TSTP Solution File: SWC122+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC122+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 11:55:24 EDT 2022
% Result : Theorem 5.57s 3.83s
% Output : Proof 5.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC122+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 21:53:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 5.57/3.83 % SZS status Theorem
% 5.57/3.83 % SZS output start Proof
% 5.57/3.83 tff(segmentP_type, type, (
% 5.57/3.83 segmentP: ( $i * $i ) > $o)).
% 5.57/3.83 tff(tptp_fun_W_49_type, type, (
% 5.57/3.83 tptp_fun_W_49: $i)).
% 5.57/3.83 tff(app_type, type, (
% 5.57/3.83 app: ( $i * $i ) > $i)).
% 5.57/3.83 tff(nil_type, type, (
% 5.57/3.83 nil: $i)).
% 5.57/3.83 tff(tptp_fun_W_6_type, type, (
% 5.57/3.83 tptp_fun_W_6: ( $i * $i ) > $i)).
% 5.57/3.83 tff(tptp_fun_X_50_type, type, (
% 5.57/3.83 tptp_fun_X_50: $i)).
% 5.57/3.83 tff(tptp_fun_U_47_type, type, (
% 5.57/3.83 tptp_fun_U_47: $i)).
% 5.57/3.83 tff(tptp_fun_V_48_type, type, (
% 5.57/3.83 tptp_fun_V_48: $i)).
% 5.57/3.83 tff(ssList_type, type, (
% 5.57/3.83 ssList: $i > $o)).
% 5.57/3.83 tff(rearsegP_type, type, (
% 5.57/3.83 rearsegP: ( $i * $i ) > $o)).
% 5.57/3.83 tff(neq_type, type, (
% 5.57/3.83 neq: ( $i * $i ) > $o)).
% 5.57/3.83 tff(1,plain,
% 5.57/3.83 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 5.57/3.83 inference(rewrite,[status(thm)],[])).
% 5.57/3.83 tff(2,plain,
% 5.57/3.83 ((ssList(V!48) & (ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 5.57/3.83 inference(rewrite,[status(thm)],[])).
% 5.57/3.83 tff(3,plain,
% 5.57/3.83 (((~(~ssList(W!49))) & (~((~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 5.57/3.83 inference(rewrite,[status(thm)],[])).
% 5.57/3.83 tff(4,plain,
% 5.57/3.83 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 5.57/3.83 inference(rewrite,[status(thm)],[])).
% 5.57/3.83 tff(5,plain,
% 5.57/3.83 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50))))))),
% 5.57/3.83 inference(monotonicity,[status(thm)],[4, 3])).
% 5.57/3.83 tff(6,plain,
% 5.57/3.83 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 5.57/3.83 inference(transitivity,[status(thm)],[5, 2])).
% 5.57/3.83 tff(7,plain,
% 5.57/3.83 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 5.57/3.83 inference(rewrite,[status(thm)],[])).
% 5.57/3.83 tff(8,plain,
% 5.57/3.83 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50))))))),
% 5.57/3.84 inference(monotonicity,[status(thm)],[7, 6])).
% 5.57/3.84 tff(9,plain,
% 5.57/3.84 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~((~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))))),
% 5.57/3.84 inference(transitivity,[status(thm)],[8, 1])).
% 5.57/3.84 tff(10,plain,
% 5.57/3.84 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X)))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(11,plain,
% 5.57/3.84 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ((~(nil = W)) & (nil = X))) | (neq(U, nil) & segmentP(V, U))) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X)))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ((~(nil = W)) & (nil = X))) | (neq(U, nil) & segmentP(V, U))) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 5.57/3.84 tff(13,plain,
% 5.57/3.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[12, 11])).
% 5.57/3.84 tff(14,plain,
% 5.57/3.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[13, 10])).
% 5.57/3.84 tff(15,plain,
% 5.57/3.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[14, 10])).
% 5.57/3.84 tff(16,plain,
% 5.57/3.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[15, 10])).
% 5.57/3.84 tff(17,plain,
% 5.57/3.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[16, 10])).
% 5.57/3.84 tff(18,plain,
% 5.57/3.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[17, 10])).
% 5.57/3.84 tff(19,plain,
% 5.57/3.84 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(U = W)) | (neq(X, nil) & ((~neq(W, nil)) | (~rearsegP(X, W)))) | (~(V = X)) | ((~(nil = W)) & (nil = X)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)) | (~ssList(X))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[18, 10])).
% 5.57/3.84 tff(20,plain,
% 5.57/3.84 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[19, 9])).
