TSTP Solution File: SWC363+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC363+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:57:25 EDT 2022
% Result : Theorem 265.92s 169.92s
% Output : Proof 266.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SWC363+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n020.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun Sep 4 00:24:59 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 265.92/169.92 % SZS status Theorem
% 265.92/169.92 % SZS output start Proof
% 265.92/169.92 tff(tptp_fun_X_50_type, type, (
% 265.92/169.92 tptp_fun_X_50: $i)).
% 265.92/169.92 tff(app_type, type, (
% 265.92/169.92 app: ( $i * $i ) > $i)).
% 265.92/169.92 tff(tptp_fun_X_3_type, type, (
% 265.92/169.92 tptp_fun_X_3: ( $i * $i ) > $i)).
% 265.92/169.92 tff(tptp_fun_Y_51_type, type, (
% 265.92/169.92 tptp_fun_Y_51: $i)).
% 265.92/169.92 tff(tptp_fun_W_49_type, type, (
% 265.92/169.92 tptp_fun_W_49: $i)).
% 265.92/169.92 tff(tptp_fun_W_2_type, type, (
% 265.92/169.92 tptp_fun_W_2: ( $i * $i ) > $i)).
% 265.92/169.92 tff(cons_type, type, (
% 265.92/169.92 cons: ( $i * $i ) > $i)).
% 265.92/169.92 tff(ssList_type, type, (
% 265.92/169.92 ssList: $i > $o)).
% 265.92/169.92 tff(memberP_type, type, (
% 265.92/169.92 memberP: ( $i * $i ) > $o)).
% 265.92/169.92 tff(ssItem_type, type, (
% 265.92/169.92 ssItem: $i > $o)).
% 265.92/169.92 tff(neq_type, type, (
% 265.92/169.92 neq: ( $i * $i ) > $o)).
% 265.92/169.92 tff(nil_type, type, (
% 265.92/169.92 nil: $i)).
% 265.92/169.92 tff(tptp_fun_V_48_type, type, (
% 265.92/169.92 tptp_fun_V_48: $i)).
% 265.92/169.92 tff(tptp_fun_U_47_type, type, (
% 265.92/169.92 tptp_fun_U_47: $i)).
% 265.92/169.92 tff(segmentP_type, type, (
% 265.92/169.92 segmentP: ( $i * $i ) > $o)).
% 265.92/169.92 tff(tptp_fun_X_8_type, type, (
% 265.92/169.92 tptp_fun_X_8: ( $i * $i ) > $i)).
% 265.92/169.92 tff(tptp_fun_W_7_type, type, (
% 265.92/169.92 tptp_fun_W_7: ( $i * $i ) > $i)).
% 265.92/169.92 tff(1,plain,
% 265.92/169.92 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 265.92/169.92 inference(rewrite,[status(thm)],[])).
% 265.92/169.92 tff(2,plain,
% 265.92/169.92 ((ssList(V!48) & (ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 265.92/169.92 inference(rewrite,[status(thm)],[])).
% 265.92/169.92 tff(3,plain,
% 265.92/169.92 ((ssList(W!49) & ((~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 265.92/169.92 inference(rewrite,[status(thm)],[])).
% 265.92/169.92 tff(4,plain,
% 265.92/169.92 (((~segmentP(V!48, U!47)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))) <=> ((~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 265.92/169.92 inference(rewrite,[status(thm)],[])).
% 265.92/169.92 tff(5,plain,
% 265.92/169.92 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 265.92/169.92 inference(rewrite,[status(thm)],[])).
% 265.92/169.92 tff(6,plain,
% 265.92/169.92 (((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & ((~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))),
% 265.92/169.92 inference(monotonicity,[status(thm)],[5, 4])).
% 265.92/169.92 tff(7,plain,
% 265.92/169.92 (((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 265.92/169.93 inference(transitivity,[status(thm)],[6, 3])).
% 265.92/169.93 tff(8,plain,
% 265.92/169.93 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 265.92/169.93 inference(rewrite,[status(thm)],[])).
% 265.92/169.93 tff(9,plain,
% 265.92/169.93 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & (ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))),
% 265.92/169.93 inference(monotonicity,[status(thm)],[8, 7])).
% 265.92/169.93 tff(10,plain,
% 265.92/169.93 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 265.92/169.93 inference(transitivity,[status(thm)],[9, 2])).
% 265.92/169.93 tff(11,plain,
% 265.92/169.93 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 265.92/169.93 inference(rewrite,[status(thm)],[])).
