ((~((~(ve1 = vvar(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(vlookup(tptp_fun_Vx_66(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty) = vsomeType(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))))) | (~((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))))),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[449, 85, 145])).
% 3.94/2.85 tff(451,plain,
% 3.94/2.85 ((~((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))) | (~((~(ve1 = vapp(tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76)))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VS_71(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))))),
% 3.94/2.85 inference(unit_resolution,[status(thm)],[450, 446])).
% 3.94/2.85 tff(452,plain,
% 3.94/2.86 (~((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))),
% 3.94/2.86 inference(unit_resolution,[status(thm)],[451, 345])).
% 3.94/2.86 tff(453,plain,
% 3.94/2.86 (((~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~(varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76) = varrow(tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), vempty), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT2_67(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))) | (ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)))),
% 3.94/2.86 inference(tautology,[status(thm)],[])).
% 3.94/2.86 tff(454,plain,
% 3.94/2.86 (ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))),
% 3.94/2.86 inference(unit_resolution,[status(thm)],[453, 452])).
% 3.94/2.86 tff(455,plain,
% 3.94/2.86 (((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))) <=> ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))))),
% 3.94/2.86 inference(rewrite,[status(thm)],[])).
% 3.94/2.86 tff(456,plain,
% 3.94/2.86 ((~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) <=> (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))),
% 3.94/2.87 inference(rewrite,[status(thm)],[])).
% 3.94/2.87 tff(457,plain,
% 3.94/2.87 (((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))) <=> ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))))),
% 3.94/2.87 inference(monotonicity,[status(thm)],[456])).
% 3.94/2.87 tff(458,plain,
% 3.94/2.87 (((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))) <=> ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))))),
% 3.94/2.87 inference(transitivity,[status(thm)],[457, 455])).
% 3.94/2.87 tff(459,plain,
% 3.94/2.87 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))),
% 3.94/2.88 inference(quant_inst,[status(thm)],[])).
% 3.94/2.88 tff(460,plain,
% 3.94/2.88 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))),
% 3.94/2.88 inference(modus_ponens,[status(thm)],[459, 458])).
% 3.94/2.88 tff(461,plain,
% 3.94/2.88 (~((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))),
% 3.94/2.88 inference(unit_resolution,[status(thm)],[460, 16])).
% 3.94/2.88 tff(462,plain,
% 3.94/2.88 (((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))) | ((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))),
% 3.94/2.88 inference(tautology,[status(thm)],[])).
% 3.94/2.88 tff(463,plain,
% 3.94/2.88 ((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.94/2.88 inference(unit_resolution,[status(thm)],[462, 461])).
% 3.94/2.88 tff(464,plain,
% 3.94/2.88 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))) | ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))),
% 3.94/2.88 inference(tautology,[status(thm)],[])).
% 3.94/2.88 tff(465,plain,
% 3.94/2.88 (![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))),
% 3.94/2.88 inference(unit_resolution,[status(thm)],[464, 176])).
% 3.94/2.88 tff(466,plain,
% 3.94/2.88 ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10)))) | (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.94/2.89 inference(quant_inst,[status(thm)],[])).
% 3.94/2.89 tff(467,plain,
% 3.94/2.89 (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.94/2.89 inference(unit_resolution,[status(thm)],[466, 465])).
% 3.94/2.89 tff(468,plain,
% 3.94/2.89 (((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))) | (tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))),
% 3.94/2.89 inference(tautology,[status(thm)],[])).
% 3.94/2.89 tff(469,plain,
% 3.94/2.89 ((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))),
% 3.94/2.89 inference(unit_resolution,[status(thm)],[468, 467])).
% 3.94/2.89 tff(470,assumption,(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))), introduced(assumption)).
% 3.94/2.89 tff(471,plain,
% 3.94/2.89 (vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)) = ve1),
% 3.94/2.89 inference(symmetry,[status(thm)],[470])).
% 3.94/2.89 tff(472,plain,
% 3.94/2.89 (tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1) = tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))),
% 3.94/2.89 inference(monotonicity,[status(thm)],[106])).
% 3.94/2.89 tff(473,plain,
% 3.94/2.89 (tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1) = tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))),
% 3.94/2.89 inference(monotonicity,[status(thm)],[106])).
% 3.94/2.89 tff(474,plain,
% 3.94/2.89 (tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1) = tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))),
% 3.94/2.89 inference(monotonicity,[status(thm)],[106])).
% 3.94/2.89 tff(475,plain,
% 3.94/2.89 (vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))))),
% 3.94/2.89 inference(monotonicity,[status(thm)],[474, 473, 472])).
% 3.94/2.89 tff(476,plain,
% 3.94/2.89 (vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))),
% 3.94/2.89 inference(symmetry,[status(thm)],[475])).
% 3.94/2.89 tff(477,plain,
% 3.94/2.89 (vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = ve1),
% 3.94/2.89 inference(transitivity,[status(thm)],[476, 471])).
% 3.94/2.89 tff(478,plain,
% 3.94/2.89 (vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(ve1, ve2)),
% 3.94/2.89 inference(monotonicity,[status(thm)],[477])).
