TSTP Solution File: SWC086+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC086+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 11:55:09 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC086+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 21:33:00 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.34 Usage: tptp [options] [-file:]file
% 0.18/0.34 -h, -? prints this message.
% 0.18/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.34 -m, -model generate model.
% 0.18/0.34 -p, -proof generate proof.
% 0.18/0.34 -c, -core generate unsat core of named formulas.
% 0.18/0.34 -st, -statistics display statistics.
% 0.18/0.34 -t:timeout set timeout (in second).
% 0.18/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.34 -<param>:<value> configuration parameter and value.
% 0.18/0.34 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(segmentP_type, type, (
% 0.20/0.48 segmentP: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_W_49_type, type, (
% 0.20/0.48 tptp_fun_W_49: $i)).
% 0.20/0.48 tff(tptp_fun_V_48_type, type, (
% 0.20/0.48 tptp_fun_V_48: $i)).
% 0.20/0.48 tff(tptp_fun_X_50_type, type, (
% 0.20/0.48 tptp_fun_X_50: $i)).
% 0.20/0.48 tff(tptp_fun_U_47_type, type, (
% 0.20/0.48 tptp_fun_U_47: $i)).
% 0.20/0.48 tff(neq_type, type, (
% 0.20/0.48 neq: ( $i * $i ) > $o)).
% 0.20/0.48 tff(nil_type, type, (
% 0.20/0.48 nil: $i)).
% 0.20/0.48 tff(ssList_type, type, (
% 0.20/0.48 ssList: $i > $o)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 ((ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 ((ssList(W!49) & ((U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))) <=> (ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (((~(~(U!47 = W!49))) & (~(((~(nil = X!50)) | (~(nil = W!49))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))) <=> ((U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(6,plain,
% 0.20/0.48 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(((~(nil = X!50)) | (~(nil = W!49))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))) <=> (ssList(W!49) & ((U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[5, 4])).
% 0.20/0.48 tff(7,plain,
% 0.20/0.48 (((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(((~(nil = X!50)) | (~(nil = W!49))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))) <=> (ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[6, 3])).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(((~(nil = X!50)) | (~(nil = W!49))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))))) <=> (ssList(V!48) & (ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[8, 7])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(((~(nil = X!50)) | (~(nil = W!49))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))))) <=> (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[9, 2])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(((~(nil = X!50)) | (~(nil = W!49))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[11, 10])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(U!47 = W!49))) & (~(((~(nil = X!50)) | (~(nil = W!49))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (~(~(V!48 = X!50))) & (~(~neq(V!48, nil))) & (~(~ssList(X!50))) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[12, 1])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 ((~![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 = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(16,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 = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (((~(nil = X)) | (~(nil = W))) & ((~neq(W, nil)) | (~segmentP(X, W)))) | (~(V = X)) | (~neq(V, nil)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & neq(Y, nil) & segmentP(V, Y) & segmentP(U, Y))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (U!47 = W!49) & (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) & (V!48 = X!50) & neq(V!48, nil) & ssList(X!50) & ![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (V!48 = X!50),
% 0.20/0.48 inference(and_elim,[status(thm)],[24])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (segmentP(V!48, W!49) <=> segmentP(X!50, W!49)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (segmentP(X!50, W!49) <=> segmentP(V!48, W!49)),
% 0.20/0.48 inference(symmetry,[status(thm)],[26])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (ssList(X!50)),
% 0.20/0.48 inference(and_elim,[status(thm)],[24])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.48 tff(34,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.48 tff(37,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[36])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (segmentP(nil, X!50) <=> (nil = X!50)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.48 tff(51,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.48 tff(54,plain,(
% 0.20/0.48 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[53])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[58, 55, 28])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (ssList(nil) <=> ssList(nil)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(61,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (ssList(nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[65, 62, 59])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (X!50 = V!48),
% 0.20/0.48 inference(symmetry,[status(thm)],[25])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (neq(X!50, nil) <=> neq(V!48, nil)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (neq(V!48, nil) <=> neq(X!50, nil)),
% 0.20/0.48 inference(symmetry,[status(thm)],[68])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (neq(V!48, nil)),
% 0.20/0.48 inference(and_elim,[status(thm)],[24])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (neq(X!50, nil)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~(X!50 = nil))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (~(X!50 = nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[73, 66])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[78, 76])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (![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(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.49 tff(85,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.49 tff(88,plain,(
% 0.20/0.49 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[87])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 (((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~segmentP(V, X!50)) | (~ssList(V)) | (~segmentP(X!50, V)))) <=> ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~segmentP(V, X!50)) | (~ssList(V)) | (~segmentP(X!50, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~segmentP(V, X!50)) | (~ssList(V)) | (~segmentP(X!50, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~segmentP(V, X!50)) | (~ssList(V)) | (~segmentP(X!50, V))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~segmentP(V, U)) | (~ssList(V)) | (~segmentP(U, V))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[96, 90, 28])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.49 tff(103,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.49 tff(106,plain,(
