%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM128+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.24s 0.45s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : COM128+1 : TPTP v9.0.0. Released v6.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Jun 19 12:24:56 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.45 % SZS status Theorem
% 0.24/0.45 % SZS output start Proof
% 0.24/0.45 tff(visFreeVar_type, type, (
% 0.24/0.45 visFreeVar: ( $i * $i ) > $o)).
% 0.24/0.45 tff(vvar_type, type, (
% 0.24/0.45 vvar: $i > $i)).
% 0.24/0.45 tff(vgensym_type, type, (
% 0.24/0.45 vgensym: $i > $i)).
% 0.24/0.45 tff(vapp_type, type, (
% 0.24/0.45 vapp: ( $i * $i ) > $i)).
% 0.24/0.45 tff(tptp_fun_Vfresh_50_type, type, (
% 0.24/0.45 tptp_fun_Vfresh_50: $i)).
% 0.24/0.45 tff(tptp_fun_Ve1_51_type, type, (
% 0.24/0.45 tptp_fun_Ve1_51: $i)).
% 0.24/0.45 tff(tptp_fun_Ve_52_type, type, (
% 0.24/0.45 tptp_fun_Ve_52: $i)).
% 0.24/0.45 tff(1,plain,
% 0.24/0.45 ((~![Ve: $i, Ve1: $i, Vfresh: $i] : (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vfresh)))))) <=> (~![Ve: $i, Ve1: $i, Vfresh: $i] : (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vfresh))))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(2,plain,
% 0.24/0.45 ((~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))) => (~(Vx = Vfresh)))) <=> (~![Ve: $i, Ve1: $i, Vfresh: $i] : (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vfresh))))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(3,axiom,(~![Ve: $i, Ve1: $i, Vx: $i, Vfresh: $i] : ((Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vx)))) => (~(Vx = Vfresh)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''fresh-unequal-var-3'')).
% 0.24/0.45 tff(4,plain,
% 0.24/0.45 (~![Ve: $i, Ve1: $i, Vfresh: $i] : (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vfresh)))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.24/0.45 tff(5,plain,
% 0.24/0.45 (~![Ve: $i, Ve1: $i, Vfresh: $i] : (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vfresh)))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.24/0.45 tff(6,plain,
% 0.24/0.45 (~![Ve: $i, Ve1: $i, Vfresh: $i] : (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vfresh)))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.24/0.45 tff(7,plain,
% 0.24/0.45 (~![Ve: $i, Ve1: $i, Vfresh: $i] : (~(Vfresh = vgensym(vapp(vapp(Ve, Ve1), vvar(Vfresh)))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.24/0.45 tff(8,plain,(
% 0.24/0.45 Vfresh!50 = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))),
% 0.24/0.45 inference(skolemize,[status(sab)],[7])).
% 0.24/0.45 tff(9,plain,
% 0.24/0.45 (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = Vfresh!50),
% 0.24/0.45 inference(symmetry,[status(thm)],[8])).
% 0.24/0.45 tff(10,plain,
% 0.24/0.45 (vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) = vvar(Vfresh!50)),
% 0.24/0.45 inference(monotonicity,[status(thm)],[9])).
% 0.24/0.45 tff(11,plain,
% 0.24/0.45 (visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) <=> visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[10])).
% 0.24/0.45 tff(12,plain,
% 0.24/0.45 (visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)) <=> visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))),
% 0.24/0.45 inference(symmetry,[status(thm)],[11])).
% 0.24/0.45 tff(13,plain,
% 0.24/0.45 ((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))) <=> (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[12])).
% 0.24/0.45 tff(14,plain,
% 0.24/0.45 (^[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))))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(15,plain,
% 0.24/0.45 (![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)))))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[14])).
% 0.24/0.45 tff(16,plain,
% 0.24/0.45 (^[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)))))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(17,plain,
% 0.24/0.45 (![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)))))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.24/0.45 tff(18,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(19,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.24/0.45 tff(20,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.24/0.45 tff(21,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(transitivity,[status(thm)],[20, 19])).
% 0.24/0.45 tff(22,plain,
% 0.24/0.45 (^[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)))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(23,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[22])).
% 0.24/0.45 tff(24,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(transitivity,[status(thm)],[23, 21])).
% 0.24/0.45 tff(25,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/sandbox/benchmark/Axioms/COM001+0.ax','isFreeVar2')).
% 0.24/0.45 tff(26,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.24/0.45 tff(27,plain,
% 0.24/0.45 (![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)))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.24/0.45 tff(28,plain,(
% 0.24/0.45 ![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)))))),
% 0.24/0.45 inference(skolemize,[status(sab)],[27])).
% 0.24/0.45 tff(29,plain,
% 0.24/0.45 (![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)))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.24/0.45 tff(30,plain,
% 0.24/0.45 (![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)))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[29, 15])).