% 265.92/169.93 tff(12,plain,
% 265.92/169.93 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))))),
% 265.92/169.93 inference(monotonicity,[status(thm)],[11, 10])).
% 265.92/169.93 tff(13,plain,
% 265.92/169.93 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~(~neq(V!48, nil))) & (~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))))),
% 265.92/169.93 inference(transitivity,[status(thm)],[12, 1])).
% 265.92/169.93 tff(14,plain,
% 265.92/169.93 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil)))))))),
% 265.92/169.93 inference(rewrite,[status(thm)],[])).
% 265.92/169.93 tff(15,plain,
% 265.92/169.93 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & neq(X, nil)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil)))))))),
% 265.92/169.93 inference(rewrite,[status(thm)],[])).
% 265.92/169.93 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | segmentP(V, U)) | ((~(nil = W)) & (nil = X))) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & neq(X, nil)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 265.92/169.93 tff(17,plain,
% 265.92/169.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[16, 15])).
% 265.92/169.93 tff(18,plain,
% 265.92/169.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[17, 14])).
% 265.92/169.93 tff(19,plain,
% 265.92/169.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[18, 14])).
% 265.92/169.93 tff(20,plain,
% 265.92/169.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[19, 14])).
% 265.92/169.93 tff(21,plain,
% 265.92/169.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[20, 14])).
% 265.92/169.93 tff(22,plain,
% 265.92/169.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[21, 14])).
% 265.92/169.93 tff(23,plain,
% 265.92/169.93 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (![Y: $i] : ((~(cons(Y, nil) = W)) | (~memberP(X, Y)) | (~ssItem(Y))) & neq(X, nil))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[22, 14])).
% 265.92/169.93 tff(24,plain,
% 265.92/169.93 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & neq(V!48, nil) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil)))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[23, 13])).
% 265.92/169.93 tff(25,plain,
% 265.92/169.93 (ssList(X!50)),
% 265.92/169.93 inference(and_elim,[status(thm)],[24])).
% 265.92/169.93 tff(26,plain,
% 265.92/169.93 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))))),
% 265.92/169.93 inference(bind,[status(th)],[])).
% 265.92/169.93 tff(27,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 265.92/169.93 inference(quant_intro,[status(thm)],[26])).
% 265.92/169.93 tff(28,plain,
% 265.92/169.93 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))))),
% 265.92/169.93 inference(bind,[status(th)],[])).
% 265.92/169.93 tff(29,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 265.92/169.93 inference(quant_intro,[status(thm)],[28])).
% 265.92/169.93 tff(30,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 265.92/169.93 inference(transitivity,[status(thm)],[29, 27])).
% 265.92/169.93 tff(31,plain,
% 265.92/169.93 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U)))))))))))),
% 265.92/169.93 inference(bind,[status(th)],[])).
% 265.92/169.93 tff(32,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 265.92/169.93 inference(quant_intro,[status(thm)],[31])).
% 265.92/169.93 tff(33,plain,
% 265.92/169.93 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & (ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))))),
% 265.92/169.93 inference(bind,[status(th)],[])).
% 265.92/169.93 tff(34,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & (ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 265.92/169.93 inference(quant_intro,[status(thm)],[33])).
% 265.92/169.93 tff(35,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 265.92/169.93 inference(rewrite,[status(thm)],[])).
% 265.92/169.93 tff(36,plain,
% 265.92/169.93 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))) <=> (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))), ((ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), rewrite((ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))), ((ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))))), (![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))) <=> ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 265.92/169.93 inference(bind,[status(th)],[])).
% 265.92/169.93 tff(37,plain,
% 265.92/169.93 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 265.92/169.93 inference(quant_intro,[status(thm)],[36])).
% 265.92/169.93 tff(38,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax3')).
% 265.92/169.93 tff(39,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[38, 37])).
% 265.92/169.93 tff(40,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (memberP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(W, cons(V, X)) = U))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[39, 35])).
% 265.92/169.93 tff(41,plain,(
% 265.92/169.93 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & (ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 265.92/169.93 inference(skolemize,[status(sab)],[40])).
% 265.92/169.93 tff(42,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (((~memberP(U, V)) | (ssList(tptp_fun_W_2(V, U)) & ssList(tptp_fun_X_3(V, U)) & (app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U))) & (memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(W, cons(V, X)) = U))))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[41, 34])).
% 265.92/169.93 tff(43,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[42, 32])).
% 265.92/169.93 tff(44,plain,
% 265.92/169.93 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[43, 30])).
