%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC217+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:30:32 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
% 0.07/0.12 % Problem : SWC217+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:38:48 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 tff(nil_type, type, (
% 0.21/0.49 nil: $i)).
% 0.21/0.49 tff(cons_type, type, (
% 0.21/0.49 cons: ( $i * $i ) > $i)).
% 0.21/0.49 tff(tptp_fun_Y_47_type, type, (
% 0.21/0.49 tptp_fun_Y_47: $i)).
% 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(ssItem_type, type, (
% 0.21/0.49 ssItem: $i > $o)).
% 0.21/0.49 tff(memberP_type, type, (
% 0.21/0.49 memberP: ( $i * $i ) > $o)).
% 0.21/0.49 tff(tptp_fun_V_46_type, type, (
% 0.21/0.49 tptp_fun_V_46: $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(1,plain,
% 0.21/0.49 ((U!45 = nil) <=> (nil = U!45)),
% 0.21/0.49 inference(commutativity,[status(thm)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 (((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)) <=> ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,plain,
% 0.21/0.49 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~neq(V!46, nil))) & ssList(U!45) & (~neq(U!45, nil)) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & (~neq(U!45, nil)) & neq(V!46, nil))),
% 0.21/0.49 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(7,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))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(8,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] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & neq(V, nil)) | (~ssList(U)) | neq(U, nil) | (~neq(V, nil))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))) & (~neq(U!45, nil)) & neq(V!46, nil)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 (neq(V!46, nil)),
% 0.21/0.49 inference(and_elim,[status(thm)],[13])).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 ((~neq(V!46, nil)) | (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))))),
% 0.21/0.49 inference(and_elim,[status(thm)],[13])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 (((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))) | (cons(Y!47, nil) = U!45)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (cons(Y!47, nil) = U!45),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 ((cons(Y!47, nil) = nil) <=> (U!45 = nil)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 ((cons(Y!47, nil) = nil) <=> (nil = U!45)),
% 0.21/0.49 inference(transitivity,[status(thm)],[19, 1])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 ((nil = U!45) <=> (cons(Y!47, nil) = nil)),
% 0.21/0.49 inference(symmetry,[status(thm)],[20])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 (ssList(U!45)),
% 0.21/0.49 inference(and_elim,[status(thm)],[13])).
% 0.21/0.49 tff(23,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(24,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)],[23])).
% 0.21/0.49 tff(25,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(26,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)],[25])).
% 0.21/0.49 tff(27,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)],[26, 24])).
% 0.21/0.49 tff(28,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(29,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(30,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)],[29])).
% 0.21/0.49 tff(31,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(32,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)],[31, 30])).
% 0.21/0.49 tff(33,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)],[32, 28])).
% 0.21/0.49 tff(34,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)],[33])).
% 0.21/0.49 tff(35,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)],[34, 27])).
% 0.21/0.49 tff(36,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(37,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(38,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)],[37, 36])).
% 0.21/0.49 tff(39,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)],[38, 35, 22])).
% 0.21/0.49 tff(40,plain,
% 0.21/0.49 (ssList(nil) <=> ssList(nil)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(41,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.21/0.49 tff(42,plain,
% 0.21/0.49 (ssList(nil)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.49 tff(43,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(44,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(45,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)],[44, 43])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[45, 42, 39])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 (~neq(U!45, nil)),
% 0.21/0.49 inference(and_elim,[status(thm)],[13])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (U!45 = nil),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (nil = U!45),
% 0.21/0.49 inference(symmetry,[status(thm)],[50])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 (cons(Y!47, nil) = nil),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[51, 21])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(56,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.49 tff(57,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[56, 54])).
% 0.21/0.49 tff(58,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(59,plain,
% 0.21/0.49 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(60,plain,
% 0.21/0.49 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.49 tff(61,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 0.21/0.49 tff(62,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.49 tff(63,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.21/0.49 tff(64,plain,(
% 0.21/0.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[63])).
% 0.21/0.49 tff(65,plain,
% 0.21/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.21/0.49 tff(66,plain,
% 0.21/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(67,plain,
% 0.21/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[68, 42, 65])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))) | ssItem(Y!47)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (ssItem(Y!47)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[70, 16])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (~(cons(Y!47, nil) = nil)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[74, 71, 69])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[75, 52])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------