TSTP Solution File: SWC333+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC333+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Tue Sep 20 11:57:10 EDT 2022
% Result : Theorem 1.21s 1.00s
% Output : Proof 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWC333+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n026.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Sep 4 00:19:39 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.32 Usage: tptp [options] [-file:]file
% 0.12/0.32 -h, -? prints this message.
% 0.12/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.32 -m, -model generate model.
% 0.12/0.32 -p, -proof generate proof.
% 0.12/0.32 -c, -core generate unsat core of named formulas.
% 0.12/0.32 -st, -statistics display statistics.
% 0.12/0.32 -t:timeout set timeout (in second).
% 0.12/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.32 -<param>:<value> configuration parameter and value.
% 0.12/0.32 -o:<output-file> file to place output in.
% 1.21/1.00 % SZS status Theorem
% 1.21/1.00 % SZS output start Proof
% 1.21/1.00 tff(segmentP_type, type, (
% 1.21/1.00 segmentP: ( $i * $i ) > $o)).
% 1.21/1.00 tff(tptp_fun_Z_51_type, type, (
% 1.21/1.00 tptp_fun_Z_51: $i)).
% 1.21/1.00 tff(tptp_fun_X_50_type, type, (
% 1.21/1.00 tptp_fun_X_50: $i)).
% 1.21/1.00 tff(tptp_fun_V_48_type, type, (
% 1.21/1.00 tptp_fun_V_48: $i)).
% 1.21/1.00 tff(totalorderedP_type, type, (
% 1.21/1.00 totalorderedP: $i > $o)).
% 1.21/1.00 tff(tptp_fun_U_47_type, type, (
% 1.21/1.00 tptp_fun_U_47: $i)).
% 1.21/1.00 tff(ssList_type, type, (
% 1.21/1.00 ssList: $i > $o)).
% 1.21/1.00 tff(neq_type, type, (
% 1.21/1.00 neq: ( $i * $i ) > $o)).
% 1.21/1.00 tff(tptp_fun_W_49_type, type, (
% 1.21/1.00 tptp_fun_W_49: $i)).
% 1.21/1.00 tff(1,plain,
% 1.21/1.00 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(2,plain,
% 1.21/1.00 ((ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(3,plain,
% 1.21/1.00 ((ssList(W!49) & ((U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))) <=> (ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(4,plain,
% 1.21/1.00 (((~(~(U!47 = W!49))) & (~(~totalorderedP(W!49))) & (~(~(V!48 = X!50))) & (~(~segmentP(X!50, W!49))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))) <=> ((U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(5,plain,
% 1.21/1.00 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(6,plain,
% 1.21/1.00 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~totalorderedP(W!49))) & (~(~(V!48 = X!50))) & (~(~segmentP(X!50, W!49))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))) <=> (ssList(W!49) & ((U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))))),
% 1.21/1.00 inference(monotonicity,[status(thm)],[5, 4])).
% 1.21/1.00 tff(7,plain,
% 1.21/1.00 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~totalorderedP(W!49))) & (~(~(V!48 = X!50))) & (~(~segmentP(X!50, W!49))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))) <=> (ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 1.21/1.00 inference(transitivity,[status(thm)],[6, 3])).
% 1.21/1.00 tff(8,plain,
% 1.21/1.00 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(9,plain,
% 1.21/1.00 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~totalorderedP(W!49))) & (~(~(V!48 = X!50))) & (~(~segmentP(X!50, W!49))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))))) <=> (ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))))),
% 1.21/1.00 inference(monotonicity,[status(thm)],[8, 7])).
% 1.21/1.00 tff(10,plain,
% 1.21/1.00 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~totalorderedP(W!49))) & (~(~(V!48 = X!50))) & (~(~segmentP(X!50, W!49))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 1.21/1.00 inference(transitivity,[status(thm)],[9, 2])).
% 1.21/1.00 tff(11,plain,
% 1.21/1.00 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 1.21/1.00 inference(rewrite,[status(thm)],[])).
