TSTP Solution File: COM139+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM139+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 18:06:14 EDT 2022
% Result : Theorem 3.05s 2.22s
% Output : Proof 3.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM139+1 : TPTP v8.1.0. Released v6.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 30 14:48:46 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.35 Usage: tptp [options] [-file:]file
% 0.15/0.35 -h, -? prints this message.
% 0.15/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.35 -m, -model generate model.
% 0.15/0.35 -p, -proof generate proof.
% 0.15/0.35 -c, -core generate unsat core of named formulas.
% 0.15/0.35 -st, -statistics display statistics.
% 0.15/0.35 -t:timeout set timeout (in second).
% 0.15/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.35 -<param>:<value> configuration parameter and value.
% 0.15/0.35 -o:<output-file> file to place output in.
% 3.05/2.22 % SZS status Theorem
% 3.05/2.22 % SZS output start Proof
% 3.05/2.22 tff(tptp_fun_Vy_76_type, type, (
% 3.05/2.22 tptp_fun_Vy_76: $i)).
% 3.05/2.22 tff(tptp_fun_Vx_79_type, type, (
% 3.05/2.22 tptp_fun_Vx_79: $i)).
% 3.05/2.22 tff(tptp_fun_Vy_2_type, type, (
% 3.05/2.22 tptp_fun_Vy_2: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(vbind_type, type, (
% 3.05/2.22 vbind: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_VC_77_type, type, (
% 3.05/2.22 tptp_fun_VC_77: $i)).
% 3.05/2.22 tff(tptp_fun_VS1_75_type, type, (
% 3.05/2.22 tptp_fun_VS1_75: $i)).
% 3.05/2.22 tff(vlookup_type, type, (
% 3.05/2.22 vlookup: ( $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_VC_4_type, type, (
% 3.05/2.22 tptp_fun_VC_4: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_VTy_1_type, type, (
% 3.05/2.22 tptp_fun_VTy_1: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Vx_3_type, type, (
% 3.05/2.22 tptp_fun_Vx_3: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(vsomeType_type, type, (
% 3.05/2.22 vsomeType: $i > $i)).
% 3.05/2.22 tff(tptp_fun_VC_5_type, type, (
% 3.05/2.22 tptp_fun_VC_5: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Vx_6_type, type, (
% 3.05/2.22 tptp_fun_Vx_6: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Vy_7_type, type, (
% 3.05/2.22 tptp_fun_Vy_7: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_VTy_8_type, type, (
% 3.05/2.22 tptp_fun_VTy_8: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(vnoType_type, type, (
% 3.05/2.22 vnoType: $i)).
% 3.05/2.22 tff(vtcheck_type, type, (
% 3.05/2.22 vtcheck: ( $i * $i * $i ) > $o)).
% 3.05/2.22 tff(tptp_fun_VT_74_type, type, (
% 3.05/2.22 tptp_fun_VT_74: $i)).
% 3.05/2.22 tff(vabs_type, type, (
% 3.05/2.22 vabs: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(veabs_type, type, (
% 3.05/2.22 veabs: $i)).
% 3.05/2.22 tff(tptp_fun_VS_78_type, type, (
% 3.05/2.22 tptp_fun_VS_78: $i)).
% 3.05/2.22 tff(tptp_fun_VT2_67_type, type, (
% 3.05/2.22 tptp_fun_VT2_67: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Ve2_69_type, type, (
% 3.05/2.22 tptp_fun_Ve2_69: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_VT1_68_type, type, (
% 3.05/2.22 tptp_fun_VT1_68: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Vx_70_type, type, (
% 3.05/2.22 tptp_fun_Vx_70: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(varrow_type, type, (
% 3.05/2.22 varrow: ( $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Vx_66_type, type, (
% 3.05/2.22 tptp_fun_Vx_66: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(vvar_type, type, (
% 3.05/2.22 vvar: $i > $i)).
% 3.05/2.22 tff(tptp_fun_VS_71_type, type, (
% 3.05/2.22 tptp_fun_VS_71: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Ve2_72_type, type, (
% 3.05/2.22 tptp_fun_Ve2_72: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Ve1_73_type, type, (
% 3.05/2.22 tptp_fun_Ve1_73: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(vapp_type, type, (
% 3.05/2.22 vapp: ( $i * $i ) > $i)).
% 3.05/2.22 tff(tptp_fun_Vx_0_type, type, (
% 3.05/2.22 tptp_fun_Vx_0: ( $i * $i * $i ) > $i)).
% 3.05/2.22 tff(vempty_type, type, (
% 3.05/2.22 vempty: $i)).
% 3.05/2.22 tff(1,plain,
% 3.05/2.22 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : refl((~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))))),
% 3.05/2.22 inference(bind,[status(th)],[])).
% 3.05/2.22 tff(2,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 3.05/2.22 inference(quant_intro,[status(thm)],[1])).
% 3.05/2.22 tff(3,plain,
% 3.05/2.22 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : trans(monotonicity(rewrite(((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> ((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))), trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1)) <=> (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> (~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))), rewrite((~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> (((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))), rewrite((((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) <=> ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))), ((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) & ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))), rewrite((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))) & ((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))), ((((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))))),
% 3.05/2.22 inference(bind,[status(th)],[])).
% 3.05/2.22 tff(4,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 3.05/2.22 inference(quant_intro,[status(thm)],[3])).
% 3.05/2.22 tff(5,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 3.05/2.22 inference(rewrite,[status(thm)],[])).
% 3.05/2.22 tff(6,plain,
% 3.05/2.22 (^[VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : rewrite((((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))))),
% 3.05/2.22 inference(bind,[status(th)],[])).
% 3.05/2.22 tff(7,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)))) <=> ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 3.05/2.22 inference(quant_intro,[status(thm)],[6])).
% 3.05/2.22 tff(8,axiom,(![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VCtx0 = VCtx1)) => (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-bind'')).
% 3.05/2.22 tff(9,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 3.05/2.22 inference(modus_ponens,[status(thm)],[8, 7])).
% 3.05/2.22 tff(10,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 3.05/2.22 inference(modus_ponens,[status(thm)],[9, 5])).
% 3.05/2.22 tff(11,plain,(
% 3.05/2.22 ![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VCtx0 = VCtx1))) | (vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))))),
% 3.05/2.22 inference(skolemize,[status(sab)],[10])).
% 3.05/2.22 tff(12,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 3.05/2.22 inference(modus_ponens,[status(thm)],[11, 4])).
% 3.05/2.22 tff(13,plain,
% 3.05/2.22 (![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))),
% 3.05/2.22 inference(modus_ponens,[status(thm)],[12, 2])).
% 3.05/2.22 tff(14,plain,
% 3.05/2.22 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))))))),
% 3.05/2.23 inference(rewrite,[status(thm)],[])).