% 0.24/0.45 tff(31,plain,
% 0.24/0.45 (((~![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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(32,plain,
% 0.24/0.45 ((~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))))) <=> (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(33,plain,
% 0.24/0.45 (((~![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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))))))),
% 0.24/0.46 inference(monotonicity,[status(thm)],[32])).
% 0.24/0.46 tff(34,plain,
% 0.24/0.46 (((~![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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))))))),
% 0.24/0.46 inference(transitivity,[status(thm)],[33, 31])).
% 0.24/0.46 tff(35,plain,
% 0.24/0.46 ((~![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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(36,plain,
% 0.24/0.46 ((~![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!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.24/0.46 tff(37,plain,
% 0.24/0.46 (~((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[36, 30])).
% 0.24/0.46 tff(38,plain,
% 0.24/0.46 (((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))))) | ((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))),
% 0.24/0.46 inference(tautology,[status(thm)],[])).
% 0.24/0.46 tff(39,plain,
% 0.24/0.46 ((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.24/0.46 tff(40,plain,
% 0.24/0.46 (^[Ve: $i] : refl((~visFreeVar(vgensym(Ve), Ve)) <=> (~visFreeVar(vgensym(Ve), Ve)))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(41,plain,
% 0.24/0.46 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve)) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[40])).
% 0.24/0.46 tff(42,plain,
% 0.24/0.46 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve)) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(43,plain,
% 0.24/0.46 (![Vv: $i, Ve: $i] : (~visFreeVar(vgensym(Ve), Ve)) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.24/0.46 tff(44,plain,
% 0.24/0.46 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))) <=> ![Vv: $i, Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.24/0.46 tff(45,plain,
% 0.24/0.46 (![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(transitivity,[status(thm)],[44, 43])).
% 0.24/0.46 tff(46,plain,
% 0.24/0.46 (^[Vv: $i, Ve: $i] : rewrite(((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(47,plain,
% 0.24/0.46 (![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ![Vv: $i, Ve: $i] : ((~visFreeVar(Vv, Ve)) | (~(vgensym(Ve) = Vv)))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[46])).
% 0.24/0.46 tff(48,plain,
% 0.24/0.46 (![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve))) <=> ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(transitivity,[status(thm)],[47, 45])).
% 0.24/0.46 tff(49,axiom,(![Vv: $i, Ve: $i] : ((vgensym(Ve) = Vv) => (~visFreeVar(Vv, Ve)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''gensym-is-fresh'')).
% 0.24/0.46 tff(50,plain,
% 0.24/0.46 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.24/0.46 tff(51,plain,
% 0.24/0.46 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.24/0.46 tff(52,plain,(
% 0.24/0.46 ![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(skolemize,[status(sab)],[51])).
% 0.24/0.46 tff(53,plain,
% 0.24/0.46 (![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[52, 41])).
% 0.24/0.46 tff(54,plain,
% 0.24/0.46 ((~![Ve: $i] : (~visFreeVar(vgensym(Ve), Ve))) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(55,plain,
% 0.24/0.46 (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.24/0.46 tff(56,plain,
% 0.24/0.46 ((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))),
% 0.24/0.46 inference(tautology,[status(thm)],[])).
% 0.24/0.46 tff(57,plain,
% 0.24/0.46 ((~((~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.24/0.46 tff(58,plain,
% 0.24/0.46 (~(visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[57, 39])).
% 0.24/0.46 tff(59,plain,
% 0.24/0.46 ((visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vapp(Ve!52, Ve1!51)) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))) | (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50)))),
% 0.24/0.46 inference(tautology,[status(thm)],[])).
% 0.24/0.46 tff(60,plain,
% 0.24/0.46 (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(Vfresh!50))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.24/0.46 tff(61,plain,
% 0.24/0.46 (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[60, 13])).
% 0.24/0.46 tff(62,plain,
% 0.24/0.46 (^[Vx: $i, Vv: $i] : refl((~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))) <=> (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(63,plain,
% 0.24/0.46 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))) <=> ![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[62])).
% 0.24/0.46 tff(64,plain,
% 0.24/0.46 (^[Vx: $i, Vv: $i] : rewrite((((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(65,plain,
% 0.24/0.46 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[64])).
% 0.24/0.46 tff(66,plain,
% 0.24/0.46 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(67,plain,
% 0.24/0.46 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.24/0.46 tff(68,plain,
% 0.24/0.46 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.24/0.46 tff(69,plain,
% 0.24/0.46 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(transitivity,[status(thm)],[68, 67])).
% 0.24/0.46 tff(70,plain,
% 0.24/0.46 (^[VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : trans(monotonicity(rewrite((((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))) <=> (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))))), rewrite((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))), ((((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))))),
% 0.24/0.46 inference(bind,[status(th)],[])).
