TSTP Solution File: NUM835+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Sun Sep 18 13:12:10 EDT 2022
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM835+2 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 15:41:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.52 % SZS status Theorem
% 0.21/0.52 % SZS output start Proof
% 0.21/0.52 tff(vplus_type, type, (
% 0.21/0.52 vplus: ( $i * $i ) > $i)).
% 0.21/0.52 tff(tptp_fun_Vd157_0_type, type, (
% 0.21/0.52 tptp_fun_Vd157_0: ( $i * $i ) > $i)).
% 0.21/0.52 tff(vd151_type, type, (
% 0.21/0.52 vd151: $i)).
% 0.21/0.52 tff(vd165_type, type, (
% 0.21/0.52 vd165: $i)).
% 0.21/0.52 tff(tptp_fun_Vd155_1_type, type, (
% 0.21/0.52 tptp_fun_Vd155_1: ( $i * $i ) > $i)).
% 0.21/0.52 tff(m_type, type, (
% 0.21/0.52 m: $i > $o)).
% 0.21/0.52 tff(v1_type, type, (
% 0.21/0.52 v1: $i)).
% 0.21/0.52 tff(1,assumption,(vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))), introduced(assumption)).
% 0.21/0.52 tff(2,plain,
% 0.21/0.52 (^[Vd170: $i] : refl((~(vd151 = vplus(vd165, Vd170))) <=> (~(vd151 = vplus(vd165, Vd170))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(3,plain,
% 0.21/0.52 (![Vd170: $i] : (~(vd151 = vplus(vd165, Vd170))) <=> ![Vd170: $i] : (~(vd151 = vplus(vd165, Vd170)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.52 tff(4,plain,
% 0.21/0.52 ((~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))) <=> (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(5,axiom,(~((?[Vd180: $i] : (vd165 = vplus(vd151, Vd180)) | ?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))) | (vd151 = vd165))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''dis(case_distinction(conseq(110)))'')).
% 0.21/0.52 tff(6,plain,
% 0.21/0.52 (~(?[Vd180: $i] : (vd165 = vplus(vd151, Vd180)) | ?[Vd170: $i] : (vd151 = vplus(vd165, Vd170)))),
% 0.21/0.52 inference(or_elim,[status(thm)],[5])).
% 0.21/0.52 tff(7,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(or_elim,[status(thm)],[6])).
% 0.21/0.52 tff(8,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.21/0.52 tff(9,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.52 tff(10,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.21/0.52 tff(11,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.21/0.52 tff(12,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.21/0.52 tff(13,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.21/0.52 tff(14,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.21/0.52 tff(15,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.21/0.52 tff(16,plain,
% 0.21/0.52 (~?[Vd170: $i] : (vd151 = vplus(vd165, Vd170))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.21/0.52 tff(17,plain,
% 0.21/0.52 (^[Vd170: $i] : refl($oeq((~(vd151 = vplus(vd165, Vd170))), (~(vd151 = vplus(vd165, Vd170)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(18,plain,(
% 0.21/0.52 ![Vd170: $i] : (~(vd151 = vplus(vd165, Vd170)))),
% 0.21/0.52 inference(nnf-neg,[status(sab)],[16, 17])).
% 0.21/0.52 tff(19,plain,
% 0.21/0.52 (![Vd170: $i] : (~(vd151 = vplus(vd165, Vd170)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[18, 3])).
% 0.21/0.52 tff(20,plain,
% 0.21/0.52 ((~![Vd170: $i] : (~(vd151 = vplus(vd165, Vd170)))) | (~(vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(21,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[20, 19, 1])).
% 0.21/0.52 tff(22,plain,(~(vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(23,plain,
% 0.21/0.52 (^[Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : rewrite((~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155)))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(24,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.52 tff(25,plain,
% 0.21/0.52 (^[Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : refl((~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(26,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.52 tff(27,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : ![Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(pull_quant,[status(thm)],[])).
