%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC333+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 05:30:55 AM UTC 2025
% Result : Theorem 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC333+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 09:07:05 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 % SZS output start Proof
% 0.22/0.47 tff(segmentP_type, type, (
% 0.22/0.47 segmentP: ( $i * $i ) > $o)).
% 0.22/0.47 tff(tptp_fun_U_45_type, type, (
% 0.22/0.47 tptp_fun_U_45: $i)).
% 0.22/0.47 tff(tptp_fun_Z_47_type, type, (
% 0.22/0.47 tptp_fun_Z_47: $i)).
% 0.22/0.47 tff(neq_type, type, (
% 0.22/0.47 neq: ( $i * $i ) > $o)).
% 0.22/0.47 tff(tptp_fun_V_46_type, type, (
% 0.22/0.47 tptp_fun_V_46: $i)).
% 0.22/0.47 tff(ssList_type, type, (
% 0.22/0.47 ssList: $i > $o)).
% 0.22/0.47 tff(totalorderedP_type, type, (
% 0.22/0.47 totalorderedP: $i > $o)).
% 0.22/0.47 tff(1,plain,
% 0.22/0.47 ((ssList(U!45) & (totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ssList(U!45) & ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)) | (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))))))) <=> (ssList(U!45) & totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)) | (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(2,plain,
% 0.22/0.47 ((totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ssList(U!45) & ((~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))) | (~segmentP(V!46, U!45)) | (~totalorderedP(U!45)))) <=> (totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ssList(U!45) & ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)) | (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(3,plain,
% 0.22/0.47 ((ssList(U!45) & (totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ssList(U!45) & ((~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))) | (~segmentP(V!46, U!45)) | (~totalorderedP(U!45))))) <=> (ssList(U!45) & (totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ssList(U!45) & ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)) | (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[2])).
% 0.22/0.47 tff(4,plain,
% 0.22/0.47 ((ssList(U!45) & (totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ssList(U!45) & ((~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))) | (~segmentP(V!46, U!45)) | (~totalorderedP(U!45))))) <=> (ssList(U!45) & totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)) | (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[3, 1])).
% 0.22/0.47 tff(5,plain,
% 0.22/0.47 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~totalorderedP(U)) | (~segmentP(V, U)) | (~ssList(V)) | ?[Y: $i] : (ssList(Y) & neq(U, Y) & segmentP(V, Y) & segmentP(Y, U) & totalorderedP(Y)) | (~ssList(U)) | (![Z: $i] : ((~totalorderedP(Z)) | (~ssList(Z)) | (~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U))) & segmentP(V, U) & totalorderedP(U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~totalorderedP(U)) | (~segmentP(V, U)) | (~ssList(V)) | ?[Y: $i] : (ssList(Y) & neq(U, Y) & segmentP(V, Y) & segmentP(Y, U) & totalorderedP(Y)) | (~ssList(U)) | (![Z: $i] : ((~totalorderedP(Z)) | (~ssList(Z)) | (~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U))) & segmentP(V, U) & totalorderedP(U)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(6,plain,
% 0.22/0.48 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~segmentP(X, W))) | (~totalorderedP(W))) | ?[Y: $i] : ((((ssList(Y) & neq(W, Y)) & segmentP(X, Y)) & segmentP(Y, W)) & totalorderedP(Y))) | ((![Z: $i] : (ssList(Z) => ((((~neq(U, Z)) | (~segmentP(V, Z))) | (~segmentP(Z, U))) | (~totalorderedP(Z)))) & segmentP(V, U)) & totalorderedP(U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~totalorderedP(U)) | (~segmentP(V, U)) | (~ssList(V)) | ?[Y: $i] : (ssList(Y) & neq(U, Y) & segmentP(V, Y) & segmentP(Y, U) & totalorderedP(Y)) | (~ssList(U)) | (![Z: $i] : ((~totalorderedP(Z)) | (~ssList(Z)) | (~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U))) & segmentP(V, U) & totalorderedP(U)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~segmentP(X, W))) | (~totalorderedP(W))) | ?[Y: $i] : ((((ssList(Y) & neq(W, Y)) & segmentP(X, Y)) & segmentP(Y, W)) & totalorderedP(Y))) | ((![Z: $i] : (ssList(Z) => ((((~neq(U, Z)) | (~segmentP(V, Z))) | (~segmentP(Z, U))) | (~totalorderedP(Z)))) & segmentP(V, U)) & totalorderedP(U)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.22/0.48 tff(8,plain,
% 0.22/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~totalorderedP(U)) | (~segmentP(V, U)) | (~ssList(V)) | ?[Y: $i] : (ssList(Y) & neq(U, Y) & segmentP(V, Y) & segmentP(Y, U) & totalorderedP(Y)) | (~ssList(U)) | (![Z: $i] : ((~totalorderedP(Z)) | (~ssList(Z)) | (~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U))) & segmentP(V, U) & totalorderedP(U))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.22/0.48 tff(9,plain,
% 0.22/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~totalorderedP(U)) | (~segmentP(V, U)) | (~ssList(V)) | ?[Y: $i] : (ssList(Y) & neq(U, Y) & segmentP(V, Y) & segmentP(Y, U) & totalorderedP(Y)) | (~ssList(U)) | (![Z: $i] : ((~totalorderedP(Z)) | (~ssList(Z)) | (~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U))) & segmentP(V, U) & totalorderedP(U))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.22/0.48 tff(10,plain,
% 0.22/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~totalorderedP(U)) | (~segmentP(V, U)) | (~ssList(V)) | ?[Y: $i] : (ssList(Y) & neq(U, Y) & segmentP(V, Y) & segmentP(Y, U) & totalorderedP(Y)) | (~ssList(U)) | (![Z: $i] : ((~totalorderedP(Z)) | (~ssList(Z)) | (~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U))) & segmentP(V, U) & totalorderedP(U))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.48 tff(11,plain,
% 0.22/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~totalorderedP(U)) | (~segmentP(V, U)) | (~ssList(V)) | ?[Y: $i] : (ssList(Y) & neq(U, Y) & segmentP(V, Y) & segmentP(Y, U) & totalorderedP(Y)) | (~ssList(U)) | (![Z: $i] : ((~totalorderedP(Z)) | (~ssList(Z)) | (~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U))) & segmentP(V, U) & totalorderedP(U))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.22/0.48 tff(12,plain,
% 0.22/0.48 (ssList(U!45) & totalorderedP(U!45) & segmentP(V!46, U!45) & ssList(V!46) & ![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) & ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)) | (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.22/0.48 tff(13,plain,
% 0.22/0.48 (segmentP(V!46, U!45)),
% 0.22/0.48 inference(and_elim,[status(thm)],[12])).
