%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM129+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:01:06 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM129+1 : TPTP v9.0.0. Released v6.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:24:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(visFreeVar_type, type, (
% 0.20/0.41 visFreeVar: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_Ve_52_type, type, (
% 0.20/0.41 tptp_fun_Ve_52: $i)).
% 0.20/0.41 tff(vgensym_type, type, (
% 0.20/0.41 vgensym: $i > $i)).
% 0.20/0.41 tff(vapp_type, type, (
% 0.20/0.41 vapp: ( $i * $i ) > $i)).
% 0.20/0.41 tff(vvar_type, type, (
% 0.20/0.41 vvar: $i > $i)).
% 0.20/0.41 tff(tptp_fun_Vx_51_type, type, (
% 0.20/0.41 tptp_fun_Vx_51: $i)).
% 0.20/0.41 tff(tptp_fun_Ve1_50_type, type, (
% 0.20/0.41 tptp_fun_Ve1_50: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 ((~![Ve: $i, Vx: $i, Ve1: $i] : (~visFreeVar(vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))), Ve1))) <=> (~![Ve: $i, Vx: $i, Ve1: $i] : (~visFreeVar(vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))), Ve1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~![Ve: $i, Vx: $i, Vfresh: $i, Ve1: $i] : ((Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))) => (~visFreeVar(Vfresh, Ve1)))) <=> (~![Ve: $i, Vx: $i, Ve1: $i] : (~visFreeVar(vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))), Ve1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,axiom,(~![Ve: $i, Vx: $i, Vfresh: $i, Ve1: $i] : ((Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))) => (~visFreeVar(Vfresh, Ve1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''fresh-free-2'')).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (~![Ve: $i, Vx: $i, Ve1: $i] : (~visFreeVar(vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))), Ve1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~![Ve: $i, Vx: $i, Ve1: $i] : (~visFreeVar(vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))), Ve1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (~![Ve: $i, Vx: $i, Ve1: $i] : (~visFreeVar(vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))), Ve1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (~![Ve: $i, Vx: $i, Ve1: $i] : (~visFreeVar(vgensym(vapp(vapp(Ve, Ve1), vvar(Vx))), Ve1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.41 tff(8,plain,(
% 0.20/0.41 visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50)),
% 0.20/0.41 inference(skolemize,[status(sab)],[7])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (^[Ve1: $i, Vv: $i, Ve2: $i] : refl((~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (^[Ve1: $i, Vv: $i, Ve2: $i] : trans(monotonicity(monotonicity(rewrite((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) <=> (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))), (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) <=> ((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))))), rewrite((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))) <=> (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))), ((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))))), rewrite((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))), ((((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (^[VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : trans(monotonicity(rewrite((((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))) <=> (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))), ((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))))), rewrite((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0))))) <=> ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))), ((((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : ((~((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2)))) | (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(VVar0, VExp0)) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(VVar0, VExp0)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))))) <=> ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.41 tff(22,axiom,(![VVar0: $i, VExp0: $i, Ve1: $i, Vv: $i, Ve2: $i] : (((VVar0 = Vv) & (VExp0 = vapp(Ve1, Ve2))) => (((visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','isFreeVar2')).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.20/0.41 tff(25,plain,(
% 0.20/0.41 ![Ve1: $i, Vv: $i, Ve2: $i] : (((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2))) & (visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[25, 14])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 12])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51))))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 ((~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))))))) <=> (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 27])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51))))) | ((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 ((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (^[Ve: $i] : refl((~visFreeVar(vgensym(Ve), Ve)) <=> (~visFreeVar(vgensym(Ve), Ve)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve)) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve)) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![Vv: $i, Ve: $i] : (~visFreeVar(vgensym(Ve), Ve)) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))) <=> ![Vv: $i, Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(transitivity,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (^[Vv: $i, Ve: $i] : rewrite(((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.42 tff(46,axiom,(![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve)))), file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',''gensym-is-fresh'')).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[47, 39])).
% 0.20/0.42 tff(49,plain,(
% 0.20/0.42 ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(skolemize,[status(sab)],[48])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[49, 38])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 ((~![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[54, 36])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ((visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vvar(Vx!51))) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 ((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[58, 57, 10])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52)))) | ((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52)))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 ((~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))))))) <=> (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))))))) <=> ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[64, 62])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((~![Ve1: $i, Vv: $i, Ve2: $i] : (~((~((~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2))) | visFreeVar(Vv, vapp(Ve1, Ve2)))) | (~(visFreeVar(Vv, Ve1) | visFreeVar(Vv, Ve2) | (~visFreeVar(Vv, vapp(Ve1, Ve2)))))))) | (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50)))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve1!50) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), vapp(Ve!52, Ve1!50))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!50), vvar(Vx!51))), Ve!52)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[67, 27, 61])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------