% 265.92/169.93 tff(45,plain,
% 265.92/169.93 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50))))))))))),
% 265.92/169.93 inference(rewrite,[status(thm)],[])).
% 265.92/169.93 tff(46,plain,
% 265.92/169.93 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50))))))))))),
% 265.92/169.93 inference(quant_inst,[status(thm)],[])).
% 265.92/169.93 tff(47,plain,
% 265.92/169.93 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(U, V)) | (~((~ssList(tptp_fun_W_2(V, U))) | (~ssList(tptp_fun_X_3(V, U))) | (~(app(tptp_fun_W_2(V, U), cons(V, tptp_fun_X_3(V, U))) = U)))))) | (~(memberP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = U))))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50)))))))))),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[46, 45])).
% 265.92/169.93 tff(48,plain,
% 265.92/169.93 (![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50)))))))))),
% 265.92/169.93 inference(unit_resolution,[status(thm)],[47, 44, 25])).
% 265.92/169.93 tff(49,plain,
% 265.92/169.93 (V!48 = X!50),
% 265.92/169.93 inference(and_elim,[status(thm)],[24])).
% 265.92/169.93 tff(50,plain,
% 265.92/169.93 (neq(V!48, nil) <=> neq(X!50, nil)),
% 265.92/169.93 inference(monotonicity,[status(thm)],[49])).
% 265.92/169.93 tff(51,plain,
% 265.92/169.93 (neq(V!48, nil)),
% 265.92/169.93 inference(and_elim,[status(thm)],[24])).
% 265.92/169.93 tff(52,plain,
% 265.92/169.93 (neq(X!50, nil)),
% 265.92/169.93 inference(modus_ponens,[status(thm)],[51, 50])).
% 265.92/169.93 tff(53,plain,
% 265.92/169.93 ((~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))) | (~neq(X!50, nil))),
% 265.92/169.93 inference(and_elim,[status(thm)],[24])).
% 265.92/169.93 tff(54,plain,
% 265.92/169.93 (~((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51)))),
% 265.92/169.93 inference(unit_resolution,[status(thm)],[53, 52])).
% 265.92/169.93 tff(55,plain,
% 265.92/169.93 (((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51))) | ssItem(Y!51)),
% 265.92/169.93 inference(tautology,[status(thm)],[])).
% 265.92/169.93 tff(56,plain,
% 265.92/169.93 (ssItem(Y!51)),
% 265.92/169.93 inference(unit_resolution,[status(thm)],[55, 54])).
% 265.92/169.93 tff(57,plain,
% 265.92/169.93 (((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50)))))))))) | ((~ssItem(Y!51)) | (~((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~(memberP(X!50, Y!51) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!51, X)) = X!50)))))))))) <=> ((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50)))))))))) | (~ssItem(Y!51)) | (~((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~(memberP(X!50, Y!51) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!51, X)) = X!50)))))))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(58,plain,
% 265.92/169.94 ((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50)))))))))) | ((~ssItem(Y!51)) | (~((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~(memberP(X!50, Y!51) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!51, X)) = X!50)))))))))),
% 265.92/169.94 inference(quant_inst,[status(thm)],[])).
% 265.92/169.94 tff(59,plain,
% 265.92/169.94 ((~![V: $i] : ((~ssItem(V)) | (~((~((~memberP(X!50, V)) | (~((~ssList(tptp_fun_W_2(V, X!50))) | (~ssList(tptp_fun_X_3(V, X!50))) | (~(app(tptp_fun_W_2(V, X!50), cons(V, tptp_fun_X_3(V, X!50))) = X!50)))))) | (~(memberP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(V, X)) = X!50)))))))))) | (~ssItem(Y!51)) | (~((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~(memberP(X!50, Y!51) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!51, X)) = X!50))))))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[58, 57])).
% 265.92/169.94 tff(60,plain,
% 265.92/169.94 (~((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~(memberP(X!50, Y!51) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!51, X)) = X!50)))))))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[59, 56, 48])).
% 265.92/169.94 tff(61,plain,
% 265.92/169.94 (((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~(memberP(X!50, Y!51) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(W, cons(Y!51, X)) = X!50))))))) | ((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))),
% 265.92/169.94 inference(tautology,[status(thm)],[])).
% 265.92/169.94 tff(62,plain,
% 265.92/169.94 ((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50))))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[61, 60])).
% 265.92/169.94 tff(63,plain,
% 265.92/169.94 (((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51))) | memberP(X!50, Y!51)),
% 265.92/169.94 inference(tautology,[status(thm)],[])).
