%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC082+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:30:07 AM UTC 2025
% Result : Theorem 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.16 % Problem : SWC082+1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.16 % Command : run_E %s %d THM
% 0.13/0.41 % Computer : n015.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8042.1875MB
% 0.13/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Fri Jun 20 08:15:46 EDT 2025
% 0.13/0.41 % CPUTime :
% 0.22/0.53 % SZS status Theorem
% 0.22/0.53 % SZS output start Proof
% 0.22/0.53 tff(segmentP_type, type, (
% 0.22/0.53 segmentP: ( $i * $i ) > $o)).
% 0.22/0.53 tff(tptp_fun_V_46_type, type, (
% 0.22/0.53 tptp_fun_V_46: $i)).
% 0.22/0.53 tff(tptp_fun_U_45_type, type, (
% 0.22/0.53 tptp_fun_U_45: $i)).
% 0.22/0.53 tff(ssList_type, type, (
% 0.22/0.53 ssList: $i > $o)).
% 0.22/0.53 tff(neq_type, type, (
% 0.22/0.53 neq: ( $i * $i ) > $o)).
% 0.22/0.53 tff(nil_type, type, (
% 0.22/0.53 nil: $i)).
% 0.22/0.53 tff(tptp_fun_Z_47_type, type, (
% 0.22/0.53 tptp_fun_Z_47: $i)).
% 0.22/0.53 tff(1,plain,
% 0.22/0.53 (^[Y: $i] : refl(((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(2,plain,
% 0.22/0.53 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.53 tff(3,plain,
% 0.22/0.53 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)) <=> (~((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y))))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))) <=> (~(~((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y))))))), rewrite((~(~((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y))))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))) <=> ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(4,plain,
% 0.22/0.53 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))) <=> ![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.53 tff(5,plain,
% 0.22/0.53 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(6,plain,
% 0.22/0.53 (((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~neq(V!46, nil))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))) <=> ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(7,plain,
% 0.22/0.53 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~neq(V!46, nil))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))) <=> (ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[6])).
% 0.22/0.53 tff(8,plain,
% 0.22/0.53 ((ssList(U!45) & ((~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) | (~neq(V!46, nil))) & ssList(U!45) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))) <=> (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y))))),
% 0.22/0.53 inference(transitivity,[status(thm)],[7, 5])).
% 0.22/0.53 tff(9,plain,
% 0.22/0.53 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~segmentP(U, Z)) | (~segmentP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(V, nil)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~segmentP(U, Z)) | (~segmentP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(V, nil)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(10,plain,
% 0.22/0.53 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & segmentP(V, Y)) & segmentP(U, Y))) | ((~(nil = W)) & (nil = X))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~segmentP(X, Z))) | (~segmentP(W, Z)))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~segmentP(U, Z)) | (~segmentP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(V, nil)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(11,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (((ssList(Y) & neq(Y, nil)) & segmentP(V, Y)) & segmentP(U, Y))) | ((~(nil = W)) & (nil = X))) | (![Z: $i] : (ssList(Z) => (((~neq(Z, nil)) | (~segmentP(X, Z))) | (~segmentP(W, Z)))) & neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.22/0.53 tff(12,plain,
% 0.22/0.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~segmentP(U, Z)) | (~segmentP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(V, nil)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.22/0.53 tff(13,plain,
% 0.22/0.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~segmentP(U, Z)) | (~segmentP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(V, nil)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.22/0.53 tff(14,plain,
% 0.22/0.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~segmentP(U, Z)) | (~segmentP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(V, nil)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.22/0.53 tff(15,plain,
% 0.22/0.53 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = U)) & (nil = V)) | (~neq(V, nil)) | (~ssList(V)) | (![Z: $i] : ((~segmentP(U, Z)) | (~segmentP(V, Z)) | (~neq(Z, nil)) | (~ssList(Z))) & neq(V, nil)) | (~ssList(U)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.22/0.53 tff(16,plain,
% 0.22/0.53 (ssList(U!45) & (~((~(nil = U!45)) & (nil = V!46))) & neq(V!46, nil) & ssList(V!46) & ((~neq(V!46, nil)) | (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.22/0.53 tff(17,plain,
% 0.22/0.53 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!46, Y) & segmentP(U!45, Y)))),
% 0.22/0.54 inference(and_elim,[status(thm)],[16])).
% 0.22/0.54 tff(18,plain,
% 0.22/0.54 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.22/0.54 tff(19,plain,
% 0.22/0.54 (![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.22/0.54 tff(20,plain,
% 0.22/0.54 (neq(V!46, nil)),
% 0.22/0.54 inference(and_elim,[status(thm)],[16])).
% 0.22/0.54 tff(21,plain,
% 0.22/0.54 ((~neq(V!46, nil)) | (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))),
% 0.22/0.54 inference(and_elim,[status(thm)],[16])).
% 0.22/0.54 tff(22,plain,
% 0.22/0.54 (~((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.22/0.54 tff(23,plain,
% 0.22/0.54 (((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | ssList(Z!47)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(24,plain,
% 0.22/0.54 (ssList(Z!47)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.22/0.54 tff(25,plain,
% 0.22/0.54 (((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | neq(Z!47, nil)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(26,plain,
% 0.22/0.54 (neq(Z!47, nil)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.22/0.54 tff(27,plain,
% 0.22/0.54 (((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | segmentP(V!46, Z!47)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(28,plain,
% 0.22/0.54 (segmentP(V!46, Z!47)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[27, 22])).
% 0.22/0.54 tff(29,plain,
% 0.22/0.54 (((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))) | segmentP(U!45, Z!47)),
% 0.22/0.54 inference(tautology,[status(thm)],[])).
% 0.22/0.54 tff(30,plain,
% 0.22/0.54 (segmentP(U!45, Z!47)),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[29, 22])).
% 0.22/0.54 tff(31,plain,
% 0.22/0.54 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | ((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | (~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(32,plain,
% 0.22/0.54 (((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47))) <=> ((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(33,plain,
% 0.22/0.54 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | ((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | ((~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))))),
% 0.22/0.54 inference(monotonicity,[status(thm)],[32])).
% 0.22/0.54 tff(34,plain,
% 0.22/0.54 (((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | ((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | (~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47)))),
% 0.22/0.54 inference(transitivity,[status(thm)],[33, 31])).
% 0.22/0.54 tff(35,plain,
% 0.22/0.54 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | ((~neq(Z!47, nil)) | (~ssList(Z!47)) | (~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(36,plain,
% 0.22/0.54 ((~![Y: $i] : ((~neq(Y, nil)) | (~ssList(Y)) | (~segmentP(U!45, Y)) | (~segmentP(V!46, Y)))) | (~segmentP(U!45, Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(Z!47, nil)) | (~ssList(Z!47))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.22/0.54 tff(37,plain,
% 0.22/0.54 ($false),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[36, 30, 28, 26, 24, 19])).
% 0.22/0.54 % SZS output end Proof
% 0.22/0.54 % E exiting
%------------------------------------------------------------------------------