% 1.21/1.00 tff(12,plain,
% 1.21/1.00 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~totalorderedP(W!49))) & (~(~(V!48 = X!50))) & (~(~segmentP(X!50, W!49))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))))),
% 1.21/1.01 inference(monotonicity,[status(thm)],[11, 10])).
% 1.21/1.01 tff(13,plain,
% 1.21/1.01 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(~totalorderedP(W!49))) & (~(~(V!48 = X!50))) & (~(~segmentP(X!50, W!49))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))))),
% 1.21/1.01 inference(transitivity,[status(thm)],[12, 1])).
% 1.21/1.01 tff(14,plain,
% 1.21/1.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U)))))))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(15,plain,
% 1.21/1.01 ((~![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] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U)))))))),
% 1.21/1.01 inference(rewrite,[status(thm)],[])).
% 1.21/1.01 tff(16,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/sandbox2/benchmark/theBenchmark.p','co1')).
% 1.21/1.01 tff(17,plain,
% 1.21/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.21/1.01 tff(18,plain,
% 1.21/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[17, 14])).
% 1.21/1.01 tff(19,plain,
% 1.21/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.21/1.01 tff(20,plain,
% 1.21/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[19, 14])).
% 1.21/1.01 tff(21,plain,
% 1.21/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[20, 14])).
% 1.21/1.01 tff(22,plain,
% 1.21/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.21/1.01 tff(23,plain,
% 1.21/1.01 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (~totalorderedP(W)) | (~(V = X)) | (~segmentP(X, W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(W, Y) & segmentP(X, Y) & segmentP(Y, W) & totalorderedP(Y)) | (![Z: $i] : ((~segmentP(V, Z)) | (~neq(U, Z)) | (~segmentP(Z, U)) | (~totalorderedP(Z)) | (~ssList(Z))) & segmentP(V, U) & totalorderedP(U))))))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[22, 14])).
% 1.21/1.01 tff(24,plain,
% 1.21/1.01 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & totalorderedP(W!49) & (V!48 = X!50) & segmentP(X!50, W!49) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) & ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47)))),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.21/1.01 tff(25,plain,
% 1.21/1.01 (V!48 = X!50),
% 1.21/1.01 inference(and_elim,[status(thm)],[24])).
% 1.21/1.01 tff(26,plain,
% 1.21/1.01 (X!50 = V!48),
% 1.21/1.01 inference(symmetry,[status(thm)],[25])).
% 1.21/1.01 tff(27,plain,
% 1.21/1.01 (segmentP(X!50, Z!51) <=> segmentP(V!48, Z!51)),
% 1.21/1.01 inference(monotonicity,[status(thm)],[26])).
% 1.21/1.01 tff(28,plain,
% 1.21/1.01 (segmentP(V!48, Z!51) <=> segmentP(X!50, Z!51)),
% 1.21/1.01 inference(symmetry,[status(thm)],[27])).
% 1.21/1.01 tff(29,plain,
% 1.21/1.01 (U!47 = W!49),
% 1.21/1.01 inference(and_elim,[status(thm)],[24])).
% 1.21/1.01 tff(30,plain,
% 1.21/1.01 (totalorderedP(U!47) <=> totalorderedP(W!49)),
% 1.21/1.01 inference(monotonicity,[status(thm)],[29])).
% 1.21/1.01 tff(31,plain,
% 1.21/1.01 (totalorderedP(W!49) <=> totalorderedP(U!47)),
% 1.21/1.01 inference(symmetry,[status(thm)],[30])).
% 1.21/1.01 tff(32,plain,
% 1.21/1.01 (totalorderedP(W!49)),
% 1.21/1.01 inference(and_elim,[status(thm)],[24])).
% 1.21/1.01 tff(33,plain,
% 1.21/1.01 (totalorderedP(U!47)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.21/1.01 tff(34,plain,
% 1.21/1.01 (segmentP(V!48, U!47) <=> segmentP(X!50, W!49)),
% 1.21/1.01 inference(monotonicity,[status(thm)],[25, 29])).
