TSTP Solution File: SWC008+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC008+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:54:36 EDT 2022
% Result : Theorem 3.00s 2.11s
% Output : Proof 3.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC008+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 20:30:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 3.00/2.11 % SZS status Theorem
% 3.00/2.11 % SZS output start Proof
% 3.00/2.11 tff(tptp_fun_V_48_type, type, (
% 3.00/2.11 tptp_fun_V_48: $i)).
% 3.00/2.11 tff(app_type, type, (
% 3.00/2.11 app: ( $i * $i ) > $i)).
% 3.00/2.11 tff(nil_type, type, (
% 3.00/2.11 nil: $i)).
% 3.00/2.11 tff(tptp_fun_W_5_type, type, (
% 3.00/2.11 tptp_fun_W_5: ( $i * $i ) > $i)).
% 3.00/2.11 tff(tptp_fun_X_50_type, type, (
% 3.00/2.11 tptp_fun_X_50: $i)).
% 3.00/2.11 tff(tptp_fun_W_49_type, type, (
% 3.00/2.11 tptp_fun_W_49: $i)).
% 3.00/2.11 tff(equalelemsP_type, type, (
% 3.00/2.11 equalelemsP: $i > $o)).
% 3.00/2.11 tff(segmentP_type, type, (
% 3.00/2.11 segmentP: ( $i * $i ) > $o)).
% 3.00/2.11 tff(frontsegP_type, type, (
% 3.00/2.11 frontsegP: ( $i * $i ) > $o)).
% 3.00/2.11 tff(neq_type, type, (
% 3.00/2.11 neq: ( $i * $i ) > $o)).
% 3.00/2.11 tff(ssList_type, type, (
% 3.00/2.11 ssList: $i > $o)).
% 3.00/2.11 tff(tptp_fun_U_47_type, type, (
% 3.00/2.11 tptp_fun_U_47: $i)).
% 3.00/2.11 tff(1,plain,
% 3.00/2.11 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(2,plain,
% 3.00/2.11 ((ssList(V!48) & (ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))) <=> (ssList(V!48) & ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(3,plain,
% 3.00/2.11 ((ssList(W!49) & (equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))) <=> (ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(4,plain,
% 3.00/2.11 (((~(~equalelemsP(W!49))) & (~(~frontsegP(X!50, W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2)))) <=> (equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(5,plain,
% 3.00/2.11 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 3.00/2.11 inference(rewrite,[status(thm)],[])).
% 3.00/2.11 tff(6,plain,
% 3.00/2.11 (((~(~ssList(W!49))) & ((~(~equalelemsP(W!49))) & (~(~frontsegP(X!50, W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))) <=> (ssList(W!49) & (equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2)))))),
% 3.00/2.12 inference(monotonicity,[status(thm)],[5, 4])).
% 3.00/2.12 tff(7,plain,
% 3.00/2.12 (((~(~ssList(W!49))) & ((~(~equalelemsP(W!49))) & (~(~frontsegP(X!50, W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))) <=> (ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))),
% 3.00/2.12 inference(transitivity,[status(thm)],[6, 3])).
% 3.00/2.12 tff(8,plain,
% 3.00/2.12 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(9,plain,
% 3.00/2.12 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~equalelemsP(W!49))) & (~(~frontsegP(X!50, W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2)))))) <=> (ssList(V!48) & (ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2)))))),
% 3.00/2.12 inference(monotonicity,[status(thm)],[8, 7])).
% 3.00/2.12 tff(10,plain,
% 3.00/2.12 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~equalelemsP(W!49))) & (~(~frontsegP(X!50, W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2)))))) <=> (ssList(V!48) & ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))),
% 3.00/2.12 inference(transitivity,[status(thm)],[9, 2])).
% 3.00/2.12 tff(11,plain,
% 3.00/2.12 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(12,plain,
% 3.00/2.12 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~equalelemsP(W!49))) & (~(~frontsegP(X!50, W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2)))))),
% 3.00/2.12 inference(monotonicity,[status(thm)],[11, 10])).
% 3.00/2.12 tff(13,plain,
% 3.00/2.12 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~equalelemsP(W!49))) & (~(~frontsegP(X!50, W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2))))),
% 3.00/2.12 inference(transitivity,[status(thm)],[12, 1])).
