%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC349+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 05:30:57 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC349+1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 09:08:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(frontsegP_type, type, (
% 0.19/0.44 frontsegP: ( $i * $i ) > $o)).
% 0.19/0.44 tff(nil_type, type, (
% 0.19/0.44 nil: $i)).
% 0.19/0.44 tff(tptp_fun_V_46_type, type, (
% 0.19/0.44 tptp_fun_V_46: $i)).
% 0.19/0.44 tff(tptp_fun_U_45_type, type, (
% 0.19/0.44 tptp_fun_U_45: $i)).
% 0.19/0.44 tff(neq_type, type, (
% 0.19/0.44 neq: ( $i * $i ) > $o)).
% 0.19/0.44 tff(ssList_type, type, (
% 0.19/0.44 ssList: $i > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 ((ssList(U!45) & (~(frontsegP(V!46, U!45) | (~ssList(V!46)) | (~ssList(nil)) | (~neq(V!46, nil)) | (~(U!45 = nil))))) <=> (ssList(U!45) & (~((~ssList(nil)) | (~(U!45 = nil)) | frontsegP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | (~ssList(V)) | (~ssList(nil)) | (~neq(V, nil)) | (~(U = nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | (~ssList(V)) | (~ssList(nil)) | (~neq(V, nil)) | (~(U = nil)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = W)) | (~(V = X))) | (~(U = W))) | (~neq(V, nil))) | frontsegP(V, U))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | (~ssList(V)) | (~ssList(nil)) | (~neq(V, nil)) | (~(U = nil)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = W)) | (~(V = X))) | (~(U = W))) | (~neq(V, nil))) | frontsegP(V, U))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | (~ssList(V)) | (~ssList(nil)) | (~neq(V, nil)) | (~(U = nil))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | (~ssList(V)) | (~ssList(nil)) | (~neq(V, nil)) | (~(U = nil))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | (~ssList(V)) | (~ssList(nil)) | (~neq(V, nil)) | (~(U = nil))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.44 tff(8,plain,
% 0.19/0.44 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (frontsegP(V, U) | (~ssList(V)) | (~ssList(nil)) | (~neq(V, nil)) | (~(U = nil))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (ssList(U!45) & (~((~ssList(nil)) | (~(U!45 = nil)) | frontsegP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (~((~ssList(nil)) | (~(U!45 = nil)) | frontsegP(V!46, U!45) | (~ssList(V!46)) | (~neq(V!46, nil)))),
% 0.19/0.44 inference(and_elim,[status(thm)],[9])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (U!45 = nil),
% 0.19/0.44 inference(or_elim,[status(thm)],[10])).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (nil = U!45),
% 0.19/0.44 inference(symmetry,[status(thm)],[11])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (frontsegP(V!46, nil) <=> frontsegP(V!46, U!45)),
% 0.19/0.44 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (frontsegP(V!46, U!45) <=> frontsegP(V!46, nil)),
% 0.19/0.44 inference(symmetry,[status(thm)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 ((~frontsegP(V!46, U!45)) <=> (~frontsegP(V!46, nil))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (~frontsegP(V!46, U!45)),
% 0.19/0.44 inference(or_elim,[status(thm)],[10])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (~frontsegP(V!46, nil)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 (ssList(V!46)),
% 0.19/0.44 inference(or_elim,[status(thm)],[10])).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(20,plain,
% 0.19/0.44 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (![U: $i] : (ssList(U) => frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.44 tff(24,axiom,(![U: $i] : (ssList(U) => frontsegP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax45')).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.44 tff(27,plain,(
% 0.19/0.44 ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.19/0.44 inference(skolemize,[status(sab)],[26])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(V!46)) | frontsegP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(V!46)) | frontsegP(V!46, nil))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(V!46)) | frontsegP(V!46, nil))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(V!46)) | frontsegP(V!46, nil)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (frontsegP(V!46, nil)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[31, 28, 18])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[32, 17])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------