% 1.21/1.01 tff(35,plain,
% 1.21/1.01 (segmentP(X!50, W!49) <=> segmentP(V!48, U!47)),
% 1.21/1.01 inference(symmetry,[status(thm)],[34])).
% 1.21/1.01 tff(36,plain,
% 1.21/1.01 (segmentP(X!50, W!49)),
% 1.21/1.01 inference(and_elim,[status(thm)],[24])).
% 1.21/1.01 tff(37,plain,
% 1.21/1.01 (segmentP(V!48, U!47)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.21/1.01 tff(38,plain,
% 1.21/1.01 ((~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))) | (~segmentP(V!48, U!47)) | (~totalorderedP(U!47))),
% 1.21/1.01 inference(and_elim,[status(thm)],[24])).
% 1.21/1.01 tff(39,plain,
% 1.21/1.01 (~((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51)))),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[38, 37, 33])).
% 1.21/1.01 tff(40,plain,
% 1.21/1.01 (((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51))) | segmentP(V!48, Z!51)),
% 1.21/1.01 inference(tautology,[status(thm)],[])).
% 1.21/1.01 tff(41,plain,
% 1.21/1.01 (segmentP(V!48, Z!51)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[40, 39])).
% 1.21/1.01 tff(42,plain,
% 1.21/1.01 (segmentP(X!50, Z!51)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[41, 28])).
% 1.21/1.01 tff(43,plain,
% 1.21/1.01 (W!49 = U!47),
% 1.21/1.01 inference(symmetry,[status(thm)],[29])).
% 1.21/1.01 tff(44,plain,
% 1.21/1.01 (segmentP(Z!51, W!49) <=> segmentP(Z!51, U!47)),
% 1.21/1.01 inference(monotonicity,[status(thm)],[43])).
% 1.21/1.01 tff(45,plain,
% 1.21/1.01 (segmentP(Z!51, U!47) <=> segmentP(Z!51, W!49)),
% 1.21/1.01 inference(symmetry,[status(thm)],[44])).
% 1.21/1.01 tff(46,plain,
% 1.21/1.01 (((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51))) | segmentP(Z!51, U!47)),
% 1.21/1.01 inference(tautology,[status(thm)],[])).
% 1.21/1.01 tff(47,plain,
% 1.21/1.01 (segmentP(Z!51, U!47)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[46, 39])).
% 1.21/1.01 tff(48,plain,
% 1.21/1.01 (segmentP(Z!51, W!49)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[47, 45])).
% 1.21/1.01 tff(49,plain,
% 1.21/1.01 (neq(W!49, Z!51) <=> neq(U!47, Z!51)),
% 1.21/1.01 inference(monotonicity,[status(thm)],[43])).
% 1.21/1.01 tff(50,plain,
% 1.21/1.01 (neq(U!47, Z!51) <=> neq(W!49, Z!51)),
% 1.21/1.01 inference(symmetry,[status(thm)],[49])).
% 1.21/1.01 tff(51,plain,
% 1.21/1.01 (((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51))) | neq(U!47, Z!51)),
% 1.21/1.01 inference(tautology,[status(thm)],[])).
% 1.21/1.01 tff(52,plain,
% 1.21/1.01 (neq(U!47, Z!51)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[51, 39])).
% 1.21/1.01 tff(53,plain,
% 1.21/1.01 (neq(W!49, Z!51)),
% 1.21/1.01 inference(modus_ponens,[status(thm)],[52, 50])).
% 1.21/1.01 tff(54,plain,
% 1.21/1.01 (((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51))) | ssList(Z!51)),
% 1.21/1.01 inference(tautology,[status(thm)],[])).
% 1.21/1.01 tff(55,plain,
% 1.21/1.01 (ssList(Z!51)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[54, 39])).