% 3.00/2.12 tff(14,plain,
% 3.00/2.12 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2)))))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(15,plain,
% 3.00/2.12 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~frontsegP(X, W))) | (~equalelemsP(W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ?[X2: $i] : ((((ssList(X2) & neq(W, X2)) & frontsegP(X, X2)) & segmentP(X2, W)) & equalelemsP(X2)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2)))))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~frontsegP(X, W))) | (~equalelemsP(W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U))))) | ?[X2: $i] : ((((ssList(X2) & neq(W, X2)) & frontsegP(X, X2)) & segmentP(X2, W)) & equalelemsP(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 3.00/2.12 tff(17,plain,
% 3.00/2.12 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.00/2.12 tff(18,plain,
% 3.00/2.12 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[17, 14])).
% 3.00/2.12 tff(19,plain,
% 3.00/2.12 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.00/2.12 tff(20,plain,
% 3.00/2.12 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[19, 14])).
% 3.00/2.12 tff(21,plain,
% 3.00/2.12 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[20, 14])).
% 3.00/2.12 tff(22,plain,
% 3.00/2.12 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[21, 14])).
% 3.00/2.12 tff(23,plain,
% 3.00/2.12 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~equalelemsP(W)) | (~frontsegP(X, W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))) | ?[X2: $i] : (ssList(X2) & neq(W, X2) & frontsegP(X, X2) & segmentP(X2, W) & equalelemsP(X2))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[22, 14])).
% 3.00/2.12 tff(24,plain,
% 3.00/2.12 (ssList(U!47) & ssList(V!48) & ssList(W!49) & equalelemsP(W!49) & frontsegP(X!50, W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) & ![X2: $i] : (~(ssList(X2) & neq(W!49, X2) & frontsegP(X!50, X2) & segmentP(X2, W!49) & equalelemsP(X2)))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[23, 13])).
% 3.00/2.12 tff(25,plain,
% 3.00/2.12 (V!48 = X!50),
% 3.00/2.12 inference(and_elim,[status(thm)],[24])).
% 3.00/2.12 tff(26,plain,
% 3.00/2.12 (X!50 = V!48),
% 3.00/2.12 inference(symmetry,[status(thm)],[25])).
% 3.00/2.12 tff(27,plain,
% 3.00/2.12 (ssList(X!50)),
% 3.00/2.12 inference(and_elim,[status(thm)],[24])).
% 3.00/2.12 tff(28,plain,
% 3.00/2.12 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(29,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[28])).
% 3.00/2.12 tff(30,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(31,plain,
% 3.00/2.12 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(32,plain,
% 3.00/2.12 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[31])).
% 3.00/2.12 tff(33,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 3.00/2.12 tff(34,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[33, 32])).
% 3.00/2.12 tff(35,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[34, 30])).
% 3.00/2.12 tff(36,plain,(
% 3.00/2.12 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 3.00/2.12 inference(skolemize,[status(sab)],[35])).
% 3.00/2.12 tff(37,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[36, 29])).
% 3.00/2.12 tff(38,plain,
% 3.00/2.12 (((~![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))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(39,plain,
% 3.00/2.12 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(40,plain,
% 3.00/2.12 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50)),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[39, 38])).
% 3.00/2.12 tff(41,plain,
% 3.00/2.12 (app(X!50, nil) = X!50),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 3.00/2.12 tff(42,plain,
% 3.00/2.12 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(43,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[42])).
% 3.00/2.12 tff(44,plain,
% 3.00/2.12 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(45,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[44])).
% 3.00/2.12 tff(46,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 3.00/2.12 inference(transitivity,[status(thm)],[45, 43])).
% 3.00/2.12 tff(47,plain,
% 3.00/2.12 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(48,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[47])).
% 3.00/2.12 tff(49,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(50,plain,
% 3.00/2.12 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))) <=> (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), rewrite((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), (![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(51,plain,
% 3.00/2.12 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[50])).
% 3.00/2.12 tff(52,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax5')).
% 3.00/2.12 tff(53,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[52, 51])).
% 3.00/2.12 tff(54,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[53, 49])).
% 3.00/2.12 tff(55,plain,(
% 3.00/2.12 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U)))))))),
% 3.00/2.12 inference(skolemize,[status(sab)],[54])).
% 3.00/2.12 tff(56,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[55, 48])).
% 3.00/2.12 tff(57,plain,
% 3.00/2.12 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[56, 46])).
% 3.00/2.12 tff(58,plain,
% 3.00/2.12 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50)))))))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(59,plain,
% 3.00/2.12 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50)))))))))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(60,plain,
% 3.00/2.12 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50))))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[59, 58])).