% 3.05/2.23 tff(15,plain,
% 3.05/2.23 ((~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) <=> (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))))))),
% 3.05/2.23 inference(rewrite,[status(thm)],[])).
% 3.05/2.23 tff(16,plain,
% 3.05/2.23 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))))))),
% 3.05/2.23 inference(monotonicity,[status(thm)],[15])).
% 3.05/2.23 tff(17,plain,
% 3.05/2.23 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))))))),
% 3.17/2.23 inference(transitivity,[status(thm)],[16, 14])).
% 3.17/2.23 tff(18,plain,
% 3.17/2.23 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))))),
% 3.17/2.23 inference(quant_inst,[status(thm)],[])).
% 3.17/2.23 tff(19,plain,
% 3.17/2.23 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))))))),
% 3.17/2.23 inference(modus_ponens,[status(thm)],[18, 17])).
% 3.17/2.23 tff(20,plain,
% 3.17/2.23 (~((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))))),
% 3.17/2.23 inference(unit_resolution,[status(thm)],[19, 13])).
% 3.17/2.23 tff(21,plain,
% 3.17/2.23 (((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))))) | ((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))),
% 3.17/2.23 inference(tautology,[status(thm)],[])).
% 3.17/2.23 tff(22,plain,
% 3.17/2.23 ((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))),
% 3.17/2.24 inference(unit_resolution,[status(thm)],[21, 20])).
% 3.17/2.24 tff(23,plain,
% 3.17/2.24 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 3.17/2.24 inference(rewrite,[status(thm)],[])).
% 3.17/2.24 tff(24,plain,
% 3.17/2.24 ((~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT)))),
% 3.17/2.24 inference(rewrite,[status(thm)],[])).
% 3.17/2.24 tff(25,axiom,(~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType)) & vtcheck(VC, vabs(Vy, VS1, veabs), VT)) => vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-abs-1'')).
% 3.17/2.24 tff(26,plain,
% 3.17/2.24 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[25, 24])).
% 3.17/2.24 tff(27,plain,
% 3.17/2.24 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[26, 23])).
% 3.17/2.24 tff(28,plain,
% 3.17/2.24 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[27, 23])).
% 3.17/2.24 tff(29,plain,
% 3.17/2.24 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[28, 23])).
% 3.17/2.24 tff(30,plain,
% 3.17/2.24 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[29, 23])).
% 3.17/2.24 tff(31,plain,
% 3.17/2.24 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[30, 23])).
% 3.17/2.24 tff(32,plain,
% 3.17/2.24 (~![Vx: $i, VS: $i, VC: $i, Vy: $i, VS1: $i, VT: $i] : ((~((~(Vx = Vy)) & (vlookup(Vx, VC) = vnoType) & vtcheck(VC, vabs(Vy, VS1, veabs), VT))) | vtcheck(vbind(Vx, VS, VC), vabs(Vy, VS1, veabs), VT))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[31, 23])).
% 3.17/2.24 tff(33,plain,(
% 3.17/2.24 ~((~((~(Vx!79 = Vy!76)) & (vlookup(Vx!79, VC!77) = vnoType) & vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74))),
% 3.17/2.24 inference(skolemize,[status(sab)],[32])).
% 3.17/2.24 tff(34,plain,
% 3.17/2.24 ((~(Vx!79 = Vy!76)) & (vlookup(Vx!79, VC!77) = vnoType) & vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)),
% 3.17/2.24 inference(or_elim,[status(thm)],[33])).
% 3.17/2.24 tff(35,plain,
% 3.17/2.24 (vlookup(Vx!79, VC!77) = vnoType),
% 3.17/2.24 inference(and_elim,[status(thm)],[34])).
% 3.17/2.24 tff(36,plain,
% 3.17/2.24 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))))))))),
% 3.17/2.24 inference(rewrite,[status(thm)],[])).
% 3.17/2.24 tff(37,plain,
% 3.17/2.24 ((~((~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) <=> (~((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))))))))),
% 3.17/2.24 inference(rewrite,[status(thm)],[])).
% 3.17/2.24 tff(38,plain,
% 3.17/2.24 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))))))))),
% 3.17/2.24 inference(monotonicity,[status(thm)],[37])).
% 3.17/2.24 tff(39,plain,
% 3.17/2.24 (((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))))) <=> ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))))))))),
% 3.17/2.24 inference(transitivity,[status(thm)],[38, 36])).
% 3.17/2.24 tff(40,plain,
% 3.17/2.24 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)) | (~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))))),
% 3.17/2.24 inference(quant_inst,[status(thm)],[])).
% 3.17/2.24 tff(41,plain,
% 3.17/2.24 ((~![VVar0: $i, VTyp0: $i, VCtx0: $i, VVar1: $i, VTyp1: $i, VCtx1: $i] : (~((~((~(vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1)))))) | (~((vbind(VVar0, VTyp0, VCtx0) = vbind(VVar1, VTyp1, VCtx1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VCtx0 = VCtx1))))))) | (~((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))))))))),
% 3.17/2.24 inference(modus_ponens,[status(thm)],[40, 39])).
% 3.17/2.24 tff(42,plain,
% 3.17/2.24 (~((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))))))),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[41, 13])).
% 3.17/2.25 tff(43,plain,
% 3.17/2.25 (((~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))))))) | ((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))))),
% 3.17/2.25 inference(tautology,[status(thm)],[])).
% 3.17/2.25 tff(44,plain,
% 3.17/2.25 ((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))))),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[43, 42])).
% 3.17/2.25 tff(45,assumption,(~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))), introduced(assumption)).
% 3.17/2.25 tff(46,plain,
% 3.17/2.25 (((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))),
% 3.17/2.25 inference(tautology,[status(thm)],[])).
% 3.17/2.25 tff(47,plain,
% 3.17/2.25 (vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[46, 45])).
% 3.17/2.25 tff(48,plain,
% 3.17/2.25 (vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)),
% 3.17/2.25 inference(symmetry,[status(thm)],[47])).
% 3.17/2.25 tff(49,plain,
% 3.17/2.25 ((~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))))) | (~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))))),
% 3.17/2.25 inference(tautology,[status(thm)],[])).
% 3.17/2.25 tff(50,plain,
% 3.17/2.25 ((~((~(vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))))) | (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))))),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[49, 48])).
% 3.17/2.25 tff(51,plain,
% 3.17/2.25 (~((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)))),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[50, 44])).
% 3.17/2.25 tff(52,plain,
% 3.17/2.25 (((~(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)) | (~(tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75))) | (tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)),
% 3.17/2.25 inference(tautology,[status(thm)],[])).
% 3.17/2.25 tff(53,plain,
% 3.17/2.25 (tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[52, 51])).
