%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC127+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:30:14 AM UTC 2025
% Result : Theorem 0.22s 0.51s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWC127+1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 08:25:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51 % SZS output start Proof
% 0.22/0.51 tff(nil_type, type, (
% 0.22/0.51 nil: $i)).
% 0.22/0.51 tff(cons_type, type, (
% 0.22/0.51 cons: ( $i * $i ) > $i)).
% 0.22/0.51 tff(tptp_fun_V_4_type, type, (
% 0.22/0.51 tptp_fun_V_4: $i > $i)).
% 0.22/0.51 tff(tptp_fun_U_45_type, type, (
% 0.22/0.51 tptp_fun_U_45: $i)).
% 0.22/0.51 tff(ssItem_type, type, (
% 0.22/0.51 ssItem: $i > $o)).
% 0.22/0.51 tff(singletonP_type, type, (
% 0.22/0.51 singletonP: $i > $o)).
% 0.22/0.51 tff(ssList_type, type, (
% 0.22/0.51 ssList: $i > $o)).
% 0.22/0.51 tff(segmentP_type, type, (
% 0.22/0.51 segmentP: ( $i * $i ) > $o)).
% 0.22/0.51 tff(tptp_fun_V_46_type, type, (
% 0.22/0.51 tptp_fun_V_46: $i)).
% 0.22/0.51 tff(neq_type, type, (
% 0.22/0.51 neq: ( $i * $i ) > $o)).
% 0.22/0.51 tff(1,plain,
% 0.22/0.51 ((U!45 = nil) <=> (nil = U!45)),
% 0.22/0.51 inference(commutativity,[status(thm)],[])).
% 0.22/0.51 tff(2,plain,
% 0.22/0.51 ((ssList(U!45) & (~(((~singletonP(U!45)) & neq(V!46, nil)) | (~segmentP(V!46, U!45)) | (~ssList(V!46)) | (~ssList(U!45)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | ((~singletonP(U!45)) & neq(V!46, nil)) | (~segmentP(V!46, U!45)) | (~ssList(V!46)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(3,plain,
% 0.22/0.51 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(4,plain,
% 0.22/0.51 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | (~segmentP(X, W))) | ((~singletonP(W)) & neq(X, nil))) | (neq(U, nil) & segmentP(V, U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(5,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | (~segmentP(X, W))) | ((~singletonP(W)) & neq(X, nil))) | (neq(U, nil) & segmentP(V, U)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.22/0.51 tff(6,plain,
% 0.22/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.22/0.51 tff(7,plain,
% 0.22/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.22/0.51 tff(8,plain,
% 0.22/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.51 tff(9,plain,
% 0.22/0.51 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (neq(U, nil) & segmentP(V, U))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.22/0.51 tff(10,plain,
% 0.22/0.51 (ssList(U!45) & (~((~ssList(U!45)) | ((~singletonP(U!45)) & neq(V!46, nil)) | (~segmentP(V!46, U!45)) | (~ssList(V!46)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.22/0.51 tff(11,plain,
% 0.22/0.51 (ssList(U!45)),
% 0.22/0.51 inference(and_elim,[status(thm)],[10])).
% 0.22/0.51 tff(12,plain,
% 0.22/0.51 (^[U: $i] : refl(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(13,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.51 tff(14,plain,
% 0.22/0.51 (^[U: $i] : rewrite(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(15,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[14])).
% 0.22/0.51 tff(16,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[15, 13])).
% 0.22/0.51 tff(17,plain,
% 0.22/0.51 (^[U: $i] : rewrite(((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(18,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[17])).
% 0.22/0.51 tff(19,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(20,plain,
% 0.22/0.51 (^[U: $i] : trans(monotonicity(rewrite((singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))) <=> (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))))), rewrite((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(21,plain,
% 0.22/0.51 (![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.51 tff(22,axiom,(![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax4')).
% 0.22/0.51 tff(23,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.22/0.51 tff(24,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.22/0.51 tff(25,plain,(
% 0.22/0.51 ![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U))))))),
% 0.22/0.51 inference(skolemize,[status(sab)],[24])).
% 0.22/0.51 tff(26,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.22/0.51 tff(27,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.22/0.51 tff(28,plain,
% 0.22/0.51 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(29,plain,
% 0.22/0.51 (((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))))))) <=> ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(30,plain,
% 0.22/0.51 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[29])).
% 0.22/0.51 tff(31,plain,
% 0.22/0.51 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[30, 28])).
% 0.22/0.51 tff(32,plain,
% 0.22/0.51 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))),
% 0.22/0.51 inference(quant_inst,[status(thm)],[])).
% 0.22/0.51 tff(33,plain,
% 0.22/0.51 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.51 tff(34,plain,
% 0.22/0.51 (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[33, 27, 11])).