% 5.57/3.84 tff(21,plain,
% 5.57/3.84 (~((neq(U!47, nil) & segmentP(V!48, U!47)) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | (neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) | (~(V!48 = X!50)) | ((~(nil = W!49)) & (nil = X!50)) | (~ssList(X!50)))),
% 5.57/3.84 inference(and_elim,[status(thm)],[20])).
% 5.57/3.84 tff(22,plain,
% 5.57/3.84 (U!47 = W!49),
% 5.57/3.84 inference(or_elim,[status(thm)],[21])).
% 5.57/3.84 tff(23,plain,
% 5.57/3.84 (W!49 = U!47),
% 5.57/3.84 inference(symmetry,[status(thm)],[22])).
% 5.57/3.84 tff(24,plain,
% 5.57/3.84 (V!48 = X!50),
% 5.57/3.84 inference(or_elim,[status(thm)],[21])).
% 5.57/3.84 tff(25,plain,
% 5.57/3.84 (X!50 = V!48),
% 5.57/3.84 inference(symmetry,[status(thm)],[24])).
% 5.57/3.84 tff(26,plain,
% 5.57/3.84 (ssList(X!50)),
% 5.57/3.84 inference(or_elim,[status(thm)],[21])).
% 5.57/3.84 tff(27,plain,
% 5.57/3.84 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(28,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[27])).
% 5.57/3.84 tff(29,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(30,plain,
% 5.57/3.84 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(31,plain,
% 5.57/3.84 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[30])).
% 5.57/3.84 tff(32,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 5.57/3.84 tff(33,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[32, 31])).
% 5.57/3.84 tff(34,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[33, 29])).
% 5.57/3.84 tff(35,plain,(
% 5.57/3.84 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 5.57/3.84 inference(skolemize,[status(sab)],[34])).
% 5.57/3.84 tff(36,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[35, 28])).
% 5.57/3.84 tff(37,plain,
% 5.57/3.84 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(38,plain,
% 5.57/3.84 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 5.57/3.84 inference(quant_inst,[status(thm)],[])).
% 5.57/3.84 tff(39,plain,
% 5.57/3.84 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50)),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[38, 37])).
% 5.57/3.84 tff(40,plain,
% 5.57/3.84 (app(X!50, nil) = X!50),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 5.57/3.84 tff(41,plain,
% 5.57/3.84 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(42,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[41])).
% 5.57/3.84 tff(43,plain,
% 5.57/3.84 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(44,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[43])).
% 5.57/3.84 tff(45,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 5.57/3.84 inference(transitivity,[status(thm)],[44, 42])).
% 5.57/3.84 tff(46,plain,
% 5.57/3.84 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(47,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[46])).
% 5.57/3.84 tff(48,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(49,plain,
% 5.57/3.84 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))) <=> (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), rewrite((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), (![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(50,plain,
% 5.57/3.84 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[49])).
% 5.57/3.84 tff(51,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax6')).
% 5.57/3.84 tff(52,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[51, 50])).
% 5.57/3.84 tff(53,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[52, 48])).
% 5.57/3.84 tff(54,plain,(
% 5.57/3.84 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U)))))))),
% 5.57/3.84 inference(skolemize,[status(sab)],[53])).
% 5.57/3.84 tff(55,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[54, 47])).
% 5.57/3.84 tff(56,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[55, 45])).
% 5.57/3.84 tff(57,plain,
% 5.57/3.84 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50)))))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(58,plain,
% 5.57/3.84 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50)))))))))),
% 5.57/3.84 inference(quant_inst,[status(thm)],[])).
% 5.57/3.84 tff(59,plain,
% 5.57/3.84 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[58, 57])).
% 5.57/3.84 tff(60,plain,
% 5.57/3.84 (![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[59, 56, 26])).
% 5.57/3.84 tff(61,plain,
% 5.57/3.84 (ssList(W!49)),
% 5.57/3.84 inference(and_elim,[status(thm)],[20])).
% 5.57/3.84 tff(62,plain,
% 5.57/3.84 (((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | ((~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | (~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(63,plain,
% 5.57/3.84 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | ((~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))))),
% 5.57/3.84 inference(quant_inst,[status(thm)],[])).
% 5.57/3.84 tff(64,plain,
% 5.57/3.84 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | (~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50)))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[63, 62])).
% 5.57/3.84 tff(65,plain,
% 5.57/3.84 (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[64, 61, 60])).
% 5.57/3.84 tff(66,plain,
% 5.57/3.84 (((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50)))))) | ((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))),
% 5.57/3.84 inference(tautology,[status(thm)],[])).
% 5.57/3.84 tff(67,plain,
% 5.57/3.84 ((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))))),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[66, 65])).