% 3.94/2.89 tff(479,plain,
% 3.94/2.89 (vapp(ve1, ve2) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)),
% 3.94/2.89 inference(symmetry,[status(thm)],[478])).
% 3.94/2.89 tff(480,plain,
% 3.94/2.89 (vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)),
% 3.94/2.89 inference(transitivity,[status(thm)],[179, 175, 479])).
% 3.94/2.89 tff(481,plain,
% 3.94/2.89 ((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.94/2.89 inference(tautology,[status(thm)],[])).
% 3.94/2.89 tff(482,plain,
% 3.94/2.89 ((~((~(vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 3.94/2.90 inference(unit_resolution,[status(thm)],[481, 480])).
% 3.94/2.90 tff(483,plain,
% 3.94/2.90 ($false),
% 3.94/2.90 inference(unit_resolution,[status(thm)],[482, 469, 463])).
% 3.94/2.90 tff(484,plain,(((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))) | (~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))), inference(lemma,lemma(discharge,[]))).
% 3.94/2.90 tff(485,plain,
% 3.94/2.90 ((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | visSomeExp(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve2_65(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(tptp_fun_Ve1red_63(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(tptp_fun_Ve1_64(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(VVx0, VVS0, VVe10))))),
% 3.94/2.90 inference(unit_resolution,[status(thm)],[484, 454])).
% 3.94/2.90 tff(486,plain,
% 3.94/2.90 (vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1)) = ve1),
% 3.94/2.90 inference(symmetry,[status(thm)],[454])).
% 3.94/2.90 tff(487,plain,
% 3.94/2.90 (vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = ve1),
% 3.94/2.90 inference(transitivity,[status(thm)],[476, 486])).
% 3.94/2.90 tff(488,plain,
% 3.94/2.90 (vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(ve1, ve2)),
% 3.94/2.90 inference(monotonicity,[status(thm)],[487])).
% 3.94/2.90 tff(489,plain,
% 3.94/2.90 (vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))),
% 3.94/2.90 inference(transitivity,[status(thm)],[488, 93])).
% 3.94/2.90 tff(490,plain,
% 3.94/2.90 ((vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) <=> (vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 3.94/2.90 inference(monotonicity,[status(thm)],[489])).
% 3.94/2.90 tff(491,plain,
% 3.94/2.90 ((vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) <=> (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 3.94/2.90 inference(transitivity,[status(thm)],[490, 252])).
% 3.94/2.90 tff(492,plain,
% 3.94/2.90 ((~(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) <=> (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.90 inference(monotonicity,[status(thm)],[491])).
% 4.01/2.90 tff(493,assumption,(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)), introduced(assumption)).
% 4.01/2.90 tff(494,plain,
% 4.01/2.90 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)))),
% 4.01/2.90 inference(quant_inst,[status(thm)],[])).
% 4.01/2.90 tff(495,plain,
% 4.01/2.90 ($false),
% 4.01/2.90 inference(unit_resolution,[status(thm)],[494, 31, 493])).
% 4.01/2.90 tff(496,plain,(~(vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))), inference(lemma,lemma(discharge,[]))).
% 4.01/2.90 tff(497,plain,
% 4.01/2.90 (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.90 inference(modus_ponens,[status(thm)],[496, 492])).
% 4.01/2.90 tff(498,plain,
% 4.01/2.90 ((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vvar(tptp_fun_Vx_44(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.90 inference(unit_resolution,[status(thm)],[261, 497])).
% 4.01/2.90 tff(499,plain,
% 4.01/2.90 (~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.90 inference(unit_resolution,[status(thm)],[341, 498, 230, 485])).
% 4.01/2.90 tff(500,plain,
% 4.01/2.90 ((tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2) <=> (ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.90 inference(commutativity,[status(thm)],[])).
% 4.01/2.90 tff(501,plain,
% 4.01/2.90 (((~(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))) | (tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2)),
% 4.01/2.90 inference(tautology,[status(thm)],[])).
% 4.01/2.90 tff(502,plain,
% 4.01/2.90 (tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2),
% 4.01/2.90 inference(unit_resolution,[status(thm)],[501, 103])).
% 4.01/2.90 tff(503,assumption,(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), introduced(assumption)).
% 4.01/2.90 tff(504,plain,
% 4.01/2.90 (vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))),
% 4.01/2.90 inference(symmetry,[status(thm)],[503])).
% 4.01/2.90 tff(505,plain,
% 4.01/2.90 (vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2),
% 4.01/2.90 inference(transitivity,[status(thm)],[504, 502])).
% 4.01/2.90 tff(506,plain,
% 4.01/2.90 ((tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) <=> (tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)),
% 4.01/2.90 inference(monotonicity,[status(thm)],[505])).
% 4.01/2.90 tff(507,plain,
% 4.01/2.90 ((tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) <=> (ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.91 inference(transitivity,[status(thm)],[506, 500])).
% 4.01/2.91 tff(508,plain,
% 4.01/2.91 ((ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) <=> (tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.91 inference(symmetry,[status(thm)],[507])).