% 3.17/2.25 tff(54,plain,
% 3.17/2.25 (((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))),
% 3.17/2.25 inference(tautology,[status(thm)],[])).
% 3.17/2.25 tff(55,plain,
% 3.17/2.25 (Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[54, 45])).
% 3.17/2.25 tff(56,plain,
% 3.17/2.25 (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vx!79),
% 3.17/2.25 inference(symmetry,[status(thm)],[55])).
% 3.17/2.25 tff(57,plain,
% 3.17/2.25 (vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vlookup(Vx!79, VC!77)),
% 3.17/2.25 inference(monotonicity,[status(thm)],[56, 53])).
% 3.17/2.25 tff(58,plain,
% 3.17/2.25 (((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))),
% 3.17/2.25 inference(tautology,[status(thm)],[])).
% 3.17/2.25 tff(59,plain,
% 3.17/2.25 (vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))),
% 3.17/2.25 inference(unit_resolution,[status(thm)],[58, 45])).
% 3.17/2.25 tff(60,plain,
% 3.17/2.25 (vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType),
% 3.17/2.25 inference(transitivity,[status(thm)],[59, 57, 35])).
% 3.17/2.25 tff(61,plain,
% 3.17/2.25 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : refl((~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))))),
% 3.17/2.25 inference(bind,[status(th)],[])).
% 3.17/2.25 tff(62,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 3.17/2.25 inference(quant_intro,[status(thm)],[61])).
% 3.17/2.25 tff(63,plain,
% 3.17/2.25 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : trans(monotonicity(rewrite(((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), trans(monotonicity(trans(monotonicity(rewrite(((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1)) <=> (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> (~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), rewrite((~(~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) <=> ((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> (((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))), rewrite((((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))), (((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) <=> ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))), rewrite((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))) & ((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))), ((((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))))),
% 3.17/2.25 inference(bind,[status(th)],[])).
% 3.17/2.25 tff(64,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 3.17/2.25 inference(quant_intro,[status(thm)],[63])).
% 3.17/2.25 tff(65,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 3.17/2.25 inference(rewrite,[status(thm)],[])).
% 3.17/2.25 tff(66,plain,
% 3.17/2.25 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : rewrite((((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))))),
% 3.17/2.25 inference(bind,[status(th)],[])).
% 3.17/2.25 tff(67,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 3.17/2.25 inference(quant_intro,[status(thm)],[66])).
% 3.17/2.25 tff(68,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) => (((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1))) & ((((VVar0 = VVar1) & (VTyp0 = VTyp1)) & (VExp0 = VExp1)) => (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-abs'')).
% 3.17/2.25 tff(69,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 3.17/2.25 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.17/2.25 tff(70,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 3.17/2.25 inference(modus_ponens,[status(thm)],[69, 65])).
% 3.17/2.25 tff(71,plain,(
% 3.17/2.25 ![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | ((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) & ((~((VVar0 = VVar1) & (VTyp0 = VTyp1) & (VExp0 = VExp1))) | (vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))))),
% 3.17/2.25 inference(skolemize,[status(sab)],[70])).
% 3.17/2.25 tff(72,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 3.17/2.25 inference(modus_ponens,[status(thm)],[71, 64])).
% 3.17/2.25 tff(73,plain,
% 3.17/2.25 (![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))),
% 3.17/2.25 inference(modus_ponens,[status(thm)],[72, 62])).
% 3.17/2.25 tff(74,plain,
% 3.17/2.25 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VVar1: $i, VTyp1: $i, VExp1: $i] : (~((~((~(vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1))) | (~((~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1)))))) | (~((vabs(VVar0, VTyp0, VExp0) = vabs(VVar1, VTyp1, VExp1)) | (~(VVar0 = VVar1)) | (~(VTyp0 = VTyp1)) | (~(VExp0 = VExp1))))))) | (~((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)) | (~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))))),
% 3.17/2.26 inference(quant_inst,[status(thm)],[])).
% 3.17/2.26 tff(75,plain,
% 3.17/2.26 (~((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)) | (~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))),
% 3.17/2.26 inference(unit_resolution,[status(thm)],[74, 73])).
% 3.17/2.26 tff(76,plain,
% 3.17/2.26 (((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)) | (~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))) | ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))),
% 3.17/2.26 inference(tautology,[status(thm)],[])).
% 3.17/2.26 tff(77,plain,
% 3.17/2.26 ((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))),
% 3.17/2.26 inference(unit_resolution,[status(thm)],[76, 75])).
% 3.17/2.26 tff(78,plain,
% 3.17/2.26 ((vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)) <=> (vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.17/2.26 inference(commutativity,[status(thm)],[])).
% 3.17/2.26 tff(79,plain,
% 3.17/2.26 ((~(vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) <=> (~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.17/2.26 inference(monotonicity,[status(thm)],[78])).
% 3.17/2.26 tff(80,assumption,(vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)), introduced(assumption)).
% 3.17/2.26 tff(81,plain,
% 3.17/2.26 (^[VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : refl((~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))))),
% 3.17/2.26 inference(bind,[status(th)],[])).
% 3.17/2.26 tff(82,plain,
% 3.17/2.26 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 3.17/2.26 inference(quant_intro,[status(thm)],[81])).
% 3.17/2.26 tff(83,plain,
% 3.17/2.26 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0))) <=> ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 3.17/2.26 inference(rewrite,[status(thm)],[])).
% 3.17/2.26 tff(84,axiom,(![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-abs'')).
% 3.17/2.26 tff(85,plain,
% 3.17/2.26 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[84, 83])).
% 3.17/2.26 tff(86,plain,(
% 3.17/2.26 ![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 3.17/2.26 inference(skolemize,[status(sab)],[85])).
% 3.17/2.26 tff(87,plain,
% 3.17/2.26 (![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[86, 82])).
% 3.17/2.26 tff(88,plain,
% 3.17/2.26 ((~![VVar0: $i, VVar1: $i, VTyp0: $i, VExp0: $i] : (~(vvar(VVar0) = vabs(VVar1, VTyp0, VExp0)))) | (~(vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)))),
% 3.17/2.26 inference(quant_inst,[status(thm)],[])).
% 3.17/2.26 tff(89,plain,
% 3.17/2.26 ($false),
% 3.17/2.26 inference(unit_resolution,[status(thm)],[88, 87, 80])).
% 3.17/2.26 tff(90,plain,(~(vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))), inference(lemma,lemma(discharge,[]))).
% 3.17/2.26 tff(91,plain,
% 3.17/2.26 (~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[90, 79])).
% 3.17/2.26 tff(92,plain,
% 3.17/2.26 (((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74)))) | (vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.17/2.26 inference(tautology,[status(thm)],[])).