% 3.00/2.12 tff(61,plain,
% 3.00/2.12 (![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50))))))))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[60, 57, 27])).
% 3.00/2.12 tff(62,plain,
% 3.00/2.12 (ssList(W!49)),
% 3.00/2.12 inference(and_elim,[status(thm)],[24])).
% 3.00/2.12 tff(63,plain,
% 3.00/2.12 (((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50))))))))) | ((~ssList(W!49)) | (~((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~(frontsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = X!50))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50))))))))) | (~ssList(W!49)) | (~((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~(frontsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = X!50))))))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(64,plain,
% 3.00/2.12 ((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50))))))))) | ((~ssList(W!49)) | (~((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~(frontsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = X!50))))))))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(65,plain,
% 3.00/2.12 ((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(X!50, V)) | (~((~ssList(tptp_fun_W_5(V, X!50))) | (~(app(V, tptp_fun_W_5(V, X!50)) = X!50)))))) | (~(frontsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = X!50))))))))) | (~ssList(W!49)) | (~((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~(frontsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = X!50)))))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[64, 63])).
% 3.00/2.12 tff(66,plain,
% 3.00/2.12 (~((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~(frontsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = X!50))))))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[65, 62, 61])).
% 3.00/2.12 tff(67,plain,
% 3.00/2.12 (((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~(frontsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = X!50)))))) | ((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))),
% 3.00/2.12 inference(tautology,[status(thm)],[])).
% 3.00/2.12 tff(68,plain,
% 3.00/2.12 ((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50))))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[67, 66])).
% 3.00/2.12 tff(69,plain,
% 3.00/2.12 (frontsegP(X!50, W!49)),
% 3.00/2.12 inference(and_elim,[status(thm)],[24])).
% 3.00/2.12 tff(70,plain,
% 3.00/2.12 ((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50))))),
% 3.00/2.12 inference(tautology,[status(thm)],[])).
% 3.00/2.12 tff(71,plain,
% 3.00/2.12 ((~((~frontsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))))) | (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50))))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[70, 69])).
% 3.00/2.12 tff(72,plain,
% 3.00/2.12 (~((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[71, 68])).
% 3.00/2.12 tff(73,plain,
% 3.00/2.12 (((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50))) | (app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50)),
% 3.00/2.12 inference(tautology,[status(thm)],[])).
% 3.00/2.12 tff(74,plain,
% 3.00/2.12 (app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[73, 72])).
% 3.00/2.12 tff(75,plain,
% 3.00/2.12 (app(app(W!49, tptp_fun_W_5(W!49, X!50)), nil) = app(X!50, nil)),
% 3.00/2.12 inference(monotonicity,[status(thm)],[74])).
% 3.00/2.12 tff(76,plain,
% 3.00/2.12 (app(app(W!49, tptp_fun_W_5(W!49, X!50)), nil) = V!48),
% 3.00/2.12 inference(transitivity,[status(thm)],[75, 41, 26])).
% 3.00/2.12 tff(77,plain,
% 3.00/2.12 (U!47 = W!49),
% 3.00/2.12 inference(and_elim,[status(thm)],[24])).
% 3.00/2.12 tff(78,plain,
% 3.00/2.12 (W!49 = U!47),
% 3.00/2.12 inference(symmetry,[status(thm)],[77])).
% 3.00/2.12 tff(79,plain,
% 3.00/2.12 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(W!49)) | (app(W!49, nil) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(W!49)) | (app(W!49, nil) = W!49))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(80,plain,
% 3.00/2.12 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(W!49)) | (app(W!49, nil) = W!49))),
% 3.00/2.12 inference(quant_inst,[status(thm)],[])).
% 3.00/2.12 tff(81,plain,
% 3.00/2.12 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(W!49)) | (app(W!49, nil) = W!49)),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[80, 79])).
% 3.00/2.12 tff(82,plain,
% 3.00/2.12 (app(W!49, nil) = W!49),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[81, 37, 62])).
% 3.00/2.12 tff(83,plain,
% 3.00/2.12 (app(W!49, nil) = U!47),
% 3.00/2.12 inference(transitivity,[status(thm)],[82, 78])).
% 3.00/2.12 tff(84,plain,
% 3.00/2.12 (((~ssList(tptp_fun_W_5(W!49, X!50))) | (~(app(W!49, tptp_fun_W_5(W!49, X!50)) = X!50))) | ssList(tptp_fun_W_5(W!49, X!50))),
% 3.00/2.12 inference(tautology,[status(thm)],[])).