% 0.21/0.52 tff(28,plain,
% 0.21/0.52 (^[Vd151: $i, Vd152: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) <=> ?[Vd157: $i] : (~(~(Vd152 = vplus(Vd151, Vd157))))), pull_quant((~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))) <=> ?[Vd155: $i] : (~(~(Vd151 = vplus(Vd152, Vd155))))), (((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))) <=> ((Vd151 = Vd152) | ?[Vd157: $i] : (~(~(Vd152 = vplus(Vd151, Vd157)))) | ?[Vd155: $i] : (~(~(Vd151 = vplus(Vd152, Vd155))))))), pull_quant(((Vd151 = Vd152) | ?[Vd157: $i] : (~(~(Vd152 = vplus(Vd151, Vd157)))) | ?[Vd155: $i] : (~(~(Vd151 = vplus(Vd152, Vd155))))) <=> ?[Vd155: $i, Vd157: $i] : ((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))), (((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))) <=> ?[Vd155: $i, Vd157: $i] : ((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))), ((~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))) <=> (~?[Vd155: $i, Vd157: $i] : ((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))), pull_quant((~?[Vd155: $i, Vd157: $i] : ((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))) <=> ![Vd155: $i, Vd157: $i] : (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))), ((~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))) <=> ![Vd155: $i, Vd157: $i] : (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))), ((m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))) <=> (m(Vd152) | ![Vd155: $i, Vd157: $i] : (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))), pull_quant((m(Vd152) | ![Vd155: $i, Vd157: $i] : (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))) <=> ![Vd155: $i, Vd157: $i] : (m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))), ((m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))) <=> ![Vd155: $i, Vd157: $i] : (m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))), ((~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))) <=> (~![Vd155: $i, Vd157: $i] : (m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))), pull_quant((~![Vd155: $i, Vd157: $i] : (m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))) <=> ?[Vd155: $i, Vd157: $i] : (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))), ((~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))) <=> ?[Vd155: $i, Vd157: $i] : (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))), (((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))))) <=> ((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | ?[Vd155: $i, Vd157: $i] : (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))), pull_quant(((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | ?[Vd155: $i, Vd157: $i] : (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))) <=> ?[Vd155: $i, Vd157: $i] : ((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))), (((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))))) <=> ?[Vd155: $i, Vd157: $i] : ((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))), ((~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> (~?[Vd155: $i, Vd157: $i] : ((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))))), pull_quant((~?[Vd155: $i, Vd157: $i] : ((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))), ((~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(29,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i] : ![Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.52 tff(30,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[29, 27])).
% 0.21/0.52 tff(31,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[30, 26])).
% 0.21/0.52 tff(32,plain,
% 0.21/0.52 (^[Vd151: $i, Vd152: $i] : rewrite((~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(33,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.52 tff(34,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))) <=> ![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[33, 31])).
% 0.21/0.52 tff(35,plain,
% 0.21/0.52 (^[Vd151: $i, Vd152: $i] : trans(monotonicity(rewrite(((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) <=> ((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))), rewrite((m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152)))) <=> (m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))), ((((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152))))) <=> (((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))))), rewrite((((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155)))))))) <=> (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))))))), ((((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152))))) <=> (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(36,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152))))) <=> ![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.52 tff(37,plain,
% 0.21/0.52 (^[Vd151: $i, Vd152: $i] : rewrite((((~m(Vd152)) | ((Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))) | (Vd151 = Vd152))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152))))) <=> (((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(38,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (((~m(Vd152)) | ((Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))) | (Vd151 = Vd152))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152))))) <=> ![Vd151: $i, Vd152: $i] : (((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.52 tff(39,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (m(Vd152) <=> (?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155)) | (Vd151 = Vd152))) <=> ![Vd151: $i, Vd152: $i] : (m(Vd152) <=> (?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155)) | (Vd151 = Vd152)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(40,plain,
% 0.21/0.52 (^[Vd151: $i, Vd152: $i] : rewrite((m(Vd152) <=> (((Vd151 = Vd152) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155))) | ?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)))) <=> (m(Vd152) <=> (?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155)) | (Vd151 = Vd152))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(41,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (m(Vd152) <=> (((Vd151 = Vd152) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155))) | ?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)))) <=> ![Vd151: $i, Vd152: $i] : (m(Vd152) <=> (?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155)) | (Vd151 = Vd152)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.52 tff(42,axiom,(![Vd151: $i, Vd152: $i] : (m(Vd152) <=> (((Vd151 = Vd152) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155))) | ?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''def(cond(conseq(105), 0), 1)'')).
% 0.21/0.52 tff(43,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (m(Vd152) <=> (?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155)) | (Vd151 = Vd152)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.52 tff(44,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (m(Vd152) <=> (?[Vd157: $i] : (Vd152 = vplus(Vd151, Vd157)) | ?[Vd155: $i] : (Vd151 = vplus(Vd152, Vd155)) | (Vd151 = Vd152)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.21/0.52 tff(45,plain,(
% 0.21/0.52 ![Vd151: $i, Vd152: $i] : (((~m(Vd152)) | ((Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))) | (Vd151 = Vd152))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152)))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[44])).