% 0.22/0.48 tff(14,plain,
% 0.22/0.48 (totalorderedP(U!45)),
% 0.22/0.48 inference(and_elim,[status(thm)],[12])).
% 0.22/0.48 tff(15,plain,
% 0.22/0.48 ((~totalorderedP(U!45)) | (~segmentP(V!46, U!45)) | (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))))),
% 0.22/0.48 inference(and_elim,[status(thm)],[12])).
% 0.22/0.48 tff(16,plain,
% 0.22/0.48 (~((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.22/0.48 tff(17,plain,
% 0.22/0.48 (((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))) | segmentP(Z!47, U!45)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(18,plain,
% 0.22/0.48 (segmentP(Z!47, U!45)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.22/0.48 tff(19,plain,
% 0.22/0.48 (((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))) | neq(U!45, Z!47)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(20,plain,
% 0.22/0.48 (neq(U!45, Z!47)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.22/0.48 tff(21,plain,
% 0.22/0.48 (((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))) | segmentP(V!46, Z!47)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(22,plain,
% 0.22/0.48 (segmentP(V!46, Z!47)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[21, 16])).
% 0.22/0.48 tff(23,plain,
% 0.22/0.48 (((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))) | ssList(Z!47)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(24,plain,
% 0.22/0.48 (ssList(Z!47)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[23, 16])).
% 0.22/0.48 tff(25,plain,
% 0.22/0.48 (((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))) | totalorderedP(Z!47)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(26,plain,
% 0.22/0.48 (totalorderedP(Z!47)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[25, 16])).
% 0.22/0.48 tff(27,plain,
% 0.22/0.48 (^[Y: $i] : refl(((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y))) <=> ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(28,plain,
% 0.22/0.48 (![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y))) <=> ![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[27])).
% 0.22/0.48 tff(29,plain,
% 0.22/0.48 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y)) <=> (~((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y))))), ((~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) <=> (~(~((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y))))))), rewrite((~(~((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y))))) <=> ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))), ((~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) <=> ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(30,plain,
% 0.22/0.48 (![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y))) <=> ![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[29])).
% 0.22/0.48 tff(31,plain,
% 0.22/0.48 (![Y: $i] : (~(ssList(Y) & neq(U!45, Y) & segmentP(V!46, Y) & segmentP(Y, U!45) & totalorderedP(Y)))),
% 0.22/0.48 inference(and_elim,[status(thm)],[12])).
% 0.22/0.48 tff(32,plain,
% 0.22/0.48 (![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.22/0.48 tff(33,plain,
% 0.22/0.48 (![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.22/0.48 tff(34,plain,
% 0.22/0.48 (((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | ((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))) <=> ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | (~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(35,plain,
% 0.22/0.49 (((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)) | (~segmentP(V!46, Z!47))) <=> ((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(36,plain,
% 0.22/0.49 (((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | ((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)) | (~segmentP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | ((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[35])).
% 0.22/0.49 tff(37,plain,
% 0.22/0.49 (((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | ((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)) | (~segmentP(V!46, Z!47)))) <=> ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | (~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)))),
% 0.22/0.49 inference(transitivity,[status(thm)],[36, 34])).
% 0.22/0.49 tff(38,plain,
% 0.22/0.49 ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | ((~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45)) | (~segmentP(V!46, Z!47)))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(39,plain,
% 0.22/0.49 ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~neq(U!45, Y)) | (~segmentP(Y, U!45)) | (~segmentP(V!46, Y)))) | (~totalorderedP(Z!47)) | (~ssList(Z!47)) | (~segmentP(V!46, Z!47)) | (~neq(U!45, Z!47)) | (~segmentP(Z!47, U!45))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.49 tff(40,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[39, 33, 26, 24, 22, 20, 18])).
% 0.22/0.49 % SZS output end Proof
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------