% 265.92/169.94 tff(64,plain,
% 265.92/169.94 (memberP(X!50, Y!51)),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[63, 54])).
% 265.92/169.94 tff(65,plain,
% 265.92/169.94 ((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50))))),
% 265.92/169.94 inference(tautology,[status(thm)],[])).
% 265.92/169.94 tff(66,plain,
% 265.92/169.94 ((~((~memberP(X!50, Y!51)) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))))) | (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50))))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[65, 64])).
% 265.92/169.94 tff(67,plain,
% 265.92/169.94 (~((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[66, 62])).
% 265.92/169.94 tff(68,plain,
% 265.92/169.94 (((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50))) | (app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50)),
% 265.92/169.94 inference(tautology,[status(thm)],[])).
% 265.92/169.94 tff(69,plain,
% 265.92/169.94 (app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[68, 67])).
% 265.92/169.94 tff(70,plain,
% 265.92/169.94 (((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50))) | ssList(tptp_fun_X_3(Y!51, X!50))),
% 265.92/169.94 inference(tautology,[status(thm)],[])).
% 265.92/169.94 tff(71,plain,
% 265.92/169.94 (ssList(tptp_fun_X_3(Y!51, X!50))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[70, 67])).
% 265.92/169.94 tff(72,plain,
% 265.92/169.94 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 265.92/169.94 inference(bind,[status(th)],[])).
% 265.92/169.94 tff(73,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(quant_intro,[status(thm)],[72])).
% 265.92/169.94 tff(74,plain,
% 265.92/169.94 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 265.92/169.94 inference(bind,[status(th)],[])).
% 265.92/169.94 tff(75,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(quant_intro,[status(thm)],[74])).
% 265.92/169.94 tff(76,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(transitivity,[status(thm)],[75, 73])).
% 265.92/169.94 tff(77,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(78,plain,
% 265.92/169.94 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 265.92/169.94 inference(bind,[status(th)],[])).
% 265.92/169.94 tff(79,plain,
% 265.92/169.94 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(quant_intro,[status(thm)],[78])).
% 265.92/169.94 tff(80,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 265.92/169.94 tff(81,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[80, 79])).
% 265.92/169.94 tff(82,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[81, 77])).
% 265.92/169.94 tff(83,plain,(
% 265.92/169.94 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(skolemize,[status(sab)],[82])).
% 265.92/169.94 tff(84,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[83, 76])).
% 265.92/169.94 tff(85,plain,
% 265.92/169.94 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_X_3(Y!51, X!50))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50)))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(86,plain,
% 265.92/169.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(tptp_fun_X_3(Y!51, X!50))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50)))))),
% 265.92/169.94 inference(quant_inst,[status(thm)],[])).
% 265.92/169.94 tff(87,plain,
% 265.92/169.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | ![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[86, 85])).
% 265.92/169.94 tff(88,plain,
% 265.92/169.94 (![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50))))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[87, 84, 71])).
% 265.92/169.94 tff(89,plain,
% 265.92/169.94 (((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50))))) | ((~ssItem(Y!51)) | (cons(Y!51, tptp_fun_X_3(Y!51, X!50)) = app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50))))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50))))) | (~ssItem(Y!51)) | (cons(Y!51, tptp_fun_X_3(Y!51, X!50)) = app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(90,plain,
% 265.92/169.94 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50))))) | ((~ssItem(Y!51)) | (cons(Y!51, tptp_fun_X_3(Y!51, X!50)) = app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50))))),
% 265.92/169.94 inference(quant_inst,[status(thm)],[])).
% 265.92/169.94 tff(91,plain,
% 265.92/169.94 ((~![V: $i] : ((~ssItem(V)) | (cons(V, tptp_fun_X_3(Y!51, X!50)) = app(cons(V, nil), tptp_fun_X_3(Y!51, X!50))))) | (~ssItem(Y!51)) | (cons(Y!51, tptp_fun_X_3(Y!51, X!50)) = app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50)))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[90, 89])).
% 265.92/169.94 tff(92,plain,
% 265.92/169.94 (cons(Y!51, tptp_fun_X_3(Y!51, X!50)) = app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[91, 56, 88])).
% 265.92/169.94 tff(93,plain,
% 265.92/169.94 (app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50)) = cons(Y!51, tptp_fun_X_3(Y!51, X!50))),
% 265.92/169.94 inference(symmetry,[status(thm)],[92])).