% 3.17/2.26 tff(93,plain,
% 3.17/2.26 ((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74)))),
% 3.17/2.26 inference(unit_resolution,[status(thm)],[92, 91])).
% 3.17/2.26 tff(94,assumption,(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))), introduced(assumption)).
% 3.17/2.26 tff(95,plain,
% 3.17/2.26 (^[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))))),
% 3.17/2.26 inference(bind,[status(th)],[])).
% 3.17/2.26 tff(96,plain,
% 3.17/2.26 (![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)))),
% 3.17/2.26 inference(quant_intro,[status(thm)],[95])).
% 3.17/2.26 tff(97,plain,
% 3.17/2.26 (![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)))),
% 3.17/2.26 inference(rewrite,[status(thm)],[])).
% 3.17/2.26 tff(98,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'')).
% 3.17/2.26 tff(99,plain,
% 3.17/2.26 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[98, 97])).
% 3.17/2.26 tff(100,plain,(
% 3.17/2.26 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.17/2.26 inference(skolemize,[status(sab)],[99])).
% 3.17/2.26 tff(101,plain,
% 3.17/2.26 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[100, 96])).
% 3.17/2.26 tff(102,plain,
% 3.17/2.26 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.17/2.26 inference(quant_inst,[status(thm)],[])).
% 3.17/2.26 tff(103,plain,
% 3.17/2.26 ($false),
% 3.17/2.26 inference(unit_resolution,[status(thm)],[102, 101, 94])).
% 3.17/2.26 tff(104,plain,(~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))), inference(lemma,lemma(discharge,[]))).
% 3.17/2.26 tff(105,plain,
% 3.17/2.26 (((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.17/2.26 inference(tautology,[status(thm)],[])).
% 3.17/2.26 tff(106,plain,
% 3.17/2.26 ((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.17/2.26 inference(unit_resolution,[status(thm)],[105, 104])).
% 3.17/2.26 tff(107,plain,
% 3.17/2.26 (vtcheck(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)),
% 3.17/2.26 inference(and_elim,[status(thm)],[34])).
% 3.17/2.26 tff(108,plain,
% 3.17/2.26 (^[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)))))))),
% 3.17/2.26 inference(bind,[status(th)],[])).
% 3.17/2.26 tff(109,plain,
% 3.17/2.26 (![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))))))),
% 3.17/2.26 inference(quant_intro,[status(thm)],[108])).
% 3.17/2.26 tff(110,plain,
% 3.17/2.26 (^[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))))))))),
% 3.17/2.26 inference(bind,[status(th)],[])).
% 3.17/2.26 tff(111,plain,
% 3.17/2.26 (![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))))))),
% 3.17/2.26 inference(quant_intro,[status(thm)],[110])).
% 3.17/2.26 tff(112,plain,
% 3.17/2.26 (^[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)))))),
% 3.17/2.26 inference(bind,[status(th)],[])).
% 3.17/2.26 tff(113,plain,
% 3.17/2.26 (![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))))),
% 3.17/2.26 inference(quant_intro,[status(thm)],[112])).
% 3.17/2.26 tff(114,plain,
% 3.17/2.26 (![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)))),
% 3.17/2.26 inference(rewrite,[status(thm)],[])).
% 3.17/2.26 tff(115,plain,
% 3.17/2.26 (^[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)))))),
% 3.17/2.26 inference(bind,[status(th)],[])).
% 3.17/2.26 tff(116,plain,
% 3.17/2.26 (![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)))),
% 3.17/2.26 inference(quant_intro,[status(thm)],[115])).
% 3.17/2.26 tff(117,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'')).
% 3.17/2.26 tff(118,plain,
% 3.17/2.26 (![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)))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[117, 116])).
% 3.17/2.26 tff(119,plain,
% 3.17/2.26 (![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)))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[118, 114])).
% 3.17/2.26 tff(120,plain,(
% 3.17/2.26 ![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)))),
% 3.17/2.26 inference(skolemize,[status(sab)],[119])).
% 3.17/2.26 tff(121,plain,
% 3.17/2.26 (![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))))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[120, 113])).
% 3.17/2.26 tff(122,plain,
% 3.17/2.26 (![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))))))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[121, 111])).
% 3.17/2.26 tff(123,plain,
% 3.17/2.26 (![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))))))),
% 3.17/2.26 inference(modus_ponens,[status(thm)],[122, 109])).
% 3.17/2.26 tff(124,plain,
% 3.17/2.26 (((~![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(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))))) <=> ((~![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(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))))),
% 3.17/2.26 inference(rewrite,[status(thm)],[])).
% 3.17/2.26 tff(125,plain,
% 3.17/2.26 ((~![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(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))))),
% 3.17/2.27 inference(quant_inst,[status(thm)],[])).
% 3.17/2.27 tff(126,plain,
% 3.17/2.27 ((~![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(VC!77, vabs(Vy!76, VS1!75, veabs), VT!74)) | (~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))))),
% 3.17/2.27 inference(modus_ponens,[status(thm)],[125, 124])).
% 3.17/2.27 tff(127,plain,
% 3.17/2.27 ((~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vapp(tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(VC!77, tptp_fun_Ve1_73(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), varrow(tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VT!74))) | (~vtcheck(VC!77, tptp_fun_Ve2_72(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VS_71(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))))),
% 3.17/2.27 inference(unit_resolution,[status(thm)],[126, 123, 107])).
% 3.17/2.27 tff(128,plain,
% 3.17/2.27 ((~((~(vabs(Vy!76, VS1!75, veabs) = vvar(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(vlookup(tptp_fun_Vx_66(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vsomeType(VT!74))))) | (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))))),
% 3.17/2.27 inference(unit_resolution,[status(thm)],[127, 106])).
% 3.17/2.27 tff(129,plain,
% 3.17/2.27 (~((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.17/2.27 inference(unit_resolution,[status(thm)],[128, 93])).
% 3.17/2.27 tff(130,plain,
% 3.17/2.27 (((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.17/2.27 inference(tautology,[status(thm)],[])).
% 3.17/2.27 tff(131,plain,
% 3.17/2.27 (vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.17/2.27 inference(unit_resolution,[status(thm)],[130, 129])).
% 3.17/2.27 tff(132,plain,
% 3.17/2.27 (vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs)),
% 3.17/2.27 inference(symmetry,[status(thm)],[131])).
% 3.17/2.27 tff(133,plain,
% 3.17/2.27 ((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))),
% 3.17/2.27 inference(tautology,[status(thm)],[])).
% 3.17/2.27 tff(134,plain,
% 3.17/2.27 ((~((~(vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = vabs(Vy!76, VS1!75, veabs))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))))) | (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))))),
% 3.17/2.27 inference(unit_resolution,[status(thm)],[133, 132])).