% 0.21/0.52 tff(46,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151)))) & (m(Vd152) | (![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157))) & ![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))) & (~(Vd151 = Vd152)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.21/0.52 tff(47,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~![Vd157: $i] : (~(Vd152 = vplus(Vd151, Vd157)))) | (~![Vd155: $i] : (~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.21/0.52 tff(48,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (~(~(Vd152 = vplus(Vd151, Vd157)))) | (~(~(Vd151 = vplus(Vd152, Vd155))))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[47, 34])).
% 0.21/0.52 tff(49,plain,
% 0.21/0.52 (![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[48, 24])).
% 0.21/0.52 tff(50,plain,
% 0.21/0.52 (((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1))))))))) <=> ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1)))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(51,plain,
% 0.21/0.52 ((~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd165 = vplus(vd151, v1)) | (vd151 = vplus(vd165, vd165)))))))) <=> (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(52,plain,
% 0.21/0.52 (((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd165 = vplus(vd151, v1)) | (vd151 = vplus(vd165, vd165))))))))) <=> ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1)))))))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.52 tff(53,plain,
% 0.21/0.52 (((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd165 = vplus(vd151, v1)) | (vd151 = vplus(vd165, vd165))))))))) <=> ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1)))))))))),
% 0.21/0.52 inference(transitivity,[status(thm)],[52, 50])).
% 0.21/0.52 tff(54,plain,
% 0.21/0.52 ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd165 = vplus(vd151, v1)) | (vd151 = vplus(vd165, vd165))))))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(55,plain,
% 0.21/0.52 ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1))))))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.52 tff(56,plain,
% 0.21/0.52 (~((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1)))))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[55, 49])).
% 0.21/0.52 tff(57,plain,
% 0.21/0.52 (((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (~(m(vd165) | (~((vd151 = vd165) | (vd151 = vplus(vd165, vd165)) | (vd165 = vplus(vd151, v1))))))) | ((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(58,plain,
% 0.21/0.53 ((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.21/0.53 tff(59,plain,
% 0.21/0.53 (((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | m(vd165)) <=> ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | m(vd165))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(60,plain,
% 0.21/0.53 ((~(~m(vd165))) <=> m(vd165)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(61,plain,
% 0.21/0.53 (($false | (~m(vd165))) <=> (~m(vd165))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(62,plain,
% 0.21/0.53 ((~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165)))))) <=> (~m(vd165))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(63,plain,
% 0.21/0.53 ((~$true) <=> $false),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(64,plain,
% 0.21/0.53 (($true | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165)))) <=> $true),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(65,plain,
% 0.21/0.53 ((vd165 = vd165) <=> $true),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(66,plain,
% 0.21/0.53 (((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165)))) <=> ($true | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.53 tff(67,plain,
% 0.21/0.53 (((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165)))) <=> $true),
% 0.21/0.53 inference(transitivity,[status(thm)],[66, 64])).
% 0.21/0.53 tff(68,plain,
% 0.21/0.53 ((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) <=> (~$true)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.53 tff(69,plain,
% 0.21/0.53 ((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) <=> $false),
% 0.21/0.53 inference(transitivity,[status(thm)],[68, 63])).
% 0.21/0.53 tff(70,plain,
% 0.21/0.53 (((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) | (~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165))))))) <=> ($false | (~m(vd165)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[69, 62])).
% 0.21/0.53 tff(71,plain,
% 0.21/0.53 (((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) | (~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165))))))) <=> (~m(vd165))),
% 0.21/0.53 inference(transitivity,[status(thm)],[70, 61])).
% 0.21/0.53 tff(72,plain,
% 0.21/0.53 ((~((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) | (~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165)))))))) <=> (~(~m(vd165)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[71])).
% 0.21/0.53 tff(73,plain,
% 0.21/0.53 ((~((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) | (~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165)))))))) <=> m(vd165)),
% 0.21/0.53 inference(transitivity,[status(thm)],[72, 60])).
% 0.21/0.53 tff(74,plain,
% 0.21/0.53 (((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) | (~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165))))))))) <=> ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | m(vd165))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.53 tff(75,plain,
% 0.21/0.53 (((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) | (~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165))))))))) <=> ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | m(vd165))),
% 0.21/0.53 inference(transitivity,[status(thm)],[74, 59])).