% 265.92/169.94 tff(94,plain,
% 265.92/169.94 (((~(cons(Y!51, nil) = W!49)) | (~memberP(X!50, Y!51)) | (~ssItem(Y!51))) | (cons(Y!51, nil) = W!49)),
% 265.92/169.94 inference(tautology,[status(thm)],[])).
% 265.92/169.94 tff(95,plain,
% 265.92/169.94 (cons(Y!51, nil) = W!49),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[94, 54])).
% 265.92/169.94 tff(96,plain,
% 265.92/169.94 (app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50)) = app(W!49, tptp_fun_X_3(Y!51, X!50))),
% 265.92/169.94 inference(monotonicity,[status(thm)],[95])).
% 265.92/169.94 tff(97,plain,
% 265.92/169.94 (app(W!49, tptp_fun_X_3(Y!51, X!50)) = app(cons(Y!51, nil), tptp_fun_X_3(Y!51, X!50))),
% 265.92/169.94 inference(symmetry,[status(thm)],[96])).
% 265.92/169.94 tff(98,plain,
% 265.92/169.94 (app(W!49, tptp_fun_X_3(Y!51, X!50)) = cons(Y!51, tptp_fun_X_3(Y!51, X!50))),
% 265.92/169.94 inference(transitivity,[status(thm)],[97, 93])).
% 265.92/169.94 tff(99,plain,
% 265.92/169.94 (app(tptp_fun_W_2(Y!51, X!50), app(W!49, tptp_fun_X_3(Y!51, X!50))) = app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50)))),
% 265.92/169.94 inference(monotonicity,[status(thm)],[98])).
% 265.92/169.94 tff(100,plain,
% 265.92/169.94 (((~ssList(tptp_fun_W_2(Y!51, X!50))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(tptp_fun_W_2(Y!51, X!50), cons(Y!51, tptp_fun_X_3(Y!51, X!50))) = X!50))) | ssList(tptp_fun_W_2(Y!51, X!50))),
% 265.92/169.94 inference(tautology,[status(thm)],[])).
% 265.92/169.94 tff(101,plain,
% 265.92/169.94 (ssList(tptp_fun_W_2(Y!51, X!50))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[100, 67])).
% 265.92/169.94 tff(102,plain,
% 265.92/169.94 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 265.92/169.94 inference(bind,[status(th)],[])).
% 265.92/169.94 tff(103,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(quant_intro,[status(thm)],[102])).
% 265.92/169.94 tff(104,plain,
% 265.92/169.94 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))),
% 265.92/169.94 inference(bind,[status(th)],[])).
% 265.92/169.94 tff(105,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(quant_intro,[status(thm)],[104])).
% 265.92/169.94 tff(106,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(transitivity,[status(thm)],[105, 103])).
% 265.92/169.94 tff(107,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(108,plain,
% 265.92/169.94 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), (![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))) <=> ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))))),
% 265.92/169.94 inference(bind,[status(th)],[])).
% 265.92/169.94 tff(109,plain,
% 265.92/169.94 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(quant_intro,[status(thm)],[108])).
% 265.92/169.94 tff(110,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (app(app(U, V), W) = app(U, app(V, W))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax82')).
% 265.92/169.94 tff(111,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[110, 109])).
% 265.92/169.94 tff(112,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[111, 107])).
% 265.92/169.94 tff(113,plain,(
% 265.92/169.94 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(skolemize,[status(sab)],[112])).
% 265.92/169.94 tff(114,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[113, 106])).
% 265.92/169.94 tff(115,plain,
% 265.92/169.94 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(tptp_fun_W_2(Y!51, X!50))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(tptp_fun_W_2(Y!51, X!50))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W))))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(116,plain,
% 265.92/169.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(tptp_fun_W_2(Y!51, X!50))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W))))))),
% 265.92/169.94 inference(quant_inst,[status(thm)],[])).
% 265.92/169.94 tff(117,plain,
% 265.92/169.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(tptp_fun_W_2(Y!51, X!50))) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W)))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[116, 115])).
% 265.92/169.94 tff(118,plain,
% 265.92/169.94 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W)))))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[117, 114, 101])).
% 265.92/169.94 tff(119,plain,
% 265.92/169.94 (ssList(W!49)),
% 265.92/169.94 inference(and_elim,[status(thm)],[24])).
% 265.92/169.94 tff(120,plain,
% 265.92/169.94 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W)))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(121,plain,
% 265.92/169.94 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W)))))),
% 265.92/169.94 inference(quant_inst,[status(thm)],[])).