% 5.57/3.84 tff(68,plain,
% 5.57/3.84 (neq(V!48, nil) <=> neq(X!50, nil)),
% 5.57/3.84 inference(monotonicity,[status(thm)],[24])).
% 5.57/3.84 tff(69,plain,
% 5.57/3.84 (neq(V!48, nil)),
% 5.57/3.84 inference(or_elim,[status(thm)],[21])).
% 5.57/3.84 tff(70,plain,
% 5.57/3.84 (neq(X!50, nil)),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[69, 68])).
% 5.57/3.84 tff(71,plain,
% 5.57/3.84 ((~(~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))))) <=> ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(72,plain,
% 5.57/3.84 ((neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))) <=> (~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(73,plain,
% 5.57/3.84 ((~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) <=> (~(~((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))))))),
% 5.57/3.84 inference(monotonicity,[status(thm)],[72])).
% 5.57/3.84 tff(74,plain,
% 5.57/3.84 ((~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))) <=> ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))))),
% 5.57/3.84 inference(transitivity,[status(thm)],[73, 71])).
% 5.57/3.84 tff(75,plain,
% 5.57/3.84 (~(neq(X!50, nil) & ((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))),
% 5.57/3.84 inference(or_elim,[status(thm)],[21])).
% 5.57/3.84 tff(76,plain,
% 5.57/3.84 ((~neq(X!50, nil)) | (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[75, 74])).
% 5.57/3.84 tff(77,plain,
% 5.57/3.84 (~((~neq(W!49, nil)) | (~rearsegP(X!50, W!49)))),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[76, 70])).
% 5.57/3.84 tff(78,plain,
% 5.57/3.84 (((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))) | rearsegP(X!50, W!49)),
% 5.57/3.84 inference(tautology,[status(thm)],[])).
% 5.57/3.84 tff(79,plain,
% 5.57/3.84 (rearsegP(X!50, W!49)),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[78, 77])).
% 5.57/3.84 tff(80,plain,
% 5.57/3.84 ((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))))),
% 5.57/3.84 inference(tautology,[status(thm)],[])).
% 5.57/3.84 tff(81,plain,
% 5.57/3.84 ((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))))),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[80, 79])).
% 5.57/3.84 tff(82,plain,
% 5.57/3.84 (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[81, 67])).
% 5.57/3.84 tff(83,plain,
% 5.57/3.84 (((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))) | (app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)),
% 5.57/3.84 inference(tautology,[status(thm)],[])).
% 5.57/3.84 tff(84,plain,
% 5.57/3.84 (app(tptp_fun_W_6(W!49, X!50), W!49) = X!50),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[83, 82])).
% 5.57/3.84 tff(85,plain,
% 5.57/3.84 (app(app(tptp_fun_W_6(W!49, X!50), W!49), nil) = app(X!50, nil)),
% 5.57/3.84 inference(monotonicity,[status(thm)],[84])).
% 5.57/3.84 tff(86,plain,
% 5.57/3.84 (app(app(tptp_fun_W_6(W!49, X!50), W!49), nil) = V!48),
% 5.57/3.84 inference(transitivity,[status(thm)],[85, 40, 25])).
% 5.57/3.84 tff(87,plain,
% 5.57/3.84 (segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49) <=> segmentP(V!48, U!47)),
% 5.57/3.84 inference(monotonicity,[status(thm)],[86, 23])).
% 5.57/3.84 tff(88,plain,
% 5.57/3.84 (segmentP(V!48, U!47) <=> segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 5.57/3.84 inference(symmetry,[status(thm)],[87])).
% 5.57/3.84 tff(89,plain,
% 5.57/3.84 ((~segmentP(V!48, U!47)) <=> (~segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))),
% 5.57/3.84 inference(monotonicity,[status(thm)],[88])).
% 5.57/3.84 tff(90,plain,
% 5.57/3.84 (neq(U!47, nil) <=> neq(W!49, nil)),
% 5.57/3.84 inference(monotonicity,[status(thm)],[22])).
% 5.57/3.84 tff(91,plain,
% 5.57/3.84 (neq(W!49, nil) <=> neq(U!47, nil)),
% 5.57/3.84 inference(symmetry,[status(thm)],[90])).
% 5.57/3.84 tff(92,plain,
% 5.57/3.84 (((~neq(W!49, nil)) | (~rearsegP(X!50, W!49))) | neq(W!49, nil)),
% 5.57/3.84 inference(tautology,[status(thm)],[])).
% 5.57/3.84 tff(93,plain,
% 5.57/3.84 (neq(W!49, nil)),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[92, 77])).
