TSTP Solution File: SWC037+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC037+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 11:54:48 EDT 2022
% Result : Theorem 0.93s 0.81s
% Output : Proof 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC037+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 21:14:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.93/0.81 % SZS status Theorem
% 0.93/0.81 % SZS output start Proof
% 0.93/0.81 tff(neq_type, type, (
% 0.93/0.81 neq: ( $i * $i ) > $o)).
% 0.93/0.81 tff(tptp_fun_X_50_type, type, (
% 0.93/0.81 tptp_fun_X_50: $i)).
% 0.93/0.81 tff(tptp_fun_Y_51_type, type, (
% 0.93/0.81 tptp_fun_Y_51: $i)).
% 0.93/0.81 tff(nil_type, type, (
% 0.93/0.81 nil: $i)).
% 0.93/0.81 tff(tptp_fun_V_48_type, type, (
% 0.93/0.81 tptp_fun_V_48: $i)).
% 0.93/0.81 tff(tptp_fun_W_49_type, type, (
% 0.93/0.81 tptp_fun_W_49: $i)).
% 0.93/0.81 tff(ssList_type, type, (
% 0.93/0.81 ssList: $i > $o)).
% 0.93/0.81 tff(segmentP_type, type, (
% 0.93/0.81 segmentP: ( $i * $i ) > $o)).
% 0.93/0.81 tff(tptp_fun_U_47_type, type, (
% 0.93/0.81 tptp_fun_U_47: $i)).
% 0.93/0.81 tff(1,plain,
% 0.93/0.81 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(2,plain,
% 0.93/0.81 ((ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(3,plain,
% 0.93/0.81 ((ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(4,plain,
% 0.93/0.81 (((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))) <=> ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(5,plain,
% 0.93/0.81 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(6,plain,
% 0.93/0.81 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 0.93/0.81 inference(monotonicity,[status(thm)],[5, 4])).
% 0.93/0.81 tff(7,plain,
% 0.93/0.81 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 0.93/0.81 inference(transitivity,[status(thm)],[6, 3])).
% 0.93/0.81 tff(8,plain,
% 0.93/0.81 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(9,plain,
% 0.93/0.81 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 0.93/0.81 inference(monotonicity,[status(thm)],[8, 7])).
% 0.93/0.81 tff(10,plain,
% 0.93/0.81 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49)))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 0.93/0.81 inference(transitivity,[status(thm)],[9, 2])).
% 0.93/0.81 tff(11,plain,
% 0.93/0.81 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(12,plain,
% 0.93/0.81 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))))),
% 0.93/0.81 inference(monotonicity,[status(thm)],[11, 10])).
% 0.93/0.81 tff(13,plain,
% 0.93/0.81 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = X!50)) | (~(nil = W!49))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))))),
% 0.93/0.81 inference(transitivity,[status(thm)],[12, 1])).
% 0.93/0.81 tff(14,plain,
% 0.93/0.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(15,plain,
% 0.93/0.81 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W)))))))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(16,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)) | (![Y: $i] : (ssList(Y) => (((~neq(Y, nil)) | (~segmentP(X, Y))) | (~segmentP(W, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.93/0.81 tff(17,plain,
% 0.93/0.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.93/0.81 tff(18,plain,
% 0.93/0.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.93/0.81 tff(19,plain,
% 0.93/0.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.93/0.81 tff(20,plain,
% 0.93/0.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.93/0.81 tff(21,plain,
% 0.93/0.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.93/0.81 tff(22,plain,
% 0.93/0.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.93/0.81 tff(23,plain,
% 0.93/0.81 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | (![Y: $i] : ((~segmentP(W, Y)) | (~segmentP(X, Y)) | (~neq(Y, nil)) | (~ssList(Y))) & ((~(nil = X)) | (~(nil = W))))))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.93/0.81 tff(24,plain,
% 0.93/0.81 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50)))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.93/0.81 tff(25,plain,
% 0.93/0.81 (nil = V!48),
% 0.93/0.81 inference(and_elim,[status(thm)],[24])).
% 0.93/0.81 tff(26,plain,
% 0.93/0.81 (V!48 = nil),
% 0.93/0.81 inference(symmetry,[status(thm)],[25])).
% 0.93/0.81 tff(27,plain,
% 0.93/0.81 (V!48 = X!50),
% 0.93/0.81 inference(and_elim,[status(thm)],[24])).
% 0.93/0.81 tff(28,plain,
% 0.93/0.81 (X!50 = V!48),
% 0.93/0.81 inference(symmetry,[status(thm)],[27])).
% 0.93/0.81 tff(29,plain,
% 0.93/0.81 (X!50 = nil),
% 0.93/0.81 inference(transitivity,[status(thm)],[28, 26])).
