%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC044+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:30:01 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC044+1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.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 08:06:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(tptp_fun_U_45_type, type, (
% 0.19/0.43 tptp_fun_U_45: $i)).
% 0.19/0.43 tff(nil_type, type, (
% 0.19/0.43 nil: $i)).
% 0.19/0.43 tff(rearsegP_type, type, (
% 0.19/0.43 rearsegP: ( $i * $i ) > $o)).
% 0.19/0.43 tff(ssList_type, type, (
% 0.19/0.43 ssList: $i > $o)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 ((~((nil = U!45) | (~ssList(U!45)) | (~ssList(nil)) | (~rearsegP(nil, U!45)))) <=> (~((~ssList(nil)) | (nil = U!45) | (~ssList(U!45)) | (~rearsegP(nil, U!45))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (~rearsegP(nil, U)))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (~rearsegP(nil, U))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (~rearsegP(X, W))) | (nil = U))))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (~rearsegP(nil, U))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (~rearsegP(X, W))) | (nil = U))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (~rearsegP(nil, U)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.43 tff(6,plain,
% 0.19/0.43 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (~rearsegP(nil, U)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (~rearsegP(nil, U)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | (~rearsegP(nil, U)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.43 tff(9,plain,(
% 0.19/0.43 ~((nil = U!45) | (~ssList(U!45)) | (~ssList(nil)) | (~rearsegP(nil, U!45)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[8])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (~((~ssList(nil)) | (nil = U!45) | (~ssList(U!45)) | (~rearsegP(nil, U!45)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (rearsegP(nil, U!45)),
% 0.19/0.43 inference(or_elim,[status(thm)],[10])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (~(nil = U!45)),
% 0.19/0.43 inference(or_elim,[status(thm)],[10])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((~(rearsegP(nil, U!45) <=> (nil = U!45))) | (~rearsegP(nil, U!45)) | (nil = U!45)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (~(rearsegP(nil, U!45) <=> (nil = U!45))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[13, 12, 11])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (ssList(U!45)),
% 0.19/0.43 inference(or_elim,[status(thm)],[10])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (^[U: $i] : refl(((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (^[U: $i] : rewrite((ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.43 tff(21,axiom,(![U: $i] : (ssList(U) => (rearsegP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax52')).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.43 tff(24,plain,(
% 0.19/0.43 ![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[23])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(U!45)) | (rearsegP(nil, U!45) <=> (nil = U!45)))) <=> ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(U!45)) | (rearsegP(nil, U!45) <=> (nil = U!45)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | ((~ssList(U!45)) | (rearsegP(nil, U!45) <=> (nil = U!45)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 ((~![U: $i] : ((~ssList(U)) | (rearsegP(nil, U) <=> (nil = U)))) | (~ssList(U!45)) | (rearsegP(nil, U!45) <=> (nil = U!45))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[28, 25, 15, 14])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------