% 3.17/2.27 tff(135,plain,
% 3.17/2.27 (~((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)))),
% 3.17/2.27 inference(unit_resolution,[status(thm)],[134, 77])).
% 3.17/2.27 tff(136,plain,
% 3.17/2.27 (((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))) | (tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs)),
% 3.17/2.27 inference(tautology,[status(thm)],[])).
% 3.17/2.27 tff(137,plain,
% 3.17/2.27 (tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs),
% 3.21/2.27 inference(unit_resolution,[status(thm)],[136, 135])).
% 3.21/2.27 tff(138,plain,
% 3.21/2.27 (veabs = tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))),
% 3.21/2.27 inference(symmetry,[status(thm)],[137])).
% 3.21/2.27 tff(139,plain,
% 3.21/2.27 (((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))) | (tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)),
% 3.21/2.27 inference(tautology,[status(thm)],[])).
% 3.21/2.27 tff(140,plain,
% 3.21/2.27 (tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75),
% 3.21/2.27 inference(unit_resolution,[status(thm)],[139, 135])).
% 3.21/2.27 tff(141,plain,
% 3.21/2.27 (((~(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)) | (~(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = VS1!75)) | (~(tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = veabs))) | (tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76)),
% 3.21/2.27 inference(tautology,[status(thm)],[])).
% 3.21/2.27 tff(142,plain,
% 3.21/2.27 (tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)) = Vy!76),
% 3.21/2.27 inference(unit_resolution,[status(thm)],[141, 135])).
% 3.21/2.27 tff(143,plain,
% 3.21/2.27 (vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77) = vbind(Vy!76, VS1!75, VC!77)),
% 3.21/2.27 inference(monotonicity,[status(thm)],[142, 140])).
% 3.21/2.27 tff(144,plain,
% 3.21/2.27 (vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77)),
% 3.21/2.27 inference(symmetry,[status(thm)],[143])).
% 3.21/2.27 tff(145,plain,
% 3.21/2.27 (vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(monotonicity,[status(thm)],[144, 138])).
% 3.21/2.27 tff(146,plain,
% 3.21/2.27 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(symmetry,[status(thm)],[145])).
% 3.21/2.27 tff(147,plain,
% 3.21/2.27 (((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(tautology,[status(thm)],[])).
% 3.21/2.27 tff(148,plain,
% 3.21/2.27 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(unit_resolution,[status(thm)],[147, 129])).
% 3.21/2.27 tff(149,plain,
% 3.21/2.27 (vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(modus_ponens,[status(thm)],[148, 146])).
% 3.21/2.27 tff(150,plain,
% 3.21/2.27 (vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)) = vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77))),
% 3.21/2.27 inference(monotonicity,[status(thm)],[142, 140])).
% 3.21/2.27 tff(151,plain,
% 3.21/2.27 (vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)) = vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77))),
% 3.21/2.27 inference(symmetry,[status(thm)],[150])).
% 3.21/2.27 tff(152,plain,
% 3.21/2.27 (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(monotonicity,[status(thm)],[151, 138])).
% 3.21/2.27 tff(153,plain,
% 3.21/2.27 (vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) <=> vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(symmetry,[status(thm)],[152])).
% 3.21/2.27 tff(154,plain,
% 3.21/2.27 ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) <=> (~vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.27 inference(monotonicity,[status(thm)],[153])).
% 3.21/2.27 tff(155,plain,
% 3.21/2.27 (((~(vabs(Vy!76, VS1!75, veabs) = vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~(VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), VC!77), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) | (VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.27 inference(tautology,[status(thm)],[])).
% 3.21/2.27 tff(156,plain,
% 3.21/2.27 (VT!74 = varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.27 inference(unit_resolution,[status(thm)],[155, 129])).
% 3.21/2.27 tff(157,plain,
% 3.21/2.27 (varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) = VT!74),
% 3.21/2.27 inference(symmetry,[status(thm)],[156])).
% 3.21/2.27 tff(158,plain,
% 3.21/2.27 (vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) <=> vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74)),
% 3.21/2.27 inference(monotonicity,[status(thm)],[132, 157])).
% 3.21/2.27 tff(159,plain,
% 3.21/2.27 (vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74) <=> vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.27 inference(symmetry,[status(thm)],[158])).
% 3.21/2.27 tff(160,plain,
% 3.21/2.27 ((~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74)) <=> (~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.27 inference(monotonicity,[status(thm)],[159])).
% 3.21/2.27 tff(161,plain,
% 3.21/2.27 (~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(Vy!76, VS1!75, veabs), VT!74)),
% 3.21/2.27 inference(or_elim,[status(thm)],[33])).
% 3.21/2.27 tff(162,plain,
% 3.21/2.27 (~vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.27 inference(modus_ponens,[status(thm)],[161, 160])).
% 3.21/2.27 tff(163,plain,
% 3.21/2.27 (^[VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : refl(((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))))),
% 3.21/2.27 inference(bind,[status(th)],[])).
% 3.21/2.27 tff(164,plain,
% 3.21/2.27 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 3.21/2.27 inference(quant_intro,[status(thm)],[163])).
% 3.21/2.27 tff(165,plain,
% 3.21/2.27 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 3.21/2.27 inference(rewrite,[status(thm)],[])).
% 3.21/2.27 tff(166,plain,
% 3.21/2.27 (^[VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : rewrite((vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))))),
% 3.21/2.27 inference(bind,[status(th)],[])).
% 3.21/2.27 tff(167,plain,
% 3.21/2.27 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT))) <=> ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 3.21/2.27 inference(quant_intro,[status(thm)],[166])).
% 3.21/2.27 tff(168,axiom,(![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), Ve, VT) => vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-abs'')).
% 3.21/2.27 tff(169,plain,
% 3.21/2.27 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[168, 167])).
% 3.21/2.28 tff(170,plain,
% 3.21/2.28 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[169, 165])).
% 3.21/2.28 tff(171,plain,(
% 3.21/2.28 ![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 3.21/2.28 inference(skolemize,[status(sab)],[170])).
% 3.21/2.28 tff(172,plain,
% 3.21/2.28 (![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[171, 164])).
% 3.21/2.28 tff(173,plain,
% 3.21/2.28 (((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(rewrite,[status(thm)],[])).
% 3.21/2.28 tff(174,plain,
% 3.21/2.28 ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(quant_inst,[status(thm)],[])).
% 3.21/2.28 tff(175,plain,
% 3.21/2.28 ((~![VC: $i, Vx: $i, Ve: $i, VS: $i, VT: $i] : ((~vtcheck(vbind(Vx, VS, VC), Ve, VT)) | vtcheck(VC, vabs(Vx, VS, Ve), varrow(VS, VT)))) | (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[174, 173])).