% 0.22/0.51 tff(35,plain,
% 0.22/0.51 (((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))) | ((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(36,plain,
% 0.22/0.51 ((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.22/0.51 tff(37,plain,
% 0.22/0.51 (~((~ssList(U!45)) | ((~singletonP(U!45)) & neq(V!46, nil)) | (~segmentP(V!46, U!45)) | (~ssList(V!46)) | (~neq(V!46, nil)) | (neq(U!45, nil) & segmentP(V!46, U!45)))),
% 0.22/0.51 inference(and_elim,[status(thm)],[10])).
% 0.22/0.51 tff(38,plain,
% 0.22/0.51 (neq(V!46, nil)),
% 0.22/0.51 inference(or_elim,[status(thm)],[37])).
% 0.22/0.51 tff(39,plain,
% 0.22/0.51 ((~(~(singletonP(U!45) | (~neq(V!46, nil))))) <=> (singletonP(U!45) | (~neq(V!46, nil)))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(40,plain,
% 0.22/0.51 (((~singletonP(U!45)) & neq(V!46, nil)) <=> (~(singletonP(U!45) | (~neq(V!46, nil))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(41,plain,
% 0.22/0.51 ((~((~singletonP(U!45)) & neq(V!46, nil))) <=> (~(~(singletonP(U!45) | (~neq(V!46, nil)))))),
% 0.22/0.51 inference(monotonicity,[status(thm)],[40])).
% 0.22/0.51 tff(42,plain,
% 0.22/0.51 ((~((~singletonP(U!45)) & neq(V!46, nil))) <=> (singletonP(U!45) | (~neq(V!46, nil)))),
% 0.22/0.51 inference(transitivity,[status(thm)],[41, 39])).
% 0.22/0.51 tff(43,plain,
% 0.22/0.51 (~((~singletonP(U!45)) & neq(V!46, nil))),
% 0.22/0.51 inference(or_elim,[status(thm)],[37])).
% 0.22/0.51 tff(44,plain,
% 0.22/0.51 (singletonP(U!45) | (~neq(V!46, nil))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.22/0.51 tff(45,plain,
% 0.22/0.51 (singletonP(U!45)),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[44, 38])).
% 0.22/0.51 tff(46,plain,
% 0.22/0.51 ((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(47,plain,
% 0.22/0.51 ((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.22/0.51 tff(48,plain,
% 0.22/0.51 (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[47, 36])).
% 0.22/0.51 tff(49,plain,
% 0.22/0.51 (((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))) | (cons(tptp_fun_V_4(U!45), nil) = U!45)),
% 0.22/0.51 inference(tautology,[status(thm)],[])).
% 0.22/0.51 tff(50,plain,
% 0.22/0.51 (cons(tptp_fun_V_4(U!45), nil) = U!45),
% 0.22/0.51 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.22/0.51 tff(51,plain,
% 0.22/0.51 ((cons(tptp_fun_V_4(U!45), nil) = nil) <=> (U!45 = nil)),
% 0.22/0.51 inference(monotonicity,[status(thm)],[50])).
% 0.22/0.51 tff(52,plain,
% 0.22/0.51 ((cons(tptp_fun_V_4(U!45), nil) = nil) <=> (nil = U!45)),
% 0.22/0.51 inference(transitivity,[status(thm)],[51, 1])).
% 0.22/0.51 tff(53,plain,
% 0.22/0.51 ((nil = U!45) <=> (cons(tptp_fun_V_4(U!45), nil) = nil)),
% 0.22/0.51 inference(symmetry,[status(thm)],[52])).
% 0.22/0.51 tff(54,plain,
% 0.22/0.51 (^[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))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(55,plain,
% 0.22/0.51 (![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)))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[54])).
% 0.22/0.51 tff(56,plain,
% 0.22/0.51 (^[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))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(57,plain,
% 0.22/0.51 (![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)))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[56])).
% 0.22/0.51 tff(58,plain,
% 0.22/0.51 (![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)))))),
% 0.22/0.51 inference(transitivity,[status(thm)],[57, 55])).
% 0.22/0.51 tff(59,plain,
% 0.22/0.51 (![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)))))),
% 0.22/0.51 inference(rewrite,[status(thm)],[])).
% 0.22/0.51 tff(60,plain,
% 0.22/0.51 (^[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)))))))),
% 0.22/0.51 inference(bind,[status(th)],[])).
% 0.22/0.51 tff(61,plain,
% 0.22/0.51 (![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)))))),
% 0.22/0.51 inference(quant_intro,[status(thm)],[60])).
% 0.22/0.51 tff(62,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.22/0.51 tff(63,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.22/0.51 tff(64,plain,
% 0.22/0.51 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.22/0.51 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.22/0.51 tff(65,plain,(
% 0.22/0.51 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.22/0.51 inference(skolemize,[status(sab)],[64])).