% 265.92/169.94 tff(122,plain,
% 265.92/169.94 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), V), W) = app(tptp_fun_W_2(Y!51, X!50), app(V, W)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[121, 120])).
% 265.92/169.94 tff(123,plain,
% 265.92/169.94 (![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W))))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[122, 119, 118])).
% 265.92/169.94 tff(124,plain,
% 265.92/169.94 (((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W))))) | ((~ssList(tptp_fun_X_3(Y!51, X!50))) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, tptp_fun_X_3(Y!51, X!50)))))) <=> ((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W))))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, tptp_fun_X_3(Y!51, X!50)))))),
% 265.92/169.94 inference(rewrite,[status(thm)],[])).
% 265.92/169.94 tff(125,plain,
% 265.92/169.94 ((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W))))) | ((~ssList(tptp_fun_X_3(Y!51, X!50))) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, tptp_fun_X_3(Y!51, X!50)))))),
% 265.92/169.94 inference(quant_inst,[status(thm)],[])).
% 265.92/169.94 tff(126,plain,
% 265.92/169.94 ((~![W: $i] : ((~ssList(W)) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), W) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, W))))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, tptp_fun_X_3(Y!51, X!50))))),
% 265.92/169.94 inference(modus_ponens,[status(thm)],[125, 124])).
% 265.92/169.94 tff(127,plain,
% 265.92/169.94 (app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = app(tptp_fun_W_2(Y!51, X!50), app(W!49, tptp_fun_X_3(Y!51, X!50)))),
% 265.92/169.94 inference(unit_resolution,[status(thm)],[126, 71, 123])).
% 265.92/169.94 tff(128,plain,
% 265.92/169.94 (app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = X!50),
% 265.92/169.94 inference(transitivity,[status(thm)],[127, 99, 69])).
% 265.92/169.94 tff(129,plain,
% 265.92/169.94 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 265.92/169.94 inference(bind,[status(th)],[])).
% 265.92/169.94 tff(130,plain,
% 265.92/169.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 265.92/169.94 inference(quant_intro,[status(thm)],[129])).
% 265.92/169.94 tff(131,plain,
% 265.92/169.94 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 265.92/169.95 inference(bind,[status(th)],[])).
% 265.92/169.95 tff(132,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 265.92/169.95 inference(quant_intro,[status(thm)],[131])).
% 265.92/169.95 tff(133,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 265.92/169.95 inference(transitivity,[status(thm)],[132, 130])).
% 265.92/169.95 tff(134,plain,
% 265.92/169.95 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U)))))))))))),
% 265.92/169.95 inference(bind,[status(th)],[])).
% 265.92/169.95 tff(135,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 265.92/169.95 inference(quant_intro,[status(thm)],[134])).
% 265.92/169.95 tff(136,plain,
% 265.92/169.95 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))))),
% 265.92/169.95 inference(bind,[status(th)],[])).
% 265.92/169.95 tff(137,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 265.92/169.95 inference(quant_intro,[status(thm)],[136])).
% 265.92/169.95 tff(138,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 265.92/169.95 inference(rewrite,[status(thm)],[])).
% 265.92/169.95 tff(139,plain,
% 265.92/169.95 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))) <=> (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), rewrite((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))), ((ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), (![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))) <=> ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), ((ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))))),
% 265.92/169.95 inference(bind,[status(th)],[])).
% 265.92/169.95 tff(140,plain,
% 265.92/169.95 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 265.92/169.95 inference(quant_intro,[status(thm)],[139])).
% 265.92/169.95 tff(141,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax7')).
% 265.92/169.95 tff(142,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[141, 140])).
% 265.92/169.95 tff(143,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (segmentP(U, V) <=> ?[W: $i] : (ssList(W) & ?[X: $i] : (ssList(X) & (app(app(W, V), X) = U))))))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[142, 138])).
% 265.92/169.95 tff(144,plain,(
% 265.92/169.95 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & (ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 265.92/169.95 inference(skolemize,[status(sab)],[143])).
% 265.92/169.95 tff(145,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~segmentP(U, V)) | (ssList(tptp_fun_W_7(V, U)) & ssList(tptp_fun_X_8(V, U)) & (app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U))) & (segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (~(ssList(X) & (app(app(W, V), X) = U))))))))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[144, 137])).
% 265.92/169.95 tff(146,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[145, 135])).
% 265.92/169.95 tff(147,plain,
% 265.92/169.95 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[146, 133])).