% 0.93/0.81 tff(30,plain,
% 0.93/0.81 (neq(Y!51, X!50) <=> neq(Y!51, nil)),
% 0.93/0.81 inference(monotonicity,[status(thm)],[29])).
% 0.93/0.81 tff(31,plain,
% 0.93/0.81 (neq(Y!51, nil) <=> neq(Y!51, X!50)),
% 0.93/0.81 inference(symmetry,[status(thm)],[30])).
% 0.93/0.81 tff(32,plain,
% 0.93/0.81 (U!47 = W!49),
% 0.93/0.81 inference(and_elim,[status(thm)],[24])).
% 0.93/0.81 tff(33,plain,
% 0.93/0.81 ((nil = U!47) <=> (nil = W!49)),
% 0.93/0.81 inference(monotonicity,[status(thm)],[32])).
% 0.93/0.81 tff(34,plain,
% 0.93/0.81 ((~(nil = U!47)) <=> (~(nil = W!49))),
% 0.93/0.81 inference(monotonicity,[status(thm)],[33])).
% 0.93/0.81 tff(35,plain,
% 0.93/0.81 (~(nil = U!47)),
% 0.93/0.81 inference(and_elim,[status(thm)],[24])).
% 0.93/0.81 tff(36,plain,
% 0.93/0.81 (~(nil = W!49)),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.93/0.81 tff(37,plain,
% 0.93/0.81 (((~(nil = W!49)) | (~(nil = X!50))) | (nil = W!49)),
% 0.93/0.81 inference(tautology,[status(thm)],[])).
% 0.93/0.81 tff(38,plain,
% 0.93/0.81 ((~(nil = W!49)) | (~(nil = X!50))),
% 0.93/0.81 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.93/0.81 tff(39,plain,
% 0.93/0.81 ((~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))) | (~((~(nil = W!49)) | (~(nil = X!50))))),
% 0.93/0.81 inference(and_elim,[status(thm)],[24])).
% 0.93/0.81 tff(40,plain,
% 0.93/0.81 (~((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51)))),
% 0.93/0.81 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.93/0.81 tff(41,plain,
% 0.93/0.81 (((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51))) | neq(Y!51, nil)),
% 0.93/0.81 inference(tautology,[status(thm)],[])).
% 0.93/0.81 tff(42,plain,
% 0.93/0.81 (neq(Y!51, nil)),
% 0.93/0.81 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.93/0.81 tff(43,plain,
% 0.93/0.81 (neq(Y!51, X!50)),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[42, 31])).
% 0.93/0.81 tff(44,plain,
% 0.93/0.81 (((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51))) | ssList(Y!51)),
% 0.93/0.81 inference(tautology,[status(thm)],[])).
% 0.93/0.81 tff(45,plain,
% 0.93/0.81 (ssList(Y!51)),
% 0.93/0.81 inference(unit_resolution,[status(thm)],[44, 40])).
% 0.93/0.81 tff(46,plain,
% 0.93/0.81 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.93/0.81 inference(bind,[status(th)],[])).
% 0.93/0.81 tff(47,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(quant_intro,[status(thm)],[46])).
% 0.93/0.81 tff(48,plain,
% 0.93/0.81 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.93/0.81 inference(bind,[status(th)],[])).
% 0.93/0.81 tff(49,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(quant_intro,[status(thm)],[48])).
% 0.93/0.81 tff(50,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(transitivity,[status(thm)],[49, 47])).
% 0.93/0.81 tff(51,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(52,plain,
% 0.93/0.81 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))))),
% 0.93/0.81 inference(bind,[status(th)],[])).
% 0.93/0.81 tff(53,plain,
% 0.93/0.81 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(quant_intro,[status(thm)],[52])).
% 0.93/0.81 tff(54,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.93/0.81 tff(55,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.93/0.81 tff(56,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.93/0.81 tff(57,plain,(
% 0.93/0.81 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(skolemize,[status(sab)],[56])).
% 0.93/0.81 tff(58,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.93/0.81 tff(59,plain,
% 0.93/0.81 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V)))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(60,plain,
% 0.93/0.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V)))))),
% 0.93/0.81 inference(quant_inst,[status(thm)],[])).
% 0.93/0.81 tff(61,plain,
% 0.93/0.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.93/0.81 tff(62,plain,
% 0.93/0.81 (![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))),
% 0.93/0.81 inference(unit_resolution,[status(thm)],[61, 58, 45])).
% 0.93/0.81 tff(63,plain,
% 0.93/0.81 (ssList(X!50)),
% 0.93/0.81 inference(and_elim,[status(thm)],[24])).
