%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC038+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 05:29:59 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
% 0.07/0.13 % Problem : SWC038+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:10:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.22/0.45 % SZS status Theorem
% 0.22/0.45 % SZS output start Proof
% 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(nil_type, type, (
% 0.22/0.45 nil: $i)).
% 0.22/0.45 tff(frontsegP_type, type, (
% 0.22/0.45 frontsegP: ( $i * $i ) > $o)).
% 0.22/0.45 tff(neq_type, type, (
% 0.22/0.45 neq: ( $i * $i ) > $o)).
% 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 ((~((nil = U!45) | (~ssList(U!45)) | (~ssList(nil)) | ((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))))) <=> (~((~ssList(nil)) | (nil = U!45) | (~ssList(U!45)) | ((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(2,plain,
% 0.22/0.45 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ((~(nil = U)) & ((~frontsegP(nil, U)) | (~neq(U, nil)))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ((~(nil = U)) & ((~frontsegP(nil, U)) | (~neq(U, nil))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(3,plain,
% 0.22/0.45 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~frontsegP(X, W)))))))))) <=> (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ((~(nil = U)) & ((~frontsegP(nil, U)) | (~neq(U, nil))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 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))) | (nil = U)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~frontsegP(X, W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.22/0.45 tff(5,plain,
% 0.22/0.45 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ((~(nil = U)) & ((~frontsegP(nil, U)) | (~neq(U, nil)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.45 tff(6,plain,
% 0.22/0.45 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ((~(nil = U)) & ((~frontsegP(nil, U)) | (~neq(U, nil)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.22/0.45 tff(7,plain,
% 0.22/0.45 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ((~(nil = U)) & ((~frontsegP(nil, U)) | (~neq(U, nil)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.45 tff(8,plain,
% 0.22/0.45 (~![U: $i] : ((nil = U) | (~ssList(U)) | (~ssList(nil)) | ((~(nil = U)) & ((~frontsegP(nil, U)) | (~neq(U, nil)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.22/0.45 tff(9,plain,(
% 0.22/0.45 ~((nil = U!45) | (~ssList(U!45)) | (~ssList(nil)) | ((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[8])).
% 0.22/0.45 tff(10,plain,
% 0.22/0.45 (~((~ssList(nil)) | (nil = U!45) | (~ssList(U!45)) | ((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.22/0.45 tff(11,plain,
% 0.22/0.45 (~(nil = U!45)),
% 0.22/0.45 inference(or_elim,[status(thm)],[10])).
% 0.22/0.45 tff(12,plain,
% 0.22/0.45 ((~(~((nil = U!45) | (~((~frontsegP(nil, U!45)) | (~neq(U!45, nil))))))) <=> ((nil = U!45) | (~((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(13,plain,
% 0.22/0.45 (((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))) <=> (~((nil = U!45) | (~((~frontsegP(nil, U!45)) | (~neq(U!45, nil))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(14,plain,
% 0.22/0.45 ((~((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil))))) <=> (~(~((nil = U!45) | (~((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[13])).
% 0.22/0.45 tff(15,plain,
% 0.22/0.45 ((~((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil))))) <=> ((nil = U!45) | (~((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[14, 12])).
% 0.22/0.45 tff(16,plain,
% 0.22/0.45 (~((~(nil = U!45)) & ((~frontsegP(nil, U!45)) | (~neq(U!45, nil))))),
% 0.22/0.45 inference(or_elim,[status(thm)],[10])).
% 0.22/0.45 tff(17,plain,
% 0.22/0.45 ((nil = U!45) | (~((~frontsegP(nil, U!45)) | (~neq(U!45, nil))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.22/0.45 tff(18,plain,
% 0.22/0.45 (~((~frontsegP(nil, U!45)) | (~neq(U!45, nil)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.22/0.45 tff(19,plain,
% 0.22/0.45 (((~frontsegP(nil, U!45)) | (~neq(U!45, nil))) | frontsegP(nil, U!45)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(20,plain,
% 0.22/0.46 (frontsegP(nil, U!45)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.22/0.46 tff(21,plain,
% 0.22/0.46 ((~(frontsegP(nil, U!45) <=> (nil = U!45))) | (~frontsegP(nil, U!45)) | (nil = U!45)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(22,plain,
% 0.22/0.46 (~(frontsegP(nil, U!45) <=> (nil = U!45))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[21, 11, 20])).
% 0.22/0.46 tff(23,plain,
% 0.22/0.46 (ssList(U!45)),
% 0.22/0.46 inference(or_elim,[status(thm)],[10])).
% 0.22/0.46 tff(24,plain,
% 0.22/0.46 (^[U: $i] : refl(((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(25,plain,
% 0.22/0.46 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[24])).
% 0.22/0.46 tff(26,plain,
% 0.22/0.46 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(27,plain,
% 0.22/0.46 (^[U: $i] : rewrite((ssList(U) => (frontsegP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(28,plain,
% 0.22/0.46 (![U: $i] : (ssList(U) => (frontsegP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.22/0.46 tff(29,axiom,(![U: $i] : (ssList(U) => (frontsegP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax46')).
% 0.22/0.46 tff(30,plain,
% 0.22/0.46 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.22/0.46 tff(31,plain,
% 0.22/0.46 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.22/0.46 tff(32,plain,(
% 0.22/0.46 ![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.22/0.46 inference(skolemize,[status(sab)],[31])).
% 0.22/0.46 tff(33,plain,
% 0.22/0.46 (![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.22/0.46 tff(34,plain,
% 0.22/0.46 (((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | ((~ssList(U!45)) | (frontsegP(nil, U!45) <=> (nil = U!45)))) <=> ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | (~ssList(U!45)) | (frontsegP(nil, U!45) <=> (nil = U!45)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(35,plain,
% 0.22/0.46 ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | ((~ssList(U!45)) | (frontsegP(nil, U!45) <=> (nil = U!45)))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(36,plain,
% 0.22/0.46 ((~![U: $i] : ((~ssList(U)) | (frontsegP(nil, U) <=> (nil = U)))) | (~ssList(U!45)) | (frontsegP(nil, U!45) <=> (nil = U!45))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.22/0.46 tff(37,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[36, 33, 23, 22])).
% 0.22/0.46 % SZS output end Proof
% 0.22/0.46 % E exiting
%------------------------------------------------------------------------------