% 4.01/2.91 tff(509,plain,
% 4.01/2.91 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))))),
% 4.01/2.91 inference(quant_inst,[status(thm)],[])).
% 4.01/2.91 tff(510,plain,
% 4.01/2.91 (~((~((~(vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 4.01/2.91 inference(unit_resolution,[status(thm)],[509, 16])).
% 4.01/2.91 tff(511,plain,
% 4.01/2.91 (((~((~(vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~((vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) | ((~(vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 4.01/2.91 inference(tautology,[status(thm)],[])).
% 4.01/2.91 tff(512,plain,
% 4.01/2.91 ((~(vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.01/2.92 inference(unit_resolution,[status(thm)],[511, 510])).
% 4.01/2.92 tff(513,plain,
% 4.01/2.92 (vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))),
% 4.01/2.92 inference(transitivity,[status(thm)],[478, 93])).
% 4.01/2.92 tff(514,plain,
% 4.01/2.92 ((vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) <=> (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.92 inference(monotonicity,[status(thm)],[513])).
% 4.01/2.92 tff(515,plain,
% 4.01/2.92 ((vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) <=> (vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.92 inference(symmetry,[status(thm)],[514])).
% 4.01/2.92 tff(516,assumption,(~((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))), introduced(assumption)).
% 4.01/2.92 tff(517,plain,
% 4.01/2.92 (vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.92 inference(unit_resolution,[status(thm)],[250, 516])).
% 4.01/2.92 tff(518,plain,
% 4.01/2.92 (vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.92 inference(modus_ponens,[status(thm)],[517, 515])).
% 4.01/2.92 tff(519,plain,
% 4.01/2.92 ((~((~(vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))) | (~(vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.01/2.93 inference(tautology,[status(thm)],[])).
% 4.01/2.93 tff(520,plain,
% 4.01/2.93 (~((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.93 inference(unit_resolution,[status(thm)],[519, 518, 512])).
% 4.01/2.93 tff(521,plain,
% 4.01/2.93 (((~(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~(ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.93 inference(tautology,[status(thm)],[])).
% 4.01/2.93 tff(522,plain,
% 4.01/2.93 (ve2 = tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 4.01/2.93 inference(unit_resolution,[status(thm)],[521, 520])).
% 4.01/2.93 tff(523,plain,
% 4.01/2.93 (tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 4.01/2.93 inference(modus_ponens,[status(thm)],[522, 508])).
% 4.01/2.93 tff(524,plain,
% 4.01/2.93 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.93 inference(tautology,[status(thm)],[])).
% 4.01/2.93 tff(525,plain,
% 4.01/2.93 (~visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.93 inference(unit_resolution,[status(thm)],[524, 516])).
% 4.01/2.93 tff(526,plain,
% 4.01/2.93 (((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | (visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.93 inference(rewrite,[status(thm)],[])).
% 4.01/2.93 tff(527,plain,
% 4.01/2.93 ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | (visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.93 inference(quant_inst,[status(thm)],[])).
% 4.01/2.93 tff(528,plain,
% 4.01/2.93 ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i] : (visValue(VExp0) | (~(VExp0 = vabs(Vx, VS, Ve))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.93 inference(modus_ponens,[status(thm)],[527, 526])).
% 4.01/2.93 tff(529,plain,
% 4.01/2.93 (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.93 inference(unit_resolution,[status(thm)],[528, 284, 525])).
% 4.01/2.93 tff(530,plain,
% 4.01/2.93 ($false),
% 4.01/2.93 inference(unit_resolution,[status(thm)],[529, 523])).
% 4.01/2.93 tff(531,plain,(((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))), inference(lemma,lemma(discharge,[]))).
% 4.01/2.93 tff(532,plain,
% 4.01/2.93 (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.93 inference(unit_resolution,[status(thm)],[531, 499, 454])).
% 4.01/2.93 tff(533,plain,
% 4.01/2.93 (((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.93 inference(tautology,[status(thm)],[])).
% 4.01/2.93 tff(534,plain,
% 4.01/2.93 ((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.93 inference(unit_resolution,[status(thm)],[533, 532])).
% 4.01/2.93 tff(535,plain,
% 4.01/2.93 ((vnoExp = vsomeExp(Veout!75)) <=> (vsomeExp(Veout!75) = vnoExp)),
% 4.01/2.93 inference(commutativity,[status(thm)],[])).
% 4.01/2.93 tff(536,plain,
% 4.01/2.93 ((~(vnoExp = vsomeExp(Veout!75))) <=> (~(vsomeExp(Veout!75) = vnoExp))),
% 4.01/2.93 inference(monotonicity,[status(thm)],[535])).
% 4.01/2.93 tff(537,assumption,(vnoExp = vsomeExp(Veout!75)), introduced(assumption)).
% 4.01/2.93 tff(538,plain,
% 4.01/2.93 (^[VExp0: $i] : refl((~(vnoExp = vsomeExp(VExp0))) <=> (~(vnoExp = vsomeExp(VExp0))))),
% 4.01/2.93 inference(bind,[status(th)],[])).