% 3.21/2.28 tff(176,plain,
% 3.21/2.28 ((~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))) | vtcheck(vbind(Vx!79, VS!78, VC!77), vabs(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))), varrow(tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.28 inference(unit_resolution,[status(thm)],[175, 172])).
% 3.21/2.28 tff(177,plain,
% 3.21/2.28 (~vtcheck(vbind(tptp_fun_Vx_70(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT1_68(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), vbind(Vx!79, VS!78, VC!77)), tptp_fun_Ve2_69(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)), tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.28 inference(unit_resolution,[status(thm)],[176, 162])).
% 3.21/2.28 tff(178,plain,
% 3.21/2.28 (~vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[177, 154])).
% 3.21/2.28 tff(179,plain,
% 3.21/2.28 (~(Vx!79 = Vy!76)),
% 3.21/2.28 inference(and_elim,[status(thm)],[34])).
% 3.21/2.28 tff(180,plain,
% 3.21/2.28 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : refl((vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))),
% 3.21/2.28 inference(bind,[status(th)],[])).
% 3.21/2.28 tff(181,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 3.21/2.28 inference(quant_intro,[status(thm)],[180])).
% 3.21/2.28 tff(182,plain,
% 3.21/2.28 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) <=> (~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))), ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> (~(~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))))), rewrite((~(~((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))) <=> ((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))), ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) <=> ((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))))), (((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)))), rewrite((((Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))), (((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))))),
% 3.21/2.28 inference(bind,[status(th)],[])).
% 3.21/2.28 tff(183,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 3.21/2.28 inference(quant_intro,[status(thm)],[182])).
% 3.21/2.28 tff(184,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 3.21/2.28 inference(rewrite,[status(thm)],[])).
% 3.21/2.28 tff(185,plain,
% 3.21/2.28 (^[Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : rewrite((((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)))),
% 3.21/2.28 inference(bind,[status(th)],[])).
% 3.21/2.28 tff(186,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT)) <=> ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 3.21/2.28 inference(quant_intro,[status(thm)],[185])).
% 3.21/2.28 tff(187,axiom,(![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)) => vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-Context-Swap'')).
% 3.21/2.28 tff(188,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[187, 186])).
% 3.21/2.28 tff(189,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[188, 184])).
% 3.21/2.28 tff(190,plain,(
% 3.21/2.28 ![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : ((~((~(Vx = Vy)) & vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT))) | vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT))),
% 3.21/2.28 inference(skolemize,[status(sab)],[189])).
% 3.21/2.28 tff(191,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[190, 183])).
% 3.21/2.28 tff(192,plain,
% 3.21/2.28 (![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[191, 181])).
% 3.21/2.28 tff(193,plain,
% 3.21/2.28 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | ((Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(rewrite,[status(thm)],[])).
% 3.21/2.28 tff(194,plain,
% 3.21/2.28 ((vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))) <=> ((Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(rewrite,[status(thm)],[])).
% 3.21/2.28 tff(195,plain,
% 3.21/2.28 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | ((Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))))),
% 3.21/2.28 inference(monotonicity,[status(thm)],[194])).
% 3.21/2.28 tff(196,plain,
% 3.21/2.28 (((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(transitivity,[status(thm)],[195, 193])).
% 3.21/2.28 tff(197,plain,
% 3.21/2.28 ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (Vx!79 = Vy!76) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(quant_inst,[status(thm)],[])).
% 3.21/2.28 tff(198,plain,
% 3.21/2.28 ((~![Vy: $i, VTy: $i, Vx: $i, VTx: $i, VC: $i, Ve: $i, VT: $i] : (vtcheck(vbind(Vy, VTy, vbind(Vx, VTx, VC)), Ve, VT) | (Vx = Vy) | (~vtcheck(vbind(Vx, VTx, vbind(Vy, VTy, VC)), Ve, VT)))) | (Vx!79 = Vy!76) | vtcheck(vbind(Vy!76, VS1!75, vbind(Vx!79, VS!78, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[197, 196])).
% 3.21/2.28 tff(199,plain,
% 3.21/2.28 (~vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))),
% 3.21/2.28 inference(unit_resolution,[status(thm)],[198, 192, 179, 178])).
% 3.21/2.28 tff(200,plain,
% 3.21/2.28 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : refl((vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))),
% 3.21/2.28 inference(bind,[status(th)],[])).
% 3.21/2.28 tff(201,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 3.21/2.28 inference(quant_intro,[status(thm)],[200])).
% 3.21/2.28 tff(202,plain,
% 3.21/2.28 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : trans(monotonicity(trans(monotonicity(rewrite(((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) <=> (~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) <=> (~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))))), rewrite((~(~((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))), ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) <=> ((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))), rewrite((((~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))), (((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))))),
% 3.21/2.28 inference(bind,[status(th)],[])).
% 3.21/2.28 tff(203,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 3.21/2.28 inference(quant_intro,[status(thm)],[202])).
% 3.21/2.28 tff(204,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 3.21/2.28 inference(rewrite,[status(thm)],[])).
% 3.21/2.28 tff(205,plain,
% 3.21/2.28 (^[Vx: $i, VS: $i, VC: $i, VT: $i] : rewrite((((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT)))),
% 3.21/2.28 inference(bind,[status(th)],[])).
% 3.21/2.28 tff(206,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT)) <=> ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 3.21/2.28 inference(quant_intro,[status(thm)],[205])).
% 3.21/2.28 tff(207,axiom,(![Vx: $i, VS: $i, VC: $i, VT: $i] : (((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT)) => vtcheck(vbind(Vx, VS, VC), veabs, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Weak-abs-IH'')).
% 3.21/2.28 tff(208,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[207, 206])).
% 3.21/2.28 tff(209,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[208, 204])).
% 3.21/2.28 tff(210,plain,(
% 3.21/2.28 ![Vx: $i, VS: $i, VC: $i, VT: $i] : ((~((vlookup(Vx, VC) = vnoType) & vtcheck(VC, veabs, VT))) | vtcheck(vbind(Vx, VS, VC), veabs, VT))),
% 3.21/2.28 inference(skolemize,[status(sab)],[209])).
% 3.21/2.28 tff(211,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[210, 203])).
% 3.21/2.28 tff(212,plain,
% 3.21/2.28 (![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[211, 201])).
% 3.21/2.28 tff(213,plain,
% 3.21/2.28 (((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | (vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))) <=> ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(rewrite,[status(thm)],[])).
% 3.21/2.28 tff(214,plain,
% 3.21/2.28 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | (vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs)))))),
% 3.21/2.28 inference(quant_inst,[status(thm)],[])).
% 3.21/2.28 tff(215,plain,
% 3.21/2.28 ((~![Vx: $i, VS: $i, VC: $i, VT: $i] : (vtcheck(vbind(Vx, VS, VC), veabs, VT) | (~(vlookup(Vx, VC) = vnoType)) | (~vtcheck(VC, veabs, VT)))) | vtcheck(vbind(Vx!79, VS!78, vbind(Vy!76, VS1!75, VC!77)), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.28 inference(modus_ponens,[status(thm)],[214, 213])).