% 0.24/0.46 tff(71,plain,
% 0.24/0.46 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : ((~((VVar0 = Vv) & (VExp0 = vvar(Vx)))) | (((~(Vx = Vv)) | visFreeVar(VVar0, VExp0)) & ((~visFreeVar(VVar0, VExp0)) | (Vx = Vv))))),
% 0.24/0.46 inference(quant_intro,[status(thm)],[70])).
% 0.24/0.46 tff(72,plain,
% 0.24/0.46 (![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv)))) <=> ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(transitivity,[status(thm)],[71, 69])).
% 0.24/0.46 tff(73,axiom,(![VVar0: $i, VExp0: $i, Vx: $i, Vv: $i] : (((VVar0 = Vv) & (VExp0 = vvar(Vx))) => (((Vx = Vv) => visFreeVar(VVar0, VExp0)) & (visFreeVar(VVar0, VExp0) => (Vx = Vv))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isFreeVar0')).
% 0.24/0.46 tff(74,plain,
% 0.24/0.46 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.24/0.46 tff(75,plain,
% 0.24/0.46 (![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[74, 66])).
% 0.24/0.46 tff(76,plain,(
% 0.24/0.46 ![Vx: $i, Vv: $i] : (((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx))) & ((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))),
% 0.24/0.46 inference(skolemize,[status(sab)],[75])).
% 0.24/0.46 tff(77,plain,
% 0.24/0.46 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[76, 65])).
% 0.24/0.46 tff(78,plain,
% 0.24/0.46 (![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[77, 63])).
% 0.24/0.47 tff(79,plain,
% 0.24/0.47 (((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) <=> ((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(80,plain,
% 0.24/0.47 ((~(~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) <=> visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(81,plain,
% 0.24/0.47 (((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | $false) <=> (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(82,plain,
% 0.24/0.47 ((~$true) <=> $false),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(83,plain,
% 0.24/0.47 (((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | $true) <=> $true),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(84,plain,
% 0.24/0.47 ((vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))) <=> $true),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(85,plain,
% 0.24/0.47 (((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) <=> ((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | $true)),
% 0.24/0.47 inference(monotonicity,[status(thm)],[84])).
% 0.24/0.47 tff(86,plain,
% 0.24/0.47 (((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) <=> $true),
% 0.24/0.47 inference(transitivity,[status(thm)],[85, 83])).
% 0.24/0.47 tff(87,plain,
% 0.24/0.47 ((~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) <=> (~$true)),
% 0.24/0.47 inference(monotonicity,[status(thm)],[86])).
% 0.24/0.47 tff(88,plain,
% 0.24/0.47 ((~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) <=> $false),
% 0.24/0.47 inference(transitivity,[status(thm)],[87, 82])).
% 0.24/0.47 tff(89,plain,
% 0.24/0.47 ((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) <=> (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(90,plain,
% 0.24/0.47 (((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) <=> ((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | $false)),
% 0.24/0.47 inference(monotonicity,[status(thm)],[89, 88])).
% 0.24/0.47 tff(91,plain,
% 0.24/0.47 (((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) <=> (~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))),
% 0.24/0.47 inference(transitivity,[status(thm)],[90, 81])).
% 0.24/0.47 tff(92,plain,
% 0.24/0.47 ((~((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))))) <=> (~(~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))))),
% 0.24/0.47 inference(monotonicity,[status(thm)],[91])).
% 0.24/0.47 tff(93,plain,
% 0.24/0.47 ((~((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))))) <=> visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))),
% 0.24/0.47 inference(transitivity,[status(thm)],[92, 80])).
% 0.24/0.47 tff(94,plain,
% 0.24/0.47 (((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | (~((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))))) <=> ((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))),
% 0.24/0.47 inference(monotonicity,[status(thm)],[93])).
% 0.24/0.47 tff(95,plain,
% 0.24/0.47 (((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | (~((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))))) <=> ((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))),
% 0.24/0.47 inference(transitivity,[status(thm)],[94, 79])).
% 0.24/0.48 tff(96,plain,
% 0.24/0.48 ((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | (~((~((~(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))) | (~((~visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))) | (vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))) = vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))))))))),
% 0.24/0.48 inference(quant_inst,[status(thm)],[])).
% 0.24/0.48 tff(97,plain,
% 0.24/0.48 ((~![Vx: $i, Vv: $i] : (~((~((~(Vx = Vv)) | visFreeVar(Vv, vvar(Vx)))) | (~((~visFreeVar(Vv, vvar(Vx))) | (Vx = Vv)))))) | visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.24/0.48 tff(98,plain,
% 0.24/0.48 (visFreeVar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50))), vvar(vgensym(vapp(vapp(Ve!52, Ve1!51), vvar(Vfresh!50)))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[97, 78])).
% 0.24/0.48 tff(99,plain,
% 0.24/0.48 ($false),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[98, 61])).
% 0.24/0.48 % SZS output end Proof
% 0.24/0.48 % E exiting
%------------------------------------------------------------------------------