%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC358+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:30:59 AM UTC 2025
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC358+1 : TPTP v9.0.0. Released v2.4.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:09:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % SZS output start Proof
% 0.18/0.43 tff(segmentP_type, type, (
% 0.18/0.43 segmentP: ( $i * $i ) > $o)).
% 0.18/0.43 tff(nil_type, type, (
% 0.18/0.43 nil: $i)).
% 0.18/0.43 tff(tptp_fun_U_45_type, type, (
% 0.18/0.43 tptp_fun_U_45: $i)).
% 0.18/0.43 tff(tptp_fun_V_46_type, type, (
% 0.18/0.43 tptp_fun_V_46: $i)).
% 0.18/0.43 tff(neq_type, type, (
% 0.18/0.43 neq: ( $i * $i ) > $o)).
% 0.18/0.43 tff(ssList_type, type, (
% 0.18/0.43 ssList: $i > $o)).
% 0.18/0.43 tff(1,plain,
% 0.18/0.43 ((ssList(U!45) & (~(segmentP(V!46, U!45) | (((~(nil = V!46)) | (~(nil = U!45))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) | (~ssList(V!46)) | (~ssList(U!45)) | (~neq(V!46, nil))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)) | (((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(2,plain,
% 0.18/0.43 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(3,plain,
% 0.18/0.43 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | segmentP(V, U)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 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(V, U)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.18/0.43 tff(5,plain,
% 0.18/0.43 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.43 tff(6,plain,
% 0.18/0.43 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.18/0.43 tff(7,plain,
% 0.18/0.43 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.43 tff(8,plain,
% 0.18/0.43 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (segmentP(V, U) | (((~(nil = V)) | (~(nil = U))) & ((~neq(U, nil)) | (~segmentP(V, U)))) | (~ssList(V)) | (~ssList(U)) | (~neq(V, nil))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.18/0.43 tff(9,plain,
% 0.18/0.43 (ssList(U!45) & (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)) | (((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.18/0.43 tff(10,plain,
% 0.18/0.43 (~((~ssList(U!45)) | segmentP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)) | (((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.18/0.43 inference(and_elim,[status(thm)],[9])).
% 0.18/0.43 tff(11,plain,
% 0.18/0.43 (~segmentP(V!46, U!45)),
% 0.18/0.43 inference(or_elim,[status(thm)],[10])).
% 0.18/0.43 tff(12,plain,
% 0.18/0.43 (((~neq(U!45, nil)) | (~segmentP(V!46, U!45))) | segmentP(V!46, U!45)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(13,plain,
% 0.18/0.43 ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.18/0.43 tff(14,plain,
% 0.18/0.43 ((~(~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(15,plain,
% 0.18/0.43 ((((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))) <=> (~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(16,plain,
% 0.18/0.43 ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> (~(~((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.43 tff(17,plain,
% 0.18/0.43 ((~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.43 tff(18,plain,
% 0.18/0.43 (~(((~(nil = U!45)) | (~(nil = V!46))) & ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 0.18/0.43 inference(or_elim,[status(thm)],[10])).
% 0.18/0.43 tff(19,plain,
% 0.18/0.43 ((~((~(nil = U!45)) | (~(nil = V!46)))) | (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.43 tff(20,plain,
% 0.18/0.43 (~((~(nil = U!45)) | (~(nil = V!46)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.18/0.43 tff(21,plain,
% 0.18/0.43 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = U!45)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(22,plain,
% 0.18/0.43 (nil = U!45),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.18/0.43 tff(23,plain,
% 0.18/0.43 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = V!46)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(24,plain,
% 0.18/0.43 (nil = V!46),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.18/0.43 tff(25,plain,
% 0.18/0.43 (U!45 = nil),
% 0.18/0.43 inference(symmetry,[status(thm)],[22])).
% 0.18/0.43 tff(26,plain,
% 0.18/0.43 (U!45 = V!46),
% 0.18/0.43 inference(transitivity,[status(thm)],[25, 24])).
% 0.18/0.43 tff(27,plain,
% 0.18/0.43 (segmentP(U!45, nil) <=> segmentP(V!46, U!45)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[26, 22])).
% 0.18/0.43 tff(28,plain,
% 0.18/0.43 (segmentP(V!46, U!45) <=> segmentP(U!45, nil)),
% 0.18/0.43 inference(symmetry,[status(thm)],[27])).
% 0.18/0.43 tff(29,plain,
% 0.18/0.43 ((~segmentP(V!46, U!45)) <=> (~segmentP(U!45, nil))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.18/0.43 tff(30,plain,
% 0.18/0.43 (~segmentP(U!45, nil)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[11, 29])).
% 0.18/0.43 tff(31,plain,
% 0.18/0.43 (ssList(U!45)),
% 0.18/0.43 inference(and_elim,[status(thm)],[9])).
% 0.18/0.43 tff(32,plain,
% 0.18/0.43 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(33,plain,
% 0.18/0.43 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.43 tff(34,plain,
% 0.18/0.43 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(35,plain,
% 0.18/0.43 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(36,plain,
% 0.18/0.43 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.43 tff(37,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.18/0.43 tff(38,plain,
% 0.18/0.43 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.43 tff(39,plain,
% 0.18/0.43 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.43 tff(40,plain,(
% 0.18/0.43 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.18/0.43 inference(skolemize,[status(sab)],[39])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(U!45)) | segmentP(U!45, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(U!45)) | segmentP(U!45, nil))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(U!45)) | segmentP(U!45, nil))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.44 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(U!45)) | segmentP(U!45, nil)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.44 tff(45,plain,
% 0.18/0.44 (segmentP(U!45, nil)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[44, 41, 31])).
% 0.18/0.44 tff(46,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[45, 30])).
% 0.18/0.44 % SZS output end Proof
% 0.18/0.44 % E exiting
%------------------------------------------------------------------------------