% 5.57/3.84 tff(94,plain,
% 5.57/3.84 (neq(U!47, nil)),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[93, 91])).
% 5.57/3.84 tff(95,plain,
% 5.57/3.84 ((~(~((~neq(U!47, nil)) | (~segmentP(V!48, U!47))))) <=> ((~neq(U!47, nil)) | (~segmentP(V!48, U!47)))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(96,plain,
% 5.57/3.84 ((neq(U!47, nil) & segmentP(V!48, U!47)) <=> (~((~neq(U!47, nil)) | (~segmentP(V!48, U!47))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(97,plain,
% 5.57/3.84 ((~(neq(U!47, nil) & segmentP(V!48, U!47))) <=> (~(~((~neq(U!47, nil)) | (~segmentP(V!48, U!47)))))),
% 5.57/3.84 inference(monotonicity,[status(thm)],[96])).
% 5.57/3.84 tff(98,plain,
% 5.57/3.84 ((~(neq(U!47, nil) & segmentP(V!48, U!47))) <=> ((~neq(U!47, nil)) | (~segmentP(V!48, U!47)))),
% 5.57/3.84 inference(transitivity,[status(thm)],[97, 95])).
% 5.57/3.84 tff(99,plain,
% 5.57/3.84 (~(neq(U!47, nil) & segmentP(V!48, U!47))),
% 5.57/3.84 inference(or_elim,[status(thm)],[21])).
% 5.57/3.84 tff(100,plain,
% 5.57/3.84 ((~neq(U!47, nil)) | (~segmentP(V!48, U!47))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[99, 98])).
% 5.57/3.84 tff(101,plain,
% 5.57/3.84 (~segmentP(V!48, U!47)),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[100, 94])).
% 5.57/3.84 tff(102,plain,
% 5.57/3.84 (~segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[101, 89])).
% 5.57/3.84 tff(103,plain,
% 5.57/3.84 (((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))) | ssList(tptp_fun_W_6(W!49, X!50))),
% 5.57/3.84 inference(tautology,[status(thm)],[])).
% 5.57/3.84 tff(104,plain,
% 5.57/3.84 (ssList(tptp_fun_W_6(W!49, X!50))),
% 5.57/3.84 inference(unit_resolution,[status(thm)],[103, 82])).
% 5.57/3.84 tff(105,plain,
% 5.57/3.84 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(106,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[105])).
% 5.57/3.84 tff(107,plain,
% 5.57/3.84 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(108,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[107])).
% 5.57/3.84 tff(109,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(transitivity,[status(thm)],[108, 106])).
% 5.57/3.84 tff(110,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(111,plain,
% 5.57/3.84 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((segmentP(U, V) => segmentP(app(app(W, U), X), V)) <=> ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))))), rewrite((ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), (![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> (ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), rewrite((ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), (![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))))),
% 5.57/3.84 inference(bind,[status(th)],[])).
% 5.57/3.84 tff(112,plain,
% 5.57/3.84 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(quant_intro,[status(thm)],[111])).
% 5.57/3.84 tff(113,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax56')).
% 5.57/3.84 tff(114,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[113, 112])).
% 5.57/3.84 tff(115,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[114, 110])).
% 5.57/3.84 tff(116,plain,(
% 5.57/3.84 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(skolemize,[status(sab)],[115])).
% 5.57/3.84 tff(117,plain,
% 5.57/3.84 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.57/3.84 inference(modus_ponens,[status(thm)],[116, 109])).
% 5.57/3.84 tff(118,plain,
% 5.57/3.84 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(119,plain,
% 5.57/3.84 (((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V)))))) <=> ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 5.57/3.84 inference(rewrite,[status(thm)],[])).
% 5.57/3.84 tff(120,plain,
% 5.57/3.84 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))))),
% 5.57/3.84 inference(monotonicity,[status(thm)],[119])).
% 5.57/3.84 tff(121,plain,
% 5.57/3.84 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 5.57/3.84 inference(transitivity,[status(thm)],[120, 118])).
% 5.57/3.84 tff(122,plain,
% 5.57/3.84 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))),
% 5.57/3.85 inference(quant_inst,[status(thm)],[])).
% 5.57/3.85 tff(123,plain,
% 5.57/3.85 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[122, 121])).
% 5.57/3.85 tff(124,plain,
% 5.57/3.85 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 5.57/3.85 inference(unit_resolution,[status(thm)],[123, 117, 61])).
% 5.57/3.85 tff(125,plain,
% 5.57/3.85 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 5.57/3.85 inference(rewrite,[status(thm)],[])).
% 5.57/3.85 tff(126,plain,
% 5.57/3.85 (((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49))))) <=> ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 5.57/3.85 inference(rewrite,[status(thm)],[])).