% 3.21/2.28 tff(216,plain,
% 3.21/2.28 ((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~vtcheck(vbind(Vy!76, VS1!75, VC!77), veabs, tptp_fun_VT2_67(VC!77, VT!74, vabs(Vy!76, VS1!75, veabs))))),
% 3.21/2.28 inference(unit_resolution,[status(thm)],[215, 212, 199])).
% 3.21/2.28 tff(217,plain,
% 3.21/2.28 (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)),
% 3.21/2.28 inference(unit_resolution,[status(thm)],[216, 149])).
% 3.21/2.28 tff(218,plain,
% 3.21/2.28 ($false),
% 3.21/2.28 inference(unit_resolution,[status(thm)],[217, 60])).
% 3.21/2.28 tff(219,plain,((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))), inference(lemma,lemma(discharge,[]))).
% 3.21/2.28 tff(220,plain,
% 3.21/2.28 (((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType))) | (vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)),
% 3.21/2.28 inference(tautology,[status(thm)],[])).
% 3.21/2.28 tff(221,plain,
% 3.21/2.28 ((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType))),
% 3.21/2.28 inference(unit_resolution,[status(thm)],[220, 217])).
% 3.21/2.28 tff(222,plain,
% 3.21/2.28 (^[VVar0: $i, VCtx0: $i, RESULT: $i] : rewrite(((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))) <=> ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))))))),
% 3.21/2.28 inference(bind,[status(th)],[])).
% 3.21/2.28 tff(223,plain,
% 3.21/2.28 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))),
% 3.21/2.28 inference(quant_intro,[status(thm)],[222])).
% 3.21/2.28 tff(224,plain,
% 3.21/2.28 (^[VVar0: $i, VCtx0: $i, RESULT: $i] : rewrite((((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(vlookup(VVar0, VCtx0) = RESULT))) <=> ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))))))),
% 3.21/2.29 inference(bind,[status(th)],[])).
% 3.21/2.29 tff(225,plain,
% 3.21/2.29 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(vlookup(VVar0, VCtx0) = RESULT))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))),
% 3.21/2.29 inference(quant_intro,[status(thm)],[224])).
% 3.21/2.29 tff(226,plain,
% 3.21/2.29 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 3.21/2.29 inference(rewrite,[status(thm)],[])).
% 3.21/2.29 tff(227,plain,
% 3.21/2.29 (^[VVar0: $i, VCtx0: $i, RESULT: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))))), quant_intro(proof_bind(^[VTy: $i, Vy: $i, Vx: $i, VC: $i] : trans(monotonicity(rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)))), (((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> (((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))), rewrite((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))), (((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))))), (?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))) <=> ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))), (((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))) <=> ((?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))))), rewrite(((?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))), (((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC)))))), (((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> ((vlookup(VVar0, VCtx0) = RESULT) => (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))))), rewrite(((vlookup(VVar0, VCtx0) = RESULT) => (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))), (((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))))),
% 3.21/2.29 inference(bind,[status(th)],[])).
% 3.21/2.29 tff(228,plain,
% 3.21/2.29 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC))))) <=> ![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 3.21/2.29 inference(quant_intro,[status(thm)],[227])).
% 3.21/2.29 tff(229,axiom,(![VVar0: $i, VCtx0: $i, RESULT: $i] : ((vlookup(VVar0, VCtx0) = RESULT) => ((?[Vx: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (Vx = Vy)) & (RESULT = vsomeType(VTy)))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC))) & (~(Vx = Vy))) & (RESULT = vlookup(Vx, VC)))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''lookup-INV'')).
% 3.21/2.29 tff(230,plain,
% 3.21/2.29 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 3.21/2.29 inference(modus_ponens,[status(thm)],[229, 228])).
% 3.21/2.29 tff(231,plain,
% 3.21/2.29 (![VVar0: $i, VCtx0: $i, RESULT: $i] : (?[Vx: $i] : ((VVar0 = Vx) & (VCtx0 = vempty) & (RESULT = vnoType)) | ?[VC: $i, Vx: $i, Vy: $i, VTy: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (Vx = Vy) & (RESULT = vsomeType(VTy))) | ?[VTy: $i, Vy: $i, Vx: $i, VC: $i] : ((VVar0 = Vx) & (VCtx0 = vbind(Vy, VTy, VC)) & (~(Vx = Vy)) & (RESULT = vlookup(Vx, VC))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 3.21/2.29 inference(modus_ponens,[status(thm)],[230, 226])).
% 3.21/2.29 tff(232,plain,(
% 3.21/2.29 ![VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(vlookup(VVar0, VCtx0) = RESULT)))),
% 3.21/2.29 inference(skolemize,[status(sab)],[231])).
% 3.21/2.29 tff(233,plain,
% 3.21/2.29 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | ((VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0)) & (VCtx0 = vempty) & (RESULT = vnoType)) | ((VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0))) & (tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0)) & (RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))) | ((VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0)) & (VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0))) & (~(tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0))) & (RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))),
% 3.21/2.29 inference(modus_ponens,[status(thm)],[232, 225])).
% 3.21/2.29 tff(234,plain,
% 3.21/2.29 (![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))),
% 3.21/2.29 inference(modus_ponens,[status(thm)],[233, 223])).
% 3.21/2.29 tff(235,plain,
% 3.21/2.29 (((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))) <=> ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))),
% 3.21/2.29 inference(rewrite,[status(thm)],[])).
% 3.21/2.29 tff(236,plain,
% 3.21/2.29 (($false | (~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))) <=> ((~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))),
% 3.21/2.29 inference(rewrite,[status(thm)],[])).
% 3.21/2.29 tff(237,plain,
% 3.21/2.29 ((~((tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) <=> (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))),
% 3.21/2.30 inference(rewrite,[status(thm)],[])).
% 3.21/2.30 tff(238,plain,
% 3.21/2.30 ((~((~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) <=> (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))),
% 3.21/2.30 inference(rewrite,[status(thm)],[])).
% 3.21/2.30 tff(239,plain,
% 3.21/2.30 ((~((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) <=> (~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType))))),
% 3.21/2.30 inference(rewrite,[status(thm)],[])).
% 3.21/2.30 tff(240,plain,
% 3.21/2.30 ((~$true) <=> $false),
% 3.21/2.30 inference(rewrite,[status(thm)],[])).
% 3.21/2.30 tff(241,plain,
% 3.21/2.30 ((vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77))) <=> $true),
% 3.21/2.30 inference(rewrite,[status(thm)],[])).