% 265.92/169.95 tff(148,plain,
% 265.92/169.95 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50))))))))))),
% 265.92/169.95 inference(rewrite,[status(thm)],[])).
% 265.92/169.95 tff(149,plain,
% 265.92/169.95 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50))))))))))),
% 265.92/169.95 inference(quant_inst,[status(thm)],[])).
% 265.92/169.95 tff(150,plain,
% 265.92/169.95 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(U, V)) | (~((~ssList(tptp_fun_W_7(V, U))) | (~ssList(tptp_fun_X_8(V, U))) | (~(app(app(tptp_fun_W_7(V, U), V), tptp_fun_X_8(V, U)) = U)))))) | (~(segmentP(U, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = U))))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50)))))))))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[149, 148])).
% 265.92/169.95 tff(151,plain,
% 265.92/169.95 (![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50)))))))))),
% 265.92/169.95 inference(unit_resolution,[status(thm)],[150, 147, 25])).
% 265.92/169.95 tff(152,plain,
% 265.92/169.95 (((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50)))))))))) | ((~ssList(W!49)) | (~((~((~segmentP(X!50, W!49)) | (~((~ssList(tptp_fun_W_7(W!49, X!50))) | (~ssList(tptp_fun_X_8(W!49, X!50))) | (~(app(app(tptp_fun_W_7(W!49, X!50), W!49), tptp_fun_X_8(W!49, X!50)) = X!50)))))) | (~(segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50)))))))))) | (~ssList(W!49)) | (~((~((~segmentP(X!50, W!49)) | (~((~ssList(tptp_fun_W_7(W!49, X!50))) | (~ssList(tptp_fun_X_8(W!49, X!50))) | (~(app(app(tptp_fun_W_7(W!49, X!50), W!49), tptp_fun_X_8(W!49, X!50)) = X!50)))))) | (~(segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50)))))))))),
% 265.92/169.95 inference(rewrite,[status(thm)],[])).
% 265.92/169.95 tff(153,plain,
% 265.92/169.95 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50)))))))))) | ((~ssList(W!49)) | (~((~((~segmentP(X!50, W!49)) | (~((~ssList(tptp_fun_W_7(W!49, X!50))) | (~ssList(tptp_fun_X_8(W!49, X!50))) | (~(app(app(tptp_fun_W_7(W!49, X!50), W!49), tptp_fun_X_8(W!49, X!50)) = X!50)))))) | (~(segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50)))))))))),
% 265.92/169.95 inference(quant_inst,[status(thm)],[])).
% 265.92/169.95 tff(154,plain,
% 265.92/169.95 ((~![V: $i] : ((~ssList(V)) | (~((~((~segmentP(X!50, V)) | (~((~ssList(tptp_fun_W_7(V, X!50))) | (~ssList(tptp_fun_X_8(V, X!50))) | (~(app(app(tptp_fun_W_7(V, X!50), V), tptp_fun_X_8(V, X!50)) = X!50)))))) | (~(segmentP(X!50, V) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, V), X) = X!50)))))))))) | (~ssList(W!49)) | (~((~((~segmentP(X!50, W!49)) | (~((~ssList(tptp_fun_W_7(W!49, X!50))) | (~ssList(tptp_fun_X_8(W!49, X!50))) | (~(app(app(tptp_fun_W_7(W!49, X!50), W!49), tptp_fun_X_8(W!49, X!50)) = X!50)))))) | (~(segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))))))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[153, 152])).
% 265.92/169.95 tff(155,plain,
% 265.92/169.95 (~((~((~segmentP(X!50, W!49)) | (~((~ssList(tptp_fun_W_7(W!49, X!50))) | (~ssList(tptp_fun_X_8(W!49, X!50))) | (~(app(app(tptp_fun_W_7(W!49, X!50), W!49), tptp_fun_X_8(W!49, X!50)) = X!50)))))) | (~(segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50)))))))),
% 265.92/169.95 inference(unit_resolution,[status(thm)],[154, 119, 151])).
% 265.92/169.95 tff(156,plain,
% 265.92/169.95 (((~((~segmentP(X!50, W!49)) | (~((~ssList(tptp_fun_W_7(W!49, X!50))) | (~ssList(tptp_fun_X_8(W!49, X!50))) | (~(app(app(tptp_fun_W_7(W!49, X!50), W!49), tptp_fun_X_8(W!49, X!50)) = X!50)))))) | (~(segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))))) | (segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50)))))),
% 265.92/169.95 inference(tautology,[status(thm)],[])).