% 4.01/2.93 tff(539,plain,
% 4.01/2.93 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0))) <=> ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 4.01/2.93 inference(quant_intro,[status(thm)],[538])).
% 4.01/2.93 tff(540,plain,
% 4.01/2.93 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0))) <=> ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 4.01/2.93 inference(rewrite,[status(thm)],[])).
% 4.01/2.93 tff(541,axiom,(![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-noExp-someExp'')).
% 4.01/2.93 tff(542,plain,
% 4.01/2.93 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 4.01/2.93 inference(modus_ponens,[status(thm)],[541, 540])).
% 4.01/2.94 tff(543,plain,(
% 4.01/2.94 ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 4.01/2.94 inference(skolemize,[status(sab)],[542])).
% 4.01/2.94 tff(544,plain,
% 4.01/2.94 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[543, 539])).
% 4.01/2.94 tff(545,plain,
% 4.01/2.94 ((~![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))) | (~(vnoExp = vsomeExp(Veout!75)))),
% 4.01/2.94 inference(quant_inst,[status(thm)],[])).
% 4.01/2.94 tff(546,plain,
% 4.01/2.94 ($false),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[545, 544, 537])).
% 4.01/2.94 tff(547,plain,(~(vnoExp = vsomeExp(Veout!75))), inference(lemma,lemma(discharge,[]))).
% 4.01/2.94 tff(548,plain,
% 4.01/2.94 (~(vsomeExp(Veout!75) = vnoExp)),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[547, 536])).
% 4.01/2.94 tff(549,assumption,(~(vsomeExp(Veout!75) = vnoExp)), introduced(assumption)).
% 4.01/2.94 tff(550,plain,
% 4.01/2.94 ((vreduce(ve2) = vsomeExp(Veout!75)) <=> (vsomeExp(Veout!75) = vreduce(ve2))),
% 4.01/2.94 inference(commutativity,[status(thm)],[])).
% 4.01/2.94 tff(551,plain,
% 4.01/2.94 (ve2 = tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))),
% 4.01/2.94 inference(symmetry,[status(thm)],[502])).
% 4.01/2.94 tff(552,plain,
% 4.01/2.94 (vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))) <=> vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))),
% 4.01/2.94 inference(monotonicity,[status(thm)],[551])).
% 4.01/2.94 tff(553,plain,
% 4.01/2.94 (vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))) <=> vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))),
% 4.01/2.94 inference(symmetry,[status(thm)],[552])).
% 4.01/2.94 tff(554,plain,
% 4.01/2.94 (((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))),
% 4.01/2.94 inference(tautology,[status(thm)],[])).
% 4.01/2.94 tff(555,plain,
% 4.01/2.94 (vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[554, 91])).
% 4.01/2.94 tff(556,plain,
% 4.01/2.94 (vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[555, 553])).
% 4.01/2.94 tff(557,assumption,(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), introduced(assumption)).
% 4.01/2.94 tff(558,assumption,(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2), introduced(assumption)).
% 4.01/2.94 tff(559,plain,
% 4.01/2.94 (ve2 = tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))),
% 4.01/2.94 inference(symmetry,[status(thm)],[558])).
% 4.01/2.94 tff(560,plain,
% 4.01/2.94 (ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 4.01/2.94 inference(transitivity,[status(thm)],[559, 557])).
% 4.01/2.94 tff(561,assumption,(visValue(ve2)), introduced(assumption)).
% 4.01/2.94 tff(562,plain,
% 4.01/2.94 (((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | ((~visValue(ve2)) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | (~visValue(ve2)) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.94 inference(rewrite,[status(thm)],[])).
% 4.01/2.94 tff(563,plain,
% 4.01/2.94 ((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | ((~visValue(ve2)) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.94 inference(quant_inst,[status(thm)],[])).
% 4.01/2.94 tff(564,plain,
% 4.01/2.94 ((~![Vx: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vvar(Vx))))) | (~visValue(ve2)) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[563, 562])).
% 4.01/2.94 tff(565,plain,
% 4.01/2.94 ($false),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[564, 436, 561, 560])).
% 4.01/2.94 tff(566,plain,((~visValue(ve2)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = ve2))), inference(lemma,lemma(discharge,[]))).
% 4.01/2.94 tff(567,plain,
% 4.01/2.94 (~visValue(ve2)),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[566, 557, 502])).
% 4.01/2.94 tff(568,plain,
% 4.01/2.94 (^[VT: $i] : refl((visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT))) <=> (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT))))),
% 4.01/2.94 inference(bind,[status(th)],[])).
% 4.01/2.94 tff(569,plain,
% 4.01/2.94 (![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT))) <=> ![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))),
% 4.01/2.94 inference(quant_intro,[status(thm)],[568])).