% 3.00/2.12 tff(85,plain,
% 3.00/2.12 (ssList(tptp_fun_W_5(W!49, X!50))),
% 3.00/2.12 inference(unit_resolution,[status(thm)],[84, 72])).
% 3.00/2.12 tff(86,plain,
% 3.00/2.12 (^[Y: $i] : refl(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(87,plain,
% 3.00/2.12 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[86])).
% 3.00/2.12 tff(88,plain,
% 3.00/2.12 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(89,plain,
% 3.00/2.12 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[88])).
% 3.00/2.12 tff(90,plain,
% 3.00/2.12 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 3.00/2.12 inference(transitivity,[status(thm)],[89, 87])).
% 3.00/2.12 tff(91,plain,
% 3.00/2.12 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47))))))),
% 3.00/2.12 inference(bind,[status(th)],[])).
% 3.00/2.12 tff(92,plain,
% 3.00/2.12 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 3.00/2.12 inference(quant_intro,[status(thm)],[91])).
% 3.00/2.12 tff(93,plain,
% 3.00/2.12 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47)))))),
% 3.00/2.12 inference(and_elim,[status(thm)],[24])).
% 3.00/2.12 tff(94,plain,
% 3.00/2.12 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[93, 92])).
% 3.00/2.12 tff(95,plain,
% 3.00/2.12 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 3.00/2.12 inference(modus_ponens,[status(thm)],[94, 90])).
% 3.00/2.12 tff(96,plain,
% 3.00/2.12 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | (~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47)))))),
% 3.00/2.12 inference(rewrite,[status(thm)],[])).
% 3.00/2.12 tff(97,plain,
% 3.00/2.12 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | ((~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47)))))),
% 3.00/2.13 inference(quant_inst,[status(thm)],[])).
% 3.00/2.13 tff(98,plain,
% 3.00/2.13 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))) | (~ssList(W!49)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[97, 96])).
% 3.00/2.13 tff(99,plain,
% 3.00/2.13 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[98, 62, 95])).
% 3.00/2.13 tff(100,plain,
% 3.00/2.13 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | (~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48))))),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(101,plain,
% 3.00/2.13 (((~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)) | (~(app(W!49, X1) = U!47)))) <=> ((~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48))))),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(102,plain,
% 3.00/2.13 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)))))),
% 3.00/2.13 inference(monotonicity,[status(thm)],[101])).
% 3.00/2.13 tff(103,plain,
% 3.00/2.13 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | (~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48))))),
% 3.00/2.13 inference(transitivity,[status(thm)],[102, 100])).
% 3.00/2.13 tff(104,plain,
% 3.00/2.13 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 3.00/2.13 inference(quant_inst,[status(thm)],[])).
% 3.00/2.13 tff(105,plain,
% 3.00/2.13 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | (~ssList(tptp_fun_W_5(W!49, X!50))) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[104, 103])).
% 3.00/2.13 tff(106,plain,
% 3.00/2.13 (![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)))),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[105, 99, 85])).
% 3.00/2.13 tff(107,plain,
% 3.00/2.13 (ssList(nil) <=> ssList(nil)),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(108,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 3.00/2.13 tff(109,plain,
% 3.00/2.13 (ssList(nil)),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[108, 107])).
% 3.00/2.13 tff(110,plain,
% 3.00/2.13 (((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)))) | ((~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), nil) = V!48)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)))) | (~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), nil) = V!48)))),
% 3.00/2.13 inference(rewrite,[status(thm)],[])).
% 3.00/2.13 tff(111,plain,
% 3.00/2.13 ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)))) | ((~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), nil) = V!48)))),
% 3.00/2.13 inference(quant_inst,[status(thm)],[])).
% 3.00/2.13 tff(112,plain,
% 3.00/2.13 ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), X1) = V!48)))) | (~ssList(nil)) | (~(app(W!49, nil) = U!47)) | (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), nil) = V!48))),
% 3.00/2.13 inference(modus_ponens,[status(thm)],[111, 110])).
% 3.00/2.13 tff(113,plain,
% 3.00/2.13 (~(app(app(W!49, tptp_fun_W_5(W!49, X!50)), nil) = V!48)),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[112, 109, 106, 83])).
% 3.00/2.13 tff(114,plain,
% 3.00/2.13 ($false),
% 3.00/2.13 inference(unit_resolution,[status(thm)],[113, 76])).
% 3.00/2.13 % SZS output end Proof
%------------------------------------------------------------------------------