% 0.21/0.53 tff(76,plain,
% 0.21/0.53 ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | (~((~((vd165 = vd165) | (~m(vd165)) | (vd165 = vplus(vd165, tptp_fun_Vd157_0(vd165, vd165))) | (vd165 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd165))))) | (~(m(vd165) | (~((vd165 = vd165) | (vd165 = vplus(vd165, vd165)) | (vd165 = vplus(vd165, vd165))))))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(77,plain,
% 0.21/0.53 ((~![Vd151: $i, Vd152: $i, Vd155: $i, Vd157: $i] : (~((~((Vd151 = Vd152) | (~m(Vd152)) | (Vd152 = vplus(Vd151, tptp_fun_Vd157_0(Vd152, Vd151))) | (Vd151 = vplus(Vd152, tptp_fun_Vd155_1(Vd152, Vd151))))) | (~(m(Vd152) | (~((Vd151 = Vd152) | (Vd152 = vplus(Vd151, Vd157)) | (Vd151 = vplus(Vd152, Vd155))))))))) | m(vd165)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.53 tff(78,plain,
% 0.21/0.53 (m(vd165)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[77, 49])).
% 0.21/0.53 tff(79,plain,
% 0.21/0.53 ((~(vd151 = vd165)) <=> (~(vd151 = vd165))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(80,plain,
% 0.21/0.53 (~(vd151 = vd165)),
% 0.21/0.53 inference(or_elim,[status(thm)],[5])).
% 0.21/0.53 tff(81,plain,
% 0.21/0.53 (~(vd151 = vd165)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.53 tff(82,plain,
% 0.21/0.53 ((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151)))),
% 0.21/0.53 inference(tautology,[status(thm)],[])).
% 0.21/0.53 tff(83,plain,
% 0.21/0.53 ((~((vd151 = vd165) | (~m(vd165)) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151))))) | (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[82, 81, 78])).
% 0.21/0.53 tff(84,plain,
% 0.21/0.53 ((vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))) | (vd151 = vplus(vd165, tptp_fun_Vd155_1(vd165, vd151)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[83, 58])).
% 0.21/0.53 tff(85,plain,
% 0.21/0.53 (vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[84, 22])).
% 0.21/0.53 tff(86,plain,
% 0.21/0.53 (^[Vd180: $i] : refl((~(vd165 = vplus(vd151, Vd180))) <=> (~(vd165 = vplus(vd151, Vd180))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(87,plain,
% 0.21/0.53 (![Vd180: $i] : (~(vd165 = vplus(vd151, Vd180))) <=> ![Vd180: $i] : (~(vd165 = vplus(vd151, Vd180)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.53 tff(88,plain,
% 0.21/0.53 ((~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))) <=> (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(89,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(or_elim,[status(thm)],[6])).
% 0.21/0.53 tff(90,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.53 tff(91,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[90, 88])).
% 0.21/0.53 tff(92,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.21/0.53 tff(93,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.53 tff(94,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[93, 88])).
% 0.21/0.53 tff(95,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[94, 88])).
% 0.21/0.53 tff(96,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.21/0.53 tff(97,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[96, 88])).
% 0.21/0.53 tff(98,plain,
% 0.21/0.53 (~?[Vd180: $i] : (vd165 = vplus(vd151, Vd180))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[97, 88])).
% 0.21/0.53 tff(99,plain,
% 0.21/0.53 (^[Vd180: $i] : refl($oeq((~(vd165 = vplus(vd151, Vd180))), (~(vd165 = vplus(vd151, Vd180)))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(100,plain,(
% 0.21/0.53 ![Vd180: $i] : (~(vd165 = vplus(vd151, Vd180)))),
% 0.21/0.53 inference(nnf-neg,[status(sab)],[98, 99])).
% 0.21/0.53 tff(101,plain,
% 0.21/0.53 (![Vd180: $i] : (~(vd165 = vplus(vd151, Vd180)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[100, 87])).
% 0.21/0.53 tff(102,plain,
% 0.21/0.53 ((~![Vd180: $i] : (~(vd165 = vplus(vd151, Vd180)))) | (~(vd165 = vplus(vd151, tptp_fun_Vd157_0(vd165, vd151))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(103,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[102, 101, 85])).
% 0.21/0.53 % SZS output end Proof
%------------------------------------------------------------------------------