% 5.57/3.85 tff(127,plain,
% 5.57/3.85 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))))),
% 5.57/3.85 inference(monotonicity,[status(thm)],[126])).
% 5.57/3.85 tff(128,plain,
% 5.57/3.85 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 5.57/3.85 inference(transitivity,[status(thm)],[127, 125])).
% 5.57/3.85 tff(129,plain,
% 5.57/3.85 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))),
% 5.57/3.85 inference(quant_inst,[status(thm)],[])).
% 5.57/3.85 tff(130,plain,
% 5.57/3.85 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[129, 128])).
% 5.57/3.85 tff(131,plain,
% 5.57/3.85 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 5.57/3.85 inference(unit_resolution,[status(thm)],[130, 61, 124])).
% 5.57/3.85 tff(132,plain,
% 5.57/3.85 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49)))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49)))),
% 5.57/3.85 inference(rewrite,[status(thm)],[])).
% 5.57/3.85 tff(133,plain,
% 5.57/3.85 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49)))),
% 5.57/3.85 inference(quant_inst,[status(thm)],[])).
% 5.57/3.85 tff(134,plain,
% 5.57/3.85 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[133, 132])).
% 5.57/3.85 tff(135,plain,
% 5.57/3.85 (![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))),
% 5.57/3.85 inference(unit_resolution,[status(thm)],[134, 131, 104])).
% 5.57/3.85 tff(136,plain,
% 5.57/3.85 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 5.57/3.85 inference(bind,[status(th)],[])).
% 5.57/3.85 tff(137,plain,
% 5.57/3.85 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.57/3.85 inference(quant_intro,[status(thm)],[136])).
% 5.57/3.85 tff(138,plain,
% 5.57/3.85 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.57/3.85 inference(rewrite,[status(thm)],[])).
% 5.57/3.85 tff(139,plain,
% 5.57/3.85 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 5.57/3.85 inference(bind,[status(th)],[])).
% 5.57/3.85 tff(140,plain,
% 5.57/3.85 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.57/3.85 inference(quant_intro,[status(thm)],[139])).
% 5.57/3.85 tff(141,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax55')).
% 5.57/3.85 tff(142,plain,
% 5.57/3.85 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[141, 140])).
% 5.57/3.85 tff(143,plain,
% 5.57/3.85 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[142, 138])).
% 5.57/3.85 tff(144,plain,(
% 5.57/3.85 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.57/3.85 inference(skolemize,[status(sab)],[143])).
% 5.57/3.85 tff(145,plain,
% 5.57/3.85 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[144, 137])).
% 5.57/3.85 tff(146,plain,
% 5.57/3.85 (((~![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))),
% 5.57/3.85 inference(rewrite,[status(thm)],[])).
% 5.57/3.85 tff(147,plain,
% 5.57/3.85 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 5.57/3.85 inference(quant_inst,[status(thm)],[])).
% 5.57/3.85 tff(148,plain,
% 5.57/3.85 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[147, 146])).
% 5.57/3.85 tff(149,plain,
% 5.57/3.85 (segmentP(W!49, W!49)),
% 5.57/3.85 inference(unit_resolution,[status(thm)],[148, 145, 61])).
% 5.57/3.85 tff(150,plain,
% 5.57/3.85 (ssList(nil) <=> ssList(nil)),
% 5.57/3.85 inference(rewrite,[status(thm)],[])).
% 5.57/3.85 tff(151,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 5.57/3.85 tff(152,plain,
% 5.57/3.85 (ssList(nil)),
% 5.57/3.85 inference(modus_ponens,[status(thm)],[151, 150])).
% 5.57/3.85 tff(153,plain,
% 5.57/3.85 (((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | ((~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | (~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))),
% 5.59/3.86 inference(rewrite,[status(thm)],[])).
% 5.59/3.86 tff(154,plain,
% 5.59/3.86 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | ((~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))),
% 5.59/3.86 inference(quant_inst,[status(thm)],[])).
% 5.59/3.86 tff(155,plain,
% 5.59/3.86 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | (~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 5.59/3.86 inference(modus_ponens,[status(thm)],[154, 153])).
% 5.59/3.86 tff(156,plain,
% 5.59/3.86 (segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 5.59/3.86 inference(unit_resolution,[status(thm)],[155, 152, 149, 135])).
% 5.59/3.86 tff(157,plain,
% 5.59/3.86 ($false),
% 5.59/3.86 inference(unit_resolution,[status(thm)],[156, 102])).
% 5.59/3.86 % SZS output end Proof
%------------------------------------------------------------------------------