% 0.22/0.52 tff(66,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.22/0.52 tff(67,plain,
% 0.22/0.52 (((~![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)))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(68,plain,
% 0.22/0.52 ((~![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)))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(69,plain,
% 0.22/0.52 ((~![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))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.22/0.52 tff(70,plain,
% 0.22/0.52 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[69, 66, 11])).
% 0.22/0.52 tff(71,plain,
% 0.22/0.52 (ssList(nil) <=> ssList(nil)),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(72,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.22/0.52 tff(73,plain,
% 0.22/0.52 (ssList(nil)),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.52 tff(74,plain,
% 0.22/0.52 (((~![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))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(75,plain,
% 0.22/0.52 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(76,plain,
% 0.22/0.52 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.22/0.52 tff(77,plain,
% 0.22/0.52 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[76, 73, 70])).
% 0.22/0.52 tff(78,plain,
% 0.22/0.52 (segmentP(V!46, U!45)),
% 0.22/0.52 inference(or_elim,[status(thm)],[37])).
% 0.22/0.52 tff(79,plain,
% 0.22/0.52 ((~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(80,plain,
% 0.22/0.52 ((neq(U!45, nil) & segmentP(V!46, U!45)) <=> (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(81,plain,
% 0.22/0.52 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> (~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.22/0.52 inference(monotonicity,[status(thm)],[80])).
% 0.22/0.52 tff(82,plain,
% 0.22/0.52 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 0.22/0.52 inference(transitivity,[status(thm)],[81, 79])).
% 0.22/0.52 tff(83,plain,
% 0.22/0.52 (~(neq(U!45, nil) & segmentP(V!46, U!45))),
% 0.22/0.52 inference(or_elim,[status(thm)],[37])).
% 0.22/0.52 tff(84,plain,
% 0.22/0.52 ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.22/0.52 tff(85,plain,
% 0.22/0.52 (~neq(U!45, nil)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[84, 78])).
% 0.22/0.52 tff(86,plain,
% 0.22/0.52 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(87,plain,
% 0.22/0.52 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.22/0.52 tff(88,plain,
% 0.22/0.52 (U!45 = nil),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[87, 77])).
% 0.22/0.52 tff(89,plain,
% 0.22/0.52 (nil = U!45),
% 0.22/0.52 inference(symmetry,[status(thm)],[88])).
% 0.22/0.52 tff(90,plain,
% 0.22/0.52 (cons(tptp_fun_V_4(U!45), nil) = nil),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[89, 53])).
% 0.22/0.52 tff(91,plain,
% 0.22/0.52 (((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))) | ssItem(tptp_fun_V_4(U!45))),
% 0.22/0.52 inference(tautology,[status(thm)],[])).
% 0.22/0.52 tff(92,plain,
% 0.22/0.52 (ssItem(tptp_fun_V_4(U!45))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[91, 48])).
% 0.22/0.52 tff(93,plain,
% 0.22/0.52 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(94,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[93])).
% 0.22/0.52 tff(95,plain,
% 0.22/0.52 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(96,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[95])).
% 0.22/0.52 tff(97,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[96, 94])).
% 0.22/0.52 tff(98,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(99,plain,
% 0.22/0.52 (^[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))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(100,plain,
% 0.22/0.52 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[99])).
% 0.22/0.52 tff(101,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax18')).
% 0.22/0.52 tff(102,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.22/0.52 tff(103,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.22/0.52 tff(104,plain,(
% 0.22/0.52 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(skolemize,[status(sab)],[103])).
% 0.22/0.52 tff(105,plain,
% 0.22/0.52 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.22/0.52 tff(106,plain,
% 0.22/0.52 (((~![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))))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(107,plain,
% 0.22/0.52 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(108,plain,
% 0.22/0.52 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.52 tff(109,plain,
% 0.22/0.52 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[108, 73, 105])).
% 0.22/0.52 tff(110,plain,
% 0.22/0.52 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = nil)))),
% 0.22/0.52 inference(rewrite,[status(thm)],[])).
% 0.22/0.52 tff(111,plain,
% 0.22/0.52 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = nil)))),
% 0.22/0.52 inference(quant_inst,[status(thm)],[])).
% 0.22/0.52 tff(112,plain,
% 0.22/0.52 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = nil))),
% 0.22/0.52 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.52 tff(113,plain,
% 0.22/0.52 (~(cons(tptp_fun_V_4(U!45), nil) = nil)),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[112, 109, 92])).
% 0.22/0.52 tff(114,plain,
% 0.22/0.52 ($false),
% 0.22/0.52 inference(unit_resolution,[status(thm)],[113, 90])).
% 0.22/0.52 % SZS output end Proof
% 0.22/0.52 % E exiting
%------------------------------------------------------------------------------