% 0.93/0.81 tff(64,plain,
% 0.93/0.81 (((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | ((~ssList(X!50)) | (neq(Y!51, X!50) <=> (~(Y!51 = X!50))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | (~ssList(X!50)) | (neq(Y!51, X!50) <=> (~(Y!51 = X!50))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(65,plain,
% 0.93/0.81 ((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | ((~ssList(X!50)) | (neq(Y!51, X!50) <=> (~(Y!51 = X!50))))),
% 0.93/0.81 inference(quant_inst,[status(thm)],[])).
% 0.93/0.81 tff(66,plain,
% 0.93/0.81 ((~![V: $i] : ((~ssList(V)) | (neq(Y!51, V) <=> (~(Y!51 = V))))) | (~ssList(X!50)) | (neq(Y!51, X!50) <=> (~(Y!51 = X!50)))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.93/0.81 tff(67,plain,
% 0.93/0.81 (neq(Y!51, X!50) <=> (~(Y!51 = X!50))),
% 0.93/0.81 inference(unit_resolution,[status(thm)],[66, 63, 62])).
% 0.93/0.81 tff(68,plain,
% 0.93/0.81 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.93/0.81 inference(bind,[status(th)],[])).
% 0.93/0.81 tff(69,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.93/0.81 inference(quant_intro,[status(thm)],[68])).
% 0.93/0.81 tff(70,plain,
% 0.93/0.81 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.93/0.81 inference(bind,[status(th)],[])).
% 0.93/0.81 tff(71,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.93/0.81 inference(quant_intro,[status(thm)],[70])).
% 0.93/0.81 tff(72,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.93/0.81 inference(transitivity,[status(thm)],[71, 69])).
% 0.93/0.81 tff(73,plain,
% 0.93/0.81 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U)))))),
% 0.93/0.81 inference(bind,[status(th)],[])).
% 0.93/0.81 tff(74,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.93/0.81 inference(quant_intro,[status(thm)],[73])).
% 0.93/0.81 tff(75,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(76,plain,
% 0.93/0.81 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 0.93/0.81 inference(bind,[status(th)],[])).
% 0.93/0.81 tff(77,plain,
% 0.93/0.81 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.93/0.81 inference(quant_intro,[status(thm)],[76])).
% 0.93/0.81 tff(78,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.93/0.81 tff(79,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.93/0.81 tff(80,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.93/0.81 tff(81,plain,(
% 0.93/0.81 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.93/0.81 inference(skolemize,[status(sab)],[80])).
% 0.93/0.81 tff(82,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.93/0.81 tff(83,plain,
% 0.93/0.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))),
% 0.93/0.81 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.93/0.81 tff(84,plain,
% 0.93/0.81 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(85,plain,
% 0.93/0.81 (((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51)))) <=> ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))),
% 0.93/0.81 inference(rewrite,[status(thm)],[])).
% 0.93/0.81 tff(86,plain,
% 0.93/0.81 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))))),
% 0.93/0.82 inference(monotonicity,[status(thm)],[85])).
% 0.93/0.82 tff(87,plain,
% 0.93/0.82 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51))))),
% 0.93/0.82 inference(transitivity,[status(thm)],[86, 84])).
% 0.93/0.82 tff(88,plain,
% 0.93/0.82 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | ((~ssList(Y!51)) | ![V: $i] : ((Y!51 = V) | (~segmentP(Y!51, V)) | (~ssList(V)) | (~segmentP(V, Y!51))))),
% 0.93/0.82 inference(quant_inst,[status(thm)],[])).
% 0.93/0.82 tff(89,plain,
% 0.93/0.82 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(U, V)) | (~ssList(V)) | (~segmentP(V, U))))) | (~ssList(Y!51)) | ![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.93/0.82 tff(90,plain,
% 0.93/0.82 (![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[89, 83, 45])).
% 0.93/0.82 tff(91,plain,
% 0.93/0.82 (nil = X!50),
% 0.93/0.82 inference(transitivity,[status(thm)],[25, 27])).
% 0.93/0.82 tff(92,plain,
% 0.93/0.82 (segmentP(Y!51, nil) <=> segmentP(Y!51, X!50)),
% 0.93/0.82 inference(monotonicity,[status(thm)],[91])).
% 0.93/0.82 tff(93,plain,
% 0.93/0.82 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.93/0.82 inference(bind,[status(th)],[])).
% 0.93/0.82 tff(94,plain,
% 0.93/0.82 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.93/0.82 inference(quant_intro,[status(thm)],[93])).
% 0.93/0.82 tff(95,plain,
% 0.93/0.82 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.93/0.82 inference(rewrite,[status(thm)],[])).
% 0.93/0.82 tff(96,plain,
% 0.93/0.82 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.93/0.82 inference(bind,[status(th)],[])).
% 0.93/0.82 tff(97,plain,
% 0.93/0.82 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.93/0.82 inference(quant_intro,[status(thm)],[96])).
