%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC206+1 : TPTP v9.0.0. Released v2.4.0.
% 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 05:30:30 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC206+1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:37:54 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(segmentP_type, type, (
% 0.20/0.48 segmentP: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_Y_47_type, type, (
% 0.20/0.48 tptp_fun_Y_47: $i)).
% 0.20/0.48 tff(nil_type, type, (
% 0.20/0.48 nil: $i)).
% 0.20/0.48 tff(tptp_fun_U_45_type, type, (
% 0.20/0.48 tptp_fun_U_45: $i)).
% 0.20/0.48 tff(neq_type, type, (
% 0.20/0.48 neq: ( $i * $i ) > $o)).
% 0.20/0.48 tff(ssList_type, type, (
% 0.20/0.48 ssList: $i > $o)).
% 0.20/0.48 tff(tptp_fun_V_46_type, type, (
% 0.20/0.48 tptp_fun_V_46: $i)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))))) & ssList(U!45) & (~neq(U!45, nil)))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))))) & (~neq(U!45, nil)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & (~neq(U!45, nil))) <=> ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))))) & ssList(U!45) & (~neq(U!45, nil)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & (~neq(U!45, nil)))) <=> (ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))))) & ssList(U!45) & (~neq(U!45, nil))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & (~neq(U!45, nil)))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))))) & (~neq(U!45, nil)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Y: $i] : ((~segmentP(U, Y)) | (~segmentP(V, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil)))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Y: $i] : ((~segmentP(U, Y)) | (~segmentP(V, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Y: $i] : ((~segmentP(U, Y)) | (~segmentP(V, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & neq(X, nil)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Y: $i] : ((~segmentP(U, Y)) | (~segmentP(V, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Y: $i] : ((~segmentP(U, Y)) | (~segmentP(V, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Y: $i] : ((~segmentP(U, Y)) | (~segmentP(V, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Y: $i] : ((~segmentP(U, Y)) | (~segmentP(V, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))))) & (~neq(U!45, nil))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (ssList(U!45)),
% 0.20/0.48 inference(and_elim,[status(thm)],[12])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.48 tff(22,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.48 tff(25,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[24])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[29, 26, 13])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (ssList(nil) <=> ssList(nil)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(32,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (ssList(nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[36, 33, 30])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (~neq(U!45, nil)),
% 0.20/0.48 inference(and_elim,[status(thm)],[12])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (U!45 = nil),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (nil = U!45),
% 0.20/0.48 inference(symmetry,[status(thm)],[41])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (segmentP(nil, Y!47) <=> segmentP(U!45, Y!47)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (segmentP(U!45, Y!47) <=> segmentP(nil, Y!47)),
% 0.20/0.48 inference(symmetry,[status(thm)],[43])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (neq(V!46, nil)),
% 0.20/0.48 inference(and_elim,[status(thm)],[12])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 ((~neq(V!46, nil)) | (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[12])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (~((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))) | segmentP(U!45, Y!47)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (segmentP(U!45, Y!47)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (segmentP(nil, Y!47)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))) | ssList(Y!47)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (ssList(Y!47)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[51, 47])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[55, 26, 52])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V))))) | ((~ssList(nil)) | (~((Y!47 = nil) <=> neq(Y!47, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V))))) | (~ssList(nil)) | (~((Y!47 = nil) <=> neq(Y!47, nil))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V))))) | ((~ssList(nil)) | (~((Y!47 = nil) <=> neq(Y!47, nil))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (~((Y!47 = V) <=> neq(Y!47, V))))) | (~ssList(nil)) | (~((Y!47 = nil) <=> neq(Y!47, nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (~((Y!47 = nil) <=> neq(Y!47, nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[59, 33, 56])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 (((~segmentP(U!45, Y!47)) | (~segmentP(V!46, Y!47)) | (~neq(Y!47, nil)) | (~ssList(Y!47))) | neq(Y!47, nil)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (neq(Y!47, nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[61, 47])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (((Y!47 = nil) <=> neq(Y!47, nil)) | (~(Y!47 = nil)) | (~neq(Y!47, nil))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (((Y!47 = nil) <=> neq(Y!47, nil)) | (~(Y!47 = nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 (~(Y!47 = nil)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[64, 60])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.48 tff(76,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.48 tff(79,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[78])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (((~ssList(Y!47)) | ![V: $i] : ((Y!47 = V) | (~segmentP(Y!47, V)) | (~ssList(V)) | (~segmentP(V, Y!47)))) <=> ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!47)) | ![V: $i] : ((Y!47 = V) | (~segmentP(Y!47, V)) | (~ssList(V)) | (~segmentP(V, Y!47))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!47)) | ![V: $i] : ((Y!47 = V) | (~segmentP(Y!47, V)) | (~ssList(V)) | (~segmentP(V, Y!47))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!47)) | ![V: $i] : ((Y!47 = V) | (~segmentP(Y!47, V)) | (~ssList(V)) | (~segmentP(V, Y!47))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[87, 81, 52])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.48 tff(94,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.48 tff(97,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(skolemize,[status(sab)],[96])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(Y!47)) | segmentP(Y!47, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(Y!47)) | segmentP(Y!47, nil))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(Y!47)) | segmentP(Y!47, nil))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(Y!47)) | segmentP(Y!47, nil)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (segmentP(Y!47, nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[101, 98, 52])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | ((~ssList(nil)) | (~segmentP(nil, Y!47)) | (Y!47 = nil) | (~segmentP(Y!47, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | (~ssList(nil)) | (~segmentP(nil, Y!47)) | (Y!47 = nil) | (~segmentP(Y!47, nil)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (((~ssList(nil)) | (Y!47 = nil) | (~segmentP(Y!47, nil)) | (~segmentP(nil, Y!47))) <=> ((~ssList(nil)) | (~segmentP(nil, Y!47)) | (Y!47 = nil) | (~segmentP(Y!47, nil)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | ((~ssList(nil)) | (Y!47 = nil) | (~segmentP(Y!47, nil)) | (~segmentP(nil, Y!47)))) <=> ((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | ((~ssList(nil)) | (~segmentP(nil, Y!47)) | (Y!47 = nil) | (~segmentP(Y!47, nil))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[104])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | ((~ssList(nil)) | (Y!47 = nil) | (~segmentP(Y!47, nil)) | (~segmentP(nil, Y!47)))) <=> ((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | (~ssList(nil)) | (~segmentP(nil, Y!47)) | (Y!47 = nil) | (~segmentP(Y!47, nil)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[105, 103])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | ((~ssList(nil)) | (Y!47 = nil) | (~segmentP(Y!47, nil)) | (~segmentP(nil, Y!47)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (Y!47 = V) | (~segmentP(Y!47, V)) | (~segmentP(V, Y!47)))) | (~ssList(nil)) | (~segmentP(nil, Y!47)) | (Y!47 = nil) | (~segmentP(Y!47, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((~segmentP(nil, Y!47)) | (Y!47 = nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[108, 33, 102, 88])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (~segmentP(nil, Y!47)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[109, 65])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[110, 50])).
% 0.20/0.49 % SZS output end Proof
% 0.20/0.49 % E exiting
%------------------------------------------------------------------------------