% 4.01/2.94 tff(570,plain,
% 4.01/2.94 (^[VT: $i] : trans(monotonicity(trans(monotonicity(rewrite((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) <=> (~(visValue(ve2) | (~vtcheck(vempty, ve2, VT))))), ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) <=> (~(~(visValue(ve2) | (~vtcheck(vempty, ve2, VT))))))), rewrite((~(~(visValue(ve2) | (~vtcheck(vempty, ve2, VT))))) <=> (visValue(ve2) | (~vtcheck(vempty, ve2, VT)))), ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) <=> (visValue(ve2) | (~vtcheck(vempty, ve2, VT))))), (((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!75))) <=> ((visValue(ve2) | (~vtcheck(vempty, ve2, VT))) | (vreduce(ve2) = vsomeExp(Veout!75))))), rewrite(((visValue(ve2) | (~vtcheck(vempty, ve2, VT))) | (vreduce(ve2) = vsomeExp(Veout!75))) <=> (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))), (((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!75))) <=> (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))))),
% 4.01/2.94 inference(bind,[status(th)],[])).
% 4.01/2.94 tff(571,plain,
% 4.01/2.94 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!75))) <=> ![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))),
% 4.01/2.94 inference(quant_intro,[status(thm)],[570])).
% 4.01/2.94 tff(572,plain,
% 4.01/2.94 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 4.01/2.94 inference(rewrite,[status(thm)],[])).
% 4.01/2.94 tff(573,plain,
% 4.01/2.94 (^[VT: $i] : rewrite(((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) => ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))) <=> ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))))),
% 4.01/2.94 inference(bind,[status(th)],[])).
% 4.01/2.94 tff(574,plain,
% 4.01/2.94 (![VT: $i] : ((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) => ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 4.01/2.94 inference(quant_intro,[status(thm)],[573])).
% 4.01/2.94 tff(575,axiom,(![VT: $i] : ((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) => ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Progress-T-app-IH2'')).
% 4.01/2.94 tff(576,plain,
% 4.01/2.94 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[575, 574])).
% 4.01/2.94 tff(577,plain,
% 4.01/2.94 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[576, 572])).
% 4.01/2.94 tff(578,plain,(
% 4.01/2.94 ![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!75)))),
% 4.01/2.94 inference(skolemize,[status(sab)],[577])).
% 4.01/2.94 tff(579,plain,
% 4.01/2.94 (![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[578, 571])).
% 4.01/2.94 tff(580,plain,
% 4.01/2.94 (![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[579, 569])).
% 4.01/2.94 tff(581,plain,
% 4.01/2.94 (((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))) | (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))) <=> ((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))) | visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.94 inference(rewrite,[status(thm)],[])).
% 4.01/2.94 tff(582,plain,
% 4.01/2.94 ((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))) | (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.94 inference(quant_inst,[status(thm)],[])).
% 4.01/2.94 tff(583,plain,
% 4.01/2.94 ((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, VT)))) | visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[582, 581])).
% 4.01/2.94 tff(584,plain,
% 4.01/2.94 (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75)) | (~vtcheck(vempty, ve2, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[583, 580])).
% 4.01/2.94 tff(585,plain,
% 4.01/2.94 (vreduce(ve2) = vsomeExp(Veout!75)),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[584, 567, 556])).
% 4.01/2.94 tff(586,plain,
% 4.01/2.94 (vsomeExp(Veout!75) = vreduce(ve2)),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[585, 550])).
% 4.01/2.94 tff(587,plain,
% 4.01/2.94 ((tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) <=> (ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.94 inference(monotonicity,[status(thm)],[502])).
% 4.01/2.94 tff(588,plain,
% 4.01/2.94 (ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[557, 587])).
% 4.01/2.94 tff(589,plain,
% 4.01/2.94 (![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx)))) <=> ![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))),
% 4.01/2.94 inference(rewrite,[status(thm)],[])).
% 4.01/2.94 tff(590,plain,
% 4.01/2.94 (^[Vx: $i, VExp0: $i, RESULT: $i] : trans(monotonicity(rewrite(((RESULT = vreduce(VExp0)) => (RESULT = vnoExp)) <=> ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))), (((VExp0 = vvar(Vx)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ((VExp0 = vvar(Vx)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))))), rewrite(((VExp0 = vvar(Vx)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))) <=> ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))), (((VExp0 = vvar(Vx)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))))),
% 4.01/2.94 inference(bind,[status(th)],[])).
% 4.01/2.94 tff(591,plain,
% 4.01/2.94 (![Vx: $i, VExp0: $i, RESULT: $i] : ((VExp0 = vvar(Vx)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))),
% 4.01/2.94 inference(quant_intro,[status(thm)],[590])).
% 4.01/2.94 tff(592,axiom,(![Vx: $i, VExp0: $i, RESULT: $i] : ((VExp0 = vvar(Vx)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','reduce0')).
% 4.01/2.94 tff(593,plain,
% 4.01/2.94 (![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[592, 591])).
% 4.01/2.94 tff(594,plain,
% 4.01/2.94 (![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[593, 589])).
% 4.01/2.94 tff(595,plain,(
% 4.01/2.94 ![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))),
% 4.01/2.94 inference(skolemize,[status(sab)],[594])).
% 4.01/2.94 tff(596,plain,
% 4.01/2.94 (((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | ((~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))))) <=> ((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))))),
% 4.01/2.94 inference(rewrite,[status(thm)],[])).