% 0.93/0.82 tff(98,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.93/0.82 tff(99,plain,
% 0.93/0.82 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.93/0.82 tff(100,plain,
% 0.93/0.82 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.93/0.82 tff(101,plain,(
% 0.93/0.82 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.93/0.82 inference(skolemize,[status(sab)],[100])).
% 0.93/0.82 tff(102,plain,
% 0.93/0.82 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.93/0.82 tff(103,plain,
% 0.93/0.82 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(Y!51)) | segmentP(Y!51, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(Y!51)) | segmentP(Y!51, nil))),
% 0.93/0.82 inference(rewrite,[status(thm)],[])).
% 0.93/0.82 tff(104,plain,
% 0.93/0.82 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(Y!51)) | segmentP(Y!51, nil))),
% 0.93/0.82 inference(quant_inst,[status(thm)],[])).
% 0.93/0.82 tff(105,plain,
% 0.93/0.82 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(Y!51)) | segmentP(Y!51, nil)),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.93/0.82 tff(106,plain,
% 0.93/0.82 (segmentP(Y!51, nil)),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[105, 102, 45])).
% 0.93/0.82 tff(107,plain,
% 0.93/0.82 (segmentP(Y!51, X!50)),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[106, 92])).
% 0.93/0.82 tff(108,plain,
% 0.93/0.82 (((~segmentP(W!49, Y!51)) | (~segmentP(X!50, Y!51)) | (~neq(Y!51, nil)) | (~ssList(Y!51))) | segmentP(X!50, Y!51)),
% 0.93/0.82 inference(tautology,[status(thm)],[])).
% 0.93/0.82 tff(109,plain,
% 0.93/0.82 (segmentP(X!50, Y!51)),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[108, 40])).
% 0.93/0.82 tff(110,plain,
% 0.93/0.82 (((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(X!50)) | (~segmentP(X!50, Y!51)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | (~ssList(X!50)) | (~segmentP(X!50, Y!51)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50))),
% 0.93/0.82 inference(rewrite,[status(thm)],[])).
% 0.93/0.82 tff(111,plain,
% 0.93/0.82 (((~ssList(X!50)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50) | (~segmentP(X!50, Y!51))) <=> ((~ssList(X!50)) | (~segmentP(X!50, Y!51)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50))),
% 0.93/0.82 inference(rewrite,[status(thm)],[])).
% 0.93/0.82 tff(112,plain,
% 0.93/0.82 (((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(X!50)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50) | (~segmentP(X!50, Y!51)))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(X!50)) | (~segmentP(X!50, Y!51)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50)))),
% 0.93/0.82 inference(monotonicity,[status(thm)],[111])).
% 0.93/0.82 tff(113,plain,
% 0.93/0.82 (((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(X!50)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50) | (~segmentP(X!50, Y!51)))) <=> ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | (~ssList(X!50)) | (~segmentP(X!50, Y!51)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50))),
% 0.93/0.82 inference(transitivity,[status(thm)],[112, 110])).
% 0.93/0.82 tff(114,plain,
% 0.93/0.82 ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | ((~ssList(X!50)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50) | (~segmentP(X!50, Y!51)))),
% 0.93/0.82 inference(quant_inst,[status(thm)],[])).
% 0.93/0.82 tff(115,plain,
% 0.93/0.82 ((~![V: $i] : ((~ssList(V)) | (~segmentP(Y!51, V)) | (Y!51 = V) | (~segmentP(V, Y!51)))) | (~ssList(X!50)) | (~segmentP(X!50, Y!51)) | (~segmentP(Y!51, X!50)) | (Y!51 = X!50)),
% 0.93/0.82 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.93/0.82 tff(116,plain,
% 0.93/0.82 (Y!51 = X!50),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[115, 63, 109, 107, 90])).
% 0.93/0.82 tff(117,plain,
% 0.93/0.82 ((~(neq(Y!51, X!50) <=> (~(Y!51 = X!50)))) | (~neq(Y!51, X!50)) | (~(Y!51 = X!50))),
% 0.93/0.82 inference(tautology,[status(thm)],[])).
% 0.93/0.82 tff(118,plain,
% 0.93/0.82 ((~(neq(Y!51, X!50) <=> (~(Y!51 = X!50)))) | (~neq(Y!51, X!50))),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.93/0.82 tff(119,plain,
% 0.93/0.82 (~neq(Y!51, X!50)),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[118, 67])).
% 0.93/0.82 tff(120,plain,
% 0.93/0.82 ($false),
% 0.93/0.82 inference(unit_resolution,[status(thm)],[119, 43])).
% 0.93/0.82 % SZS output end Proof
%------------------------------------------------------------------------------