% 3.21/2.30 tff(242,plain,
% 3.21/2.30 ((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)))) <=> (~$true)),
% 3.21/2.30 inference(monotonicity,[status(thm)],[241])).
% 3.21/2.30 tff(243,plain,
% 3.21/2.30 ((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)))) <=> $false),
% 3.21/2.30 inference(transitivity,[status(thm)],[242, 240])).
% 3.21/2.30 tff(244,plain,
% 3.21/2.30 (((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (~((~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))) <=> ($false | (~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))))),
% 3.21/2.30 inference(monotonicity,[status(thm)],[243, 239, 238, 237])).
% 3.21/2.30 tff(245,plain,
% 3.21/2.30 (((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (~((~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))) <=> ((~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))),
% 3.21/2.30 inference(transitivity,[status(thm)],[244, 236])).
% 3.21/2.30 tff(246,plain,
% 3.21/2.30 (((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (~((~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))))) <=> ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))))),
% 3.21/2.30 inference(monotonicity,[status(thm)],[245])).
% 3.21/2.30 tff(247,plain,
% 3.21/2.30 (((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (~((~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))))) <=> ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))))),
% 3.21/2.31 inference(transitivity,[status(thm)],[246, 235])).
% 3.21/2.31 tff(248,plain,
% 3.21/2.31 ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | ((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)))) | (~((~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)) | (~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))) | (~((~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))))),
% 3.21/2.31 inference(quant_inst,[status(thm)],[])).
% 3.21/2.31 tff(249,plain,
% 3.21/2.31 ((~![VVar0: $i, VCtx0: $i, RESULT: $i] : ((~(vlookup(VVar0, VCtx0) = RESULT)) | (~((~(RESULT = vnoType)) | (~(VCtx0 = vempty)) | (~(VVar0 = tptp_fun_Vx_0(RESULT, VCtx0, VVar0))))) | (~((~(VVar0 = tptp_fun_Vx_3(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_2(RESULT, VCtx0, VVar0), tptp_fun_VTy_1(RESULT, VCtx0, VVar0), tptp_fun_VC_4(RESULT, VCtx0, VVar0)))) | (~(tptp_fun_Vx_3(RESULT, VCtx0, VVar0) = tptp_fun_Vy_2(RESULT, VCtx0, VVar0))) | (~(RESULT = vsomeType(tptp_fun_VTy_1(RESULT, VCtx0, VVar0)))))) | (~((tptp_fun_Vx_6(RESULT, VCtx0, VVar0) = tptp_fun_Vy_7(RESULT, VCtx0, VVar0)) | (~(VVar0 = tptp_fun_Vx_6(RESULT, VCtx0, VVar0))) | (~(VCtx0 = vbind(tptp_fun_Vy_7(RESULT, VCtx0, VVar0), tptp_fun_VTy_8(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))) | (~(RESULT = vlookup(tptp_fun_Vx_6(RESULT, VCtx0, VVar0), tptp_fun_VC_5(RESULT, VCtx0, VVar0)))))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vempty)) | (~(Vx!79 = tptp_fun_Vx_0(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vnoType)))) | (~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))),
% 3.21/2.31 inference(modus_ponens,[status(thm)],[248, 247])).
% 3.21/2.31 tff(250,plain,
% 3.21/2.31 ((~((~(Vx!79 = tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_8(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_7(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vlookup(tptp_fun_Vx_6(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_5(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))) | (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))))),
% 3.21/2.31 inference(unit_resolution,[status(thm)],[249, 234, 221])).
% 3.21/2.31 tff(251,plain,
% 3.21/2.31 (~((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))))),
% 3.21/2.31 inference(unit_resolution,[status(thm)],[250, 219])).
% 3.21/2.31 tff(252,plain,
% 3.21/2.31 (((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))),
% 3.21/2.31 inference(tautology,[status(thm)],[])).
% 3.21/2.31 tff(253,plain,
% 3.21/2.31 (vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))),
% 3.21/2.31 inference(unit_resolution,[status(thm)],[252, 251])).
% 3.21/2.31 tff(254,plain,
% 3.21/2.31 (vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77)),
% 3.21/2.31 inference(symmetry,[status(thm)],[253])).
% 3.21/2.31 tff(255,plain,
% 3.21/2.31 ((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))),
% 3.21/2.31 inference(tautology,[status(thm)],[])).
% 3.21/2.31 tff(256,plain,
% 3.21/2.31 ((~((~(vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)) = vbind(Vy!76, VS1!75, VC!77))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))))) | (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))))),
% 3.21/2.32 inference(unit_resolution,[status(thm)],[255, 254])).
% 3.21/2.32 tff(257,plain,
% 3.21/2.32 (~((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77)))),
% 3.21/2.32 inference(unit_resolution,[status(thm)],[256, 22])).
% 3.21/2.32 tff(258,plain,
% 3.21/2.32 (((~(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)) | (~(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VS1!75)) | (~(tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = VC!77))) | (tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76)),
% 3.21/2.32 inference(tautology,[status(thm)],[])).
% 3.21/2.32 tff(259,plain,
% 3.21/2.32 (tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = Vy!76),
% 3.21/2.32 inference(unit_resolution,[status(thm)],[258, 257])).
% 3.21/2.32 tff(260,plain,
% 3.21/2.32 (((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))),
% 3.21/2.32 inference(tautology,[status(thm)],[])).
% 3.21/2.32 tff(261,plain,
% 3.21/2.32 (tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)),
% 3.21/2.32 inference(unit_resolution,[status(thm)],[260, 251])).
% 3.21/2.32 tff(262,plain,
% 3.21/2.32 (((~(vbind(Vy!76, VS1!75, VC!77) = vbind(tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79), tptp_fun_VC_4(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)) = vsomeType(tptp_fun_VTy_1(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (~(Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))) | (~(tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79) = tptp_fun_Vy_2(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)))) | (Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79))),
% 3.21/2.32 inference(tautology,[status(thm)],[])).
% 3.21/2.32 tff(263,plain,
% 3.21/2.32 (Vx!79 = tptp_fun_Vx_3(vlookup(Vx!79, vbind(Vy!76, VS1!75, VC!77)), vbind(Vy!76, VS1!75, VC!77), Vx!79)),
% 3.21/2.32 inference(unit_resolution,[status(thm)],[262, 251])).
% 3.21/2.32 tff(264,plain,
% 3.21/2.32 (Vx!79 = Vy!76),
% 3.21/2.32 inference(transitivity,[status(thm)],[263, 261, 259])).
% 3.21/2.32 tff(265,plain,
% 3.21/2.32 ($false),
% 3.21/2.32 inference(unit_resolution,[status(thm)],[179, 264])).
% 3.21/2.32 % SZS output end Proof
%------------------------------------------------------------------------------