% 4.01/2.94 tff(597,plain,
% 4.01/2.94 (((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) <=> ((~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))))),
% 4.01/2.94 inference(rewrite,[status(thm)],[])).
% 4.01/2.94 tff(598,plain,
% 4.01/2.94 (((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | ((~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2)))))),
% 4.01/2.94 inference(monotonicity,[status(thm)],[597])).
% 4.01/2.94 tff(599,plain,
% 4.01/2.94 (((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))))),
% 4.01/2.94 inference(transitivity,[status(thm)],[598, 596])).
% 4.01/2.94 tff(600,plain,
% 4.01/2.94 ((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2))) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.94 inference(quant_inst,[status(thm)],[])).
% 4.01/2.94 tff(601,plain,
% 4.01/2.94 ((~![Vx: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vvar(Vx))))) | (~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2)))),
% 4.01/2.94 inference(modus_ponens,[status(thm)],[600, 599])).
% 4.01/2.94 tff(602,plain,
% 4.01/2.94 ((~(ve2 = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(ve2)))),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[601, 595])).
% 4.01/2.94 tff(603,plain,
% 4.01/2.94 ($false),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[602, 588, 586, 549])).
% 4.01/2.94 tff(604,plain,((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (vsomeExp(Veout!75) = vnoExp)), inference(lemma,lemma(discharge,[]))).
% 4.01/2.94 tff(605,plain,
% 4.01/2.94 (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[604, 548])).
% 4.01/2.94 tff(606,plain,
% 4.01/2.94 (((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))) | (tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.94 inference(tautology,[status(thm)],[])).
% 4.01/2.94 tff(607,plain,
% 4.01/2.94 ((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.01/2.94 inference(unit_resolution,[status(thm)],[606, 605])).
% 4.01/2.94 tff(608,plain,
% 4.01/2.94 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.01/2.95 inference(rewrite,[status(thm)],[])).
% 4.01/2.95 tff(609,plain,
% 4.01/2.95 (((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.01/2.95 inference(rewrite,[status(thm)],[])).
% 4.01/2.95 tff(610,plain,
% 4.01/2.95 ((~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) <=> (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.95 inference(rewrite,[status(thm)],[])).
% 4.01/2.95 tff(611,plain,
% 4.01/2.95 ((~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) <=> (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.01/2.95 inference(rewrite,[status(thm)],[])).
% 4.01/2.95 tff(612,plain,
% 4.01/2.95 ((~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) <=> (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.01/2.95 inference(rewrite,[status(thm)],[])).
% 4.01/2.95 tff(613,plain,
% 4.01/2.95 (((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.01/2.96 inference(monotonicity,[status(thm)],[612, 611, 610])).
% 4.01/2.96 tff(614,plain,
% 4.01/2.96 (((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.01/2.96 inference(transitivity,[status(thm)],[613, 609])).
% 4.01/2.96 tff(615,plain,
% 4.01/2.96 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))))),
% 4.07/2.97 inference(monotonicity,[status(thm)],[614])).
% 4.07/2.97 tff(616,plain,
% 4.07/2.97 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.07/2.97 inference(transitivity,[status(thm)],[615, 608])).
% 4.07/2.97 tff(617,plain,
% 4.07/2.97 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | ((~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))))),
% 4.07/2.97 inference(quant_inst,[status(thm)],[])).
% 4.07/2.97 tff(618,plain,
% 4.07/2.97 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_66(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_66(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_Ve2_69(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_68(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC, VT, Ve), tptp_fun_VT1_68(VC, VT, Ve), VC), tptp_fun_Ve2_69(VC, VT, Ve), tptp_fun_VT2_67(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_73(VC, VT, Ve), tptp_fun_Ve2_72(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_73(VC, VT, Ve), varrow(tptp_fun_VS_71(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_72(VC, VT, Ve), tptp_fun_VS_71(VC, VT, Ve))))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)))) | (~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.07/2.98 inference(modus_ponens,[status(thm)],[617, 616])).
% 4.07/2.98 tff(619,plain,
% 4.07/2.98 ((~((~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_66(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty) = vsomeType(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))))) | (~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[618, 85, 555])).
% 4.07/2.98 tff(620,plain,
% 4.07/2.98 ((~((~vtcheck(vbind(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_70(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)) = varrow(tptp_fun_VT1_68(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT2_67(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) | (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[619, 607])).
% 4.07/2.98 tff(621,plain,
% 4.07/2.98 (~((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[620, 534])).
% 4.07/2.98 tff(622,plain,
% 4.07/2.98 (((~vtcheck(vempty, tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), varrow(tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VS_71(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.07/2.98 inference(tautology,[status(thm)],[])).
% 4.07/2.98 tff(623,plain,
% 4.07/2.98 (tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[622, 621])).
% 4.07/2.98 tff(624,assumption,(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), introduced(assumption)).
% 4.07/2.98 tff(625,plain,
% 4.07/2.98 (ve2 = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))),
% 4.07/2.98 inference(transitivity,[status(thm)],[551, 624])).