% 1.21/1.01 tff(56,plain,
% 1.21/1.01 (((~segmentP(V!48, Z!51)) | (~neq(U!47, Z!51)) | (~segmentP(Z!51, U!47)) | (~totalorderedP(Z!51)) | (~ssList(Z!51))) | totalorderedP(Z!51)),
% 1.21/1.01 inference(tautology,[status(thm)],[])).
% 1.21/1.01 tff(57,plain,
% 1.21/1.01 (totalorderedP(Z!51)),
% 1.21/1.01 inference(unit_resolution,[status(thm)],[56, 39])).
% 1.21/1.01 tff(58,plain,
% 1.21/1.01 (^[Y: $i] : refl(((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y))) <=> ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y))))),
% 1.21/1.01 inference(bind,[status(th)],[])).
% 1.21/1.01 tff(59,plain,
% 1.21/1.01 (![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y))) <=> ![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))),
% 1.21/1.02 inference(quant_intro,[status(thm)],[58])).
% 1.21/1.02 tff(60,plain,
% 1.21/1.02 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y)) <=> (~((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y))))), ((~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) <=> (~(~((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y))))))), rewrite((~(~((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y))))) <=> ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))), ((~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) <=> ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))))),
% 1.21/1.02 inference(bind,[status(th)],[])).
% 1.21/1.02 tff(61,plain,
% 1.21/1.02 (![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y))) <=> ![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))),
% 1.21/1.02 inference(quant_intro,[status(thm)],[60])).
% 1.21/1.02 tff(62,plain,
% 1.21/1.02 (![Y: $i] : (~(ssList(Y) & neq(W!49, Y) & segmentP(X!50, Y) & segmentP(Y, W!49) & totalorderedP(Y)))),
% 1.21/1.02 inference(and_elim,[status(thm)],[24])).
% 1.21/1.02 tff(63,plain,
% 1.21/1.02 (![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.21/1.02 tff(64,plain,
% 1.21/1.02 (![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[63, 59])).
% 1.21/1.02 tff(65,plain,
% 1.21/1.02 (((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))) | ((~totalorderedP(Z!51)) | (~ssList(Z!51)) | (~segmentP(Z!51, W!49)) | (~neq(W!49, Z!51)) | (~segmentP(X!50, Z!51)))) <=> ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))) | (~totalorderedP(Z!51)) | (~ssList(Z!51)) | (~segmentP(Z!51, W!49)) | (~neq(W!49, Z!51)) | (~segmentP(X!50, Z!51)))),
% 1.21/1.02 inference(rewrite,[status(thm)],[])).
% 1.21/1.02 tff(66,plain,
% 1.21/1.02 ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))) | ((~totalorderedP(Z!51)) | (~ssList(Z!51)) | (~segmentP(Z!51, W!49)) | (~neq(W!49, Z!51)) | (~segmentP(X!50, Z!51)))),
% 1.21/1.02 inference(quant_inst,[status(thm)],[])).
% 1.21/1.02 tff(67,plain,
% 1.21/1.02 ((~![Y: $i] : ((~totalorderedP(Y)) | (~ssList(Y)) | (~segmentP(Y, W!49)) | (~neq(W!49, Y)) | (~segmentP(X!50, Y)))) | (~totalorderedP(Z!51)) | (~ssList(Z!51)) | (~segmentP(Z!51, W!49)) | (~neq(W!49, Z!51)) | (~segmentP(X!50, Z!51))),
% 1.21/1.02 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.21/1.02 tff(68,plain,
% 1.21/1.02 ((~segmentP(Z!51, W!49)) | (~neq(W!49, Z!51)) | (~segmentP(X!50, Z!51))),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[67, 64, 57, 55])).
% 1.21/1.02 tff(69,plain,
% 1.21/1.02 ($false),
% 1.21/1.02 inference(unit_resolution,[status(thm)],[68, 53, 48, 42])).
% 1.21/1.02 % SZS output end Proof
%------------------------------------------------------------------------------