%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC047+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:30:02 AM UTC 2025
% Result : Theorem 0.22s 0.45s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC047+1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n001.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 08:10:35 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 % SZS output start Proof
% 0.22/0.45 tff(rearsegP_type, type, (
% 0.22/0.45 rearsegP: ( $i * $i ) > $o)).
% 0.22/0.45 tff(tptp_fun_U_45_type, type, (
% 0.22/0.45 tptp_fun_U_45: $i)).
% 0.22/0.45 tff(neq_type, type, (
% 0.22/0.45 neq: ( $i * $i ) > $o)).
% 0.22/0.45 tff(nil_type, type, (
% 0.22/0.45 nil: $i)).
% 0.22/0.45 tff(ssList_type, type, (
% 0.22/0.45 ssList: $i > $o)).
% 0.22/0.45 tff(1,plain,
% 0.22/0.45 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(2,plain,
% 0.22/0.45 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.45 tff(3,plain,
% 0.22/0.45 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y))))), ((~(ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))), ((~(ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(4,plain,
% 0.22/0.45 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.45 tff(5,plain,
% 0.22/0.45 ((ssList(U!45) & neq(U!45, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y)))) <=> (ssList(U!45) & neq(U!45, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(6,plain,
% 0.22/0.45 ((~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(U, Y)))) <=> (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(U, Y))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(7,plain,
% 0.22/0.45 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~(X = W))) | (((~(nil = V)) | (nil = U)) & ((~neq(V, nil)) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & rearsegP(V, Y)) & rearsegP(U, Y)))))))))) <=> (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(U, Y))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(8,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~(X = W))) | (((~(nil = V)) | (nil = U)) & ((~neq(V, nil)) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & rearsegP(V, Y)) & rearsegP(U, Y)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.22/0.45 tff(9,plain,
% 0.22/0.45 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(U, Y)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.45 tff(10,plain,
% 0.22/0.45 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(U, Y)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.22/0.45 tff(11,plain,
% 0.22/0.45 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(U, Y)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.22/0.45 tff(12,plain,
% 0.22/0.45 (~![U: $i] : ((~ssList(U)) | (~neq(U, nil)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & rearsegP(U, Y)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.22/0.45 tff(13,plain,
% 0.22/0.45 (ssList(U!45) & neq(U!45, nil) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.22/0.45 tff(14,plain,
% 0.22/0.45 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & rearsegP(U!45, Y)))),
% 0.22/0.45 inference(and_elim,[status(thm)],[13])).
% 0.22/0.45 tff(15,plain,
% 0.22/0.45 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.22/0.45 tff(16,plain,
% 0.22/0.45 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.22/0.45 tff(17,plain,
% 0.22/0.45 (neq(U!45, nil)),
% 0.22/0.45 inference(and_elim,[status(thm)],[13])).
% 0.22/0.45 tff(18,plain,
% 0.22/0.45 (ssList(U!45)),
% 0.22/0.45 inference(and_elim,[status(thm)],[13])).
% 0.22/0.45 tff(19,plain,
% 0.22/0.45 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~rearsegP(U!45, U!45)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~rearsegP(U!45, U!45)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(20,plain,
% 0.22/0.45 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))) | ((~ssList(U!45)) | (~neq(U!45, nil)) | (~rearsegP(U!45, U!45)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(21,plain,
% 0.22/0.45 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~rearsegP(U!45, Y)))) | (~ssList(U!45)) | (~neq(U!45, nil)) | (~rearsegP(U!45, U!45))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.22/0.45 tff(22,plain,
% 0.22/0.45 (~rearsegP(U!45, U!45)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[21, 18, 17, 16])).
% 0.22/0.45 tff(23,plain,
% 0.22/0.45 (^[U: $i] : refl(((~ssList(U)) | rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(24,plain,
% 0.22/0.45 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.45 tff(25,plain,
% 0.22/0.45 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(26,plain,
% 0.22/0.45 (^[U: $i] : rewrite((ssList(U) => rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(27,plain,
% 0.22/0.45 (![U: $i] : (ssList(U) => rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.45 tff(28,axiom,(![U: $i] : (ssList(U) => rearsegP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax49')).
% 0.22/0.45 tff(29,plain,
% 0.22/0.45 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.45 tff(30,plain,
% 0.22/0.45 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.22/0.45 tff(31,plain,(
% 0.22/0.45 ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.22/0.45 inference(skolemize,[status(sab)],[30])).
% 0.22/0.45 tff(32,plain,
% 0.22/0.45 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.22/0.45 tff(33,plain,
% 0.22/0.45 (((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(U!45)) | rearsegP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(U!45)) | rearsegP(U!45, U!45))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(34,plain,
% 0.22/0.45 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(U!45)) | rearsegP(U!45, U!45))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(35,plain,
% 0.22/0.45 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(U!45)) | rearsegP(U!45, U!45)),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.22/0.45 tff(36,plain,
% 0.22/0.45 ($false),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[35, 32, 18, 22])).
% 0.22/0.45 % SZS output end Proof
% 0.22/0.46 % E exiting
%------------------------------------------------------------------------------