% 4.07/2.98 tff(626,plain,
% 4.07/2.98 (((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | ((~visValue(ve2)) | (~(ve2 = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))) <=> ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | (~visValue(ve2)) | (~(ve2 = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.07/2.98 inference(rewrite,[status(thm)],[])).
% 4.07/2.98 tff(627,plain,
% 4.07/2.98 ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | ((~visValue(ve2)) | (~(ve2 = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))))),
% 4.07/2.98 inference(quant_inst,[status(thm)],[])).
% 4.07/2.98 tff(628,plain,
% 4.07/2.98 ((~![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))) | (~visValue(ve2)) | (~(ve2 = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.07/2.98 inference(modus_ponens,[status(thm)],[627, 626])).
% 4.07/2.98 tff(629,plain,
% 4.07/2.98 ($false),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[628, 125, 561, 625])).
% 4.07/2.98 tff(630,plain,((~visValue(ve2)) | (~(tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_73(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_72(vempty, tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))), inference(lemma,lemma(discharge,[]))).
% 4.07/2.98 tff(631,plain,
% 4.07/2.98 (~visValue(ve2)),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[630, 623])).
% 4.07/2.98 tff(632,plain,
% 4.07/2.98 (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!75))),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[584, 556])).
% 4.07/2.98 tff(633,plain,
% 4.07/2.98 (vreduce(ve2) = vsomeExp(Veout!75)),
% 4.07/2.98 inference(unit_resolution,[status(thm)],[632, 631])).
% 4.07/2.98 tff(634,assumption,(vreduce(ve2) = vsomeExp(Veout!75)), introduced(assumption)).
% 4.07/2.98 tff(635,plain,
% 4.07/2.98 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))))),
% 4.07/2.98 inference(quant_inst,[status(thm)],[])).
% 4.07/2.98 tff(636,plain,
% 4.07/2.98 (~((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))),
% 4.07/2.99 inference(unit_resolution,[status(thm)],[635, 16])).
% 4.07/2.99 tff(637,plain,
% 4.07/2.99 (((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)) | (~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))) | ((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))),
% 4.07/2.99 inference(tautology,[status(thm)],[])).
% 4.07/2.99 tff(638,plain,
% 4.07/2.99 ((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 4.07/2.99 inference(unit_resolution,[status(thm)],[637, 636])).
% 4.07/2.99 tff(639,plain,
% 4.07/2.99 (vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))),
% 4.07/2.99 inference(symmetry,[status(thm)],[517])).
% 4.07/2.99 tff(640,plain,
% 4.07/2.99 (vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2)),
% 4.07/2.99 inference(transitivity,[status(thm)],[639, 175, 479])).
% 4.07/2.99 tff(641,plain,
% 4.07/2.99 ((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 4.07/3.00 inference(tautology,[status(thm)],[])).
% 4.07/3.00 tff(642,plain,
% 4.07/3.00 ((~((~(vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vapp(vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))), ve2))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))))) | (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))))),
% 4.07/3.00 inference(unit_resolution,[status(thm)],[641, 640])).
% 4.07/3.00 tff(643,plain,
% 4.07/3.00 (~((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)))),
% 4.07/3.00 inference(unit_resolution,[status(thm)],[642, 638])).
% 4.07/3.00 tff(644,plain,
% 4.07/3.00 (((~(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2))), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)))))) | (~(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2))) | (tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2)),
% 4.07/3.00 inference(tautology,[status(thm)],[])).
% 4.07/3.00 tff(645,plain,
% 4.07/3.00 (tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = ve2),
% 4.07/3.00 inference(unit_resolution,[status(thm)],[644, 643])).
% 4.07/3.00 tff(646,plain,
% 4.07/3.00 (vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) = vreduce(ve2)),
% 4.07/3.00 inference(monotonicity,[status(thm)],[645])).
% 4.07/3.00 tff(647,plain,
% 4.07/3.00 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.07/3.00 inference(tautology,[status(thm)],[])).
% 4.07/3.00 tff(648,plain,
% 4.07/3.00 (tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.07/3.00 inference(unit_resolution,[status(thm)],[647, 516])).
% 4.07/3.00 tff(649,plain,
% 4.07/3.00 (tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vsomeExp(Veout!75)),
% 4.07/3.00 inference(transitivity,[status(thm)],[648, 646, 634])).
% 4.07/3.00 tff(650,plain,
% 4.07/3.00 (visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) <=> visSomeExp(vsomeExp(Veout!75))),
% 4.07/3.00 inference(monotonicity,[status(thm)],[649])).
% 4.07/3.00 tff(651,plain,
% 4.07/3.00 (visSomeExp(vsomeExp(Veout!75)) <=> visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.07/3.00 inference(symmetry,[status(thm)],[650])).
% 4.07/3.00 tff(652,assumption,(visSomeExp(vsomeExp(Veout!75))), introduced(assumption)).
% 4.07/3.00 tff(653,plain,
% 4.07/3.00 (visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.07/3.00 inference(modus_ponens,[status(thm)],[652, 651])).
% 4.07/3.00 tff(654,plain,
% 4.07/3.00 (((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))),
% 4.07/3.00 inference(tautology,[status(thm)],[])).