% 265.92/169.95 tff(157,plain,
% 265.92/169.95 (segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))),
% 265.92/169.95 inference(unit_resolution,[status(thm)],[156, 155])).
% 265.92/169.95 tff(158,plain,
% 265.92/169.95 (U!47 = W!49),
% 265.92/169.95 inference(and_elim,[status(thm)],[24])).
% 265.92/169.95 tff(159,plain,
% 265.92/169.95 (W!49 = U!47),
% 265.92/169.95 inference(symmetry,[status(thm)],[158])).
% 265.92/169.95 tff(160,plain,
% 265.92/169.95 (X!50 = V!48),
% 265.92/169.95 inference(symmetry,[status(thm)],[49])).
% 265.92/169.95 tff(161,plain,
% 265.92/169.95 (segmentP(X!50, W!49) <=> segmentP(V!48, U!47)),
% 265.92/169.95 inference(monotonicity,[status(thm)],[160, 159])).
% 265.92/169.95 tff(162,plain,
% 265.92/169.95 (segmentP(V!48, U!47) <=> segmentP(X!50, W!49)),
% 265.92/169.95 inference(symmetry,[status(thm)],[161])).
% 265.92/169.95 tff(163,plain,
% 265.92/169.95 ((~segmentP(V!48, U!47)) <=> (~segmentP(X!50, W!49))),
% 265.92/169.95 inference(monotonicity,[status(thm)],[162])).
% 265.92/169.95 tff(164,plain,
% 265.92/169.95 (~segmentP(V!48, U!47)),
% 265.92/169.95 inference(and_elim,[status(thm)],[24])).
% 265.92/169.95 tff(165,plain,
% 265.92/169.95 (~segmentP(X!50, W!49)),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[164, 163])).
% 265.92/169.95 tff(166,plain,
% 265.92/169.95 ((~(segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50)))))) | segmentP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))),
% 265.92/169.95 inference(tautology,[status(thm)],[])).
% 265.92/169.95 tff(167,plain,
% 265.92/169.95 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))),
% 265.92/169.95 inference(unit_resolution,[status(thm)],[166, 165, 157])).
% 265.92/169.95 tff(168,plain,
% 265.92/169.95 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))) | ((~ssList(tptp_fun_W_2(Y!51, X!50))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50))))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))) | (~ssList(tptp_fun_W_2(Y!51, X!50))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50))))),
% 265.92/169.95 inference(rewrite,[status(thm)],[])).
% 265.92/169.95 tff(169,plain,
% 265.92/169.95 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))) | ((~ssList(tptp_fun_W_2(Y!51, X!50))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50))))),
% 265.92/169.95 inference(quant_inst,[status(thm)],[])).
% 265.92/169.95 tff(170,plain,
% 265.92/169.95 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~(app(app(W, W!49), X) = X!50))))) | (~ssList(tptp_fun_W_2(Y!51, X!50))) | ![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50)))),
% 265.92/169.95 inference(modus_ponens,[status(thm)],[169, 168])).
% 265.92/169.95 tff(171,plain,
% 265.92/169.95 (![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50)))),
% 265.92/169.95 inference(unit_resolution,[status(thm)],[170, 101, 167])).
% 265.92/169.95 tff(172,plain,
% 265.92/169.95 (((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50)))) | ((~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = X!50)))) <=> ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50)))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = X!50)))),
% 265.92/169.95 inference(rewrite,[status(thm)],[])).
% 265.92/169.95 tff(173,plain,
% 265.92/169.95 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50)))) | ((~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = X!50)))),
% 265.92/169.95 inference(quant_inst,[status(thm)],[])).
% 265.92/169.95 tff(174,plain,
% 265.92/169.95 ((~![X: $i] : ((~ssList(X)) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), X) = X!50)))) | (~ssList(tptp_fun_X_3(Y!51, X!50))) | (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = X!50))),
% 266.09/170.13 inference(modus_ponens,[status(thm)],[173, 172])).
% 266.09/170.13 tff(175,plain,
% 266.09/170.13 (~(app(app(tptp_fun_W_2(Y!51, X!50), W!49), tptp_fun_X_3(Y!51, X!50)) = X!50)),
% 266.09/170.13 inference(unit_resolution,[status(thm)],[174, 71, 171])).
% 266.09/170.13 tff(176,plain,
% 266.09/170.13 ($false),
% 266.09/170.13 inference(unit_resolution,[status(thm)],[175, 128])).
% 266.09/170.13 % SZS output end Proof
%------------------------------------------------------------------------------