%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC385+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 05:31:05 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC385+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:11:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(neq_type, type, (
% 0.19/0.42 neq: ( $i * $i ) > $o)).
% 0.19/0.42 tff(nil_type, type, (
% 0.19/0.42 nil: $i)).
% 0.19/0.42 tff(tptp_fun_V_46_type, type, (
% 0.19/0.42 tptp_fun_V_46: $i)).
% 0.19/0.42 tff(segmentP_type, type, (
% 0.19/0.42 segmentP: ( $i * $i ) > $o)).
% 0.19/0.42 tff(tptp_fun_U_45_type, type, (
% 0.19/0.42 tptp_fun_U_45: $i)).
% 0.19/0.42 tff(singletonP_type, type, (
% 0.19/0.42 singletonP: $i > $o)).
% 0.19/0.42 tff(ssList_type, type, (
% 0.19/0.42 ssList: $i > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 ((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)) | (singletonP(U!45) & 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)) | (singletonP(U!45) & segmentP(V!46, U!45)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (singletonP(U) & segmentP(V, U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (singletonP(U) & segmentP(V, U)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 ((~![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))) | (singletonP(U) & segmentP(V, U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (singletonP(U) & segmentP(V, U)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(4,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))) | (singletonP(U) & segmentP(V, U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (singletonP(U) & segmentP(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (singletonP(U) & segmentP(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (singletonP(U) & segmentP(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~singletonP(U)) & neq(V, nil)) | (~segmentP(V, U)) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)) | (singletonP(U) & segmentP(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (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)) | (singletonP(U!45) & segmentP(V!46, U!45))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (~((~ssList(U!45)) | ((~singletonP(U!45)) & neq(V!46, nil)) | (~segmentP(V!46, U!45)) | (~ssList(V!46)) | (~neq(V!46, nil)) | (singletonP(U!45) & segmentP(V!46, U!45)))),
% 0.19/0.42 inference(and_elim,[status(thm)],[9])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (neq(V!46, nil)),
% 0.19/0.42 inference(or_elim,[status(thm)],[10])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (segmentP(V!46, U!45)),
% 0.19/0.42 inference(or_elim,[status(thm)],[10])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 ((~(~((~singletonP(U!45)) | (~segmentP(V!46, U!45))))) <=> ((~singletonP(U!45)) | (~segmentP(V!46, U!45)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 ((singletonP(U!45) & segmentP(V!46, U!45)) <=> (~((~singletonP(U!45)) | (~segmentP(V!46, U!45))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 ((~(singletonP(U!45) & segmentP(V!46, U!45))) <=> (~(~((~singletonP(U!45)) | (~segmentP(V!46, U!45)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 ((~(singletonP(U!45) & segmentP(V!46, U!45))) <=> ((~singletonP(U!45)) | (~segmentP(V!46, U!45)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[15, 13])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (~(singletonP(U!45) & segmentP(V!46, U!45))),
% 0.19/0.43 inference(or_elim,[status(thm)],[10])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 ((~singletonP(U!45)) | (~segmentP(V!46, U!45))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (~singletonP(U!45)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[18, 12])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 ((~(~(singletonP(U!45) | (~neq(V!46, nil))))) <=> (singletonP(U!45) | (~neq(V!46, nil)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(21,plain,
% 0.19/0.43 (((~singletonP(U!45)) & neq(V!46, nil)) <=> (~(singletonP(U!45) | (~neq(V!46, nil))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 ((~((~singletonP(U!45)) & neq(V!46, nil))) <=> (~(~(singletonP(U!45) | (~neq(V!46, nil)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 ((~((~singletonP(U!45)) & neq(V!46, nil))) <=> (singletonP(U!45) | (~neq(V!46, nil)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (~((~singletonP(U!45)) & neq(V!46, nil))),
% 0.19/0.43 inference(or_elim,[status(thm)],[10])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (singletonP(U!45) | (~neq(V!46, nil))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[25, 19, 11])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------