% 4.07/3.00 tff(655,plain,
% 4.07/3.00 (~visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))),
% 4.07/3.00 inference(unit_resolution,[status(thm)],[654, 516])).
% 4.07/3.00 tff(656,plain,
% 4.07/3.00 ($false),
% 4.07/3.00 inference(unit_resolution,[status(thm)],[655, 653])).
% 4.07/3.00 tff(657,plain,(((~(vreduce(vapp(ve1, ve2)) = vnoExp)) | (~(vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))) = vapp(vabs(tptp_fun_Vx_59(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_VS_58(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))), tptp_fun_Ve1_57(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))), tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visValue(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))) | (~(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))) = vreduce(tptp_fun_Ve2_55(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2))))))) | visSomeExp(tptp_fun_Ve2red_56(vreduce(vapp(ve1, ve2)), vapp(tptp_fun_Ve1_73(vempty, VT!76, vapp(ve1, ve2)), tptp_fun_Ve2_72(vempty, VT!76, vapp(ve1, ve2)))))) | (~visSomeExp(vsomeExp(Veout!75))) | (~(vreduce(ve2) = vsomeExp(Veout!75))) | (~(ve1 = vabs(tptp_fun_Vx_70(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_VT1_68(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1), tptp_fun_Ve2_69(vempty, varrow(tptp_fun_VS_71(vempty, VT!76, vapp(ve1, ve2)), VT!76), ve1))))), inference(lemma,lemma(discharge,[]))).
% 4.07/3.00 tff(658,plain,
% 4.07/3.00 (~visSomeExp(vsomeExp(Veout!75))),
% 4.07/3.00 inference(unit_resolution,[status(thm)],[657, 633, 499, 454])).
% 4.07/3.00 tff(659,plain,
% 4.07/3.00 (((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!75))) <=> ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!75)))),
% 4.07/3.00 inference(rewrite,[status(thm)],[])).
% 4.07/3.00 tff(660,plain,
% 4.07/3.00 ((visSomeExp(vsomeExp(Veout!75)) | $false) <=> visSomeExp(vsomeExp(Veout!75))),
% 4.07/3.00 inference(rewrite,[status(thm)],[])).
% 4.07/3.00 tff(661,plain,
% 4.07/3.00 ((vsomeExp(Veout!75) = vsomeExp(Veout!75)) <=> $true),
% 4.07/3.00 inference(rewrite,[status(thm)],[])).
% 4.07/3.00 tff(662,plain,
% 4.07/3.00 ((~(vsomeExp(Veout!75) = vsomeExp(Veout!75))) <=> (~$true)),
% 4.07/3.00 inference(monotonicity,[status(thm)],[661])).
% 4.07/3.00 tff(663,plain,
% 4.07/3.00 ((~(vsomeExp(Veout!75) = vsomeExp(Veout!75))) <=> $false),
% 4.07/3.00 inference(transitivity,[status(thm)],[662, 128])).
% 4.07/3.00 tff(664,plain,
% 4.07/3.00 ((visSomeExp(vsomeExp(Veout!75)) | (~(vsomeExp(Veout!75) = vsomeExp(Veout!75)))) <=> (visSomeExp(vsomeExp(Veout!75)) | $false)),
% 4.07/3.00 inference(monotonicity,[status(thm)],[663])).
% 4.07/3.00 tff(665,plain,
% 4.07/3.00 ((visSomeExp(vsomeExp(Veout!75)) | (~(vsomeExp(Veout!75) = vsomeExp(Veout!75)))) <=> visSomeExp(vsomeExp(Veout!75))),
% 4.07/3.00 inference(transitivity,[status(thm)],[664, 660])).
% 4.07/3.00 tff(666,plain,
% 4.07/3.00 (((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | (visSomeExp(vsomeExp(Veout!75)) | (~(vsomeExp(Veout!75) = vsomeExp(Veout!75))))) <=> ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!75)))),
% 4.07/3.00 inference(monotonicity,[status(thm)],[665])).
% 4.07/3.00 tff(667,plain,
% 4.07/3.00 (((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | (visSomeExp(vsomeExp(Veout!75)) | (~(vsomeExp(Veout!75) = vsomeExp(Veout!75))))) <=> ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!75)))),
% 4.07/3.01 inference(transitivity,[status(thm)],[666, 659])).
% 4.07/3.01 tff(668,plain,
% 4.07/3.01 ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | (visSomeExp(vsomeExp(Veout!75)) | (~(vsomeExp(Veout!75) = vsomeExp(Veout!75))))),
% 4.07/3.01 inference(quant_inst,[status(thm)],[])).
% 4.07/3.01 tff(669,plain,
% 4.07/3.01 ((~![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))) | visSomeExp(vsomeExp(Veout!75))),
% 4.07/3.01 inference(modus_ponens,[status(thm)],[668, 667])).
% 4.07/3.01 tff(670,plain,
% 4.07/3.01 ($false),
% 4.07/3.01 inference(unit_resolution,[status(thm)],[669, 202, 658])).
% 4.07/3.01 % SZS output end Proof
%------------------------------------------------------------------------------