% 0.20/0.49 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(skolemize,[status(sab)],[105])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (segmentP(X!50, nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[110, 107, 28])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (((~ssList(nil)) | (X!50 = nil) | (~segmentP(nil, X!50)) | (~segmentP(X!50, nil))) <=> ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(nil, X!50)) | (~segmentP(X!50, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[113])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(nil, X!50)) | (~segmentP(X!50, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(nil, X!50)) | (~segmentP(X!50, nil)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(V, X!50)) | (~segmentP(X!50, V)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[117, 62, 111, 97])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (~segmentP(nil, X!50)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[118, 74])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (~(nil = X!50)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[120, 119, 42])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (((~(nil = W!49)) | (~(nil = X!50))) | (nil = X!50)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 ((~(nil = W!49)) | (~(nil = X!50))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 ((~(~((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 ((((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))) <=> (~((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 ((~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) <=> (~(~((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[125])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 ((~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))) <=> ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[126, 124])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (~(((~(nil = W!49)) | (~(nil = X!50))) & ((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[24])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 ((~((~(nil = W!49)) | (~(nil = X!50)))) | (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (~((~neq(W!49, nil)) | (~segmentP(X!50, W!49)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[129, 123])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (((~neq(W!49, nil)) | (~segmentP(X!50, W!49))) | segmentP(X!50, W!49)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (segmentP(X!50, W!49)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (segmentP(V!48, W!49)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[132, 27])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (U!47 = W!49),
% 0.20/0.49 inference(and_elim,[status(thm)],[24])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (W!49 = U!47),
% 0.20/0.49 inference(symmetry,[status(thm)],[134])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (segmentP(W!49, W!49) <=> segmentP(U!47, W!49)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (ssList(W!49)),
% 0.20/0.49 inference(and_elim,[status(thm)],[24])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(142,plain,
% 0.20/0.49 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.49 tff(143,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax55')).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.20/0.49 tff(146,plain,(
% 0.20/0.49 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.49 inference(skolemize,[status(sab)],[145])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 (segmentP(W!49, W!49)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[150, 147, 137])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 (segmentP(U!47, W!49)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[151, 136])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 (((~neq(W!49, nil)) | (~segmentP(X!50, W!49))) | neq(W!49, nil)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 (neq(W!49, nil)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[153, 130])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (^[Y: $i] : refl(((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(156,plain,
% 0.20/0.49 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[155])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 (^[Y: $i] : trans(monotonicity(rewrite((ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)) <=> (~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> (~(~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))))), rewrite((~(~((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y))))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))), ((~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y))) <=> ![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[157])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (![Y: $i] : (~(ssList(Y) & neq(Y, nil) & segmentP(V!48, Y) & segmentP(U!47, Y)))),
% 0.20/0.49 inference(and_elim,[status(thm)],[24])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 (![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)) | (~segmentP(V!48, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)) | (~segmentP(V!48, W!49)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 (((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49))) <=> ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)) | (~segmentP(V!48, W!49)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)) | (~segmentP(V!48, W!49))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[163])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49)))) <=> ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)) | (~segmentP(V!48, W!49)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[164, 162])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | ((~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(V!48, W!49)) | (~segmentP(U!47, W!49)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 ((~![Y: $i] : ((~ssList(Y)) | (~neq(Y, nil)) | (~segmentP(V!48, Y)) | (~segmentP(U!47, Y)))) | (~ssList(W!49)) | (~neq(W!49, nil)) | (~segmentP(U!47, W!49)) | (~segmentP(V!48, W!49))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 ((~neq(W!49, nil)) | (~segmentP(U!47, W!49)) | (~segmentP(V!48, W!49))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[167, 137, 161])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (~segmentP(V!48, W!49)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[168, 154, 152])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[169, 133])).
% 0.20/0.50 % SZS output end Proof
%------------------------------------------------------------------------------