%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC019+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:29:56 AM UTC 2025
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.13 % Problem : SWC019+1 : TPTP v9.0.0. Released v2.4.0.
% 0.14/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 08:00:35 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(tptp_fun_U_45_type, type, (
% 0.21/0.49 tptp_fun_U_45: $i)).
% 0.21/0.49 tff(nil_type, type, (
% 0.21/0.49 nil: $i)).
% 0.21/0.49 tff(neq_type, type, (
% 0.21/0.49 neq: ( $i * $i ) > $o)).
% 0.21/0.49 tff(ssList_type, type, (
% 0.21/0.49 ssList: $i > $o)).
% 0.21/0.49 tff(frontsegP_type, type, (
% 0.21/0.49 frontsegP: ( $i * $i ) > $o)).
% 0.21/0.49 tff(1,plain,
% 0.21/0.49 (((~(nil = U!45)) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y)))) <=> ((~(nil = U!45)) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 ((~![U: $i] : ((nil = U) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(U, Y)))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(U, Y))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | ((nil = V) & (nil = U)))))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(U, Y))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & frontsegP(V, Y)) & frontsegP(U, Y))) | ((nil = V) & (nil = U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(U, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(U, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(U, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 (~![U: $i] : ((nil = U) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & frontsegP(U, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 ((~(nil = U!45)) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (ssList(U!45)),
% 0.21/0.49 inference(and_elim,[status(thm)],[9])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (^[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))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (![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)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (^[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))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 (![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)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (![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)))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[14, 12])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 (![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)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (^[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)))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (![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)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.49 tff(19,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.21/0.49 tff(22,plain,(
% 0.21/0.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[21])).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 (((~![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)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 ((~![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)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(26,plain,
% 0.21/0.49 ((~![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))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.49 tff(27,plain,
% 0.21/0.49 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.21/0.49 tff(28,plain,
% 0.21/0.49 (ssList(nil) <=> ssList(nil)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(29,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.21/0.49 tff(30,plain,
% 0.21/0.49 (ssList(nil)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.49 tff(31,plain,
% 0.21/0.49 (((~![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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(32,plain,
% 0.21/0.49 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(33,plain,
% 0.21/0.49 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.49 tff(34,plain,
% 0.21/0.49 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[33, 30, 27])).
% 0.21/0.49 tff(35,plain,
% 0.21/0.49 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(36,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.49 tff(37,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(38,plain,
% 0.21/0.49 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(39,plain,
% 0.21/0.49 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.49 tff(40,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax42')).
% 0.21/0.49 tff(41,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.49 tff(43,plain,(
% 0.21/0.49 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.21/0.49 inference(skolemize,[status(sab)],[42])).
% 0.21/0.49 tff(44,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.21/0.49 tff(45,plain,
% 0.21/0.49 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (frontsegP(U!45, U!45)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[47, 44, 10])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y))))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))), ((~(ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & frontsegP(U!45, Y)))),
% 0.21/0.49 inference(and_elim,[status(thm)],[9])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(U!45, U!45)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(U!45, U!45)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(U!45, U!45)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~frontsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~frontsegP(U!45, U!45))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 ((~neq(U!45, nil)) | (~frontsegP(U!45, U!45))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[58, 10, 55])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (~neq(U!45, nil)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[59, 48])).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (U!45 = nil),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[62, 34])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 (nil = U!45),
% 0.21/0.50 inference(symmetry,[status(thm)],[63])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 (~(nil = U!45)),
% 0.21/0.50 inference(and_elim,[status(thm)],[9])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------