TSTP Solution File: SWC007+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC007+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 11:54:35 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC007+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 20:34:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.56 % SZS status Theorem
% 0.19/0.56 % SZS output start Proof
% 0.19/0.56 tff(tptp_fun_V_48_type, type, (
% 0.19/0.56 tptp_fun_V_48: $i)).
% 0.19/0.56 tff(app_type, type, (
% 0.19/0.56 app: ( $i * $i ) > $i)).
% 0.19/0.56 tff(tptp_fun_W_5_type, type, (
% 0.19/0.56 tptp_fun_W_5: ( $i * $i ) > $i)).
% 0.19/0.56 tff(tptp_fun_W_49_type, type, (
% 0.19/0.56 tptp_fun_W_49: $i)).
% 0.19/0.56 tff(tptp_fun_X_50_type, type, (
% 0.19/0.56 tptp_fun_X_50: $i)).
% 0.19/0.56 tff(tptp_fun_U_47_type, type, (
% 0.19/0.56 tptp_fun_U_47: $i)).
% 0.19/0.56 tff(ssList_type, type, (
% 0.19/0.56 ssList: $i > $o)).
% 0.19/0.56 tff(nil_type, type, (
% 0.19/0.56 nil: $i)).
% 0.19/0.56 tff(frontsegP_type, type, (
% 0.19/0.56 frontsegP: ( $i * $i ) > $o)).
% 0.19/0.56 tff(1,plain,
% 0.19/0.56 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(2,plain,
% 0.19/0.56 ((ssList(V!48) & (ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))) <=> (ssList(V!48) & ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(3,plain,
% 0.19/0.56 ((ssList(W!49) & ((nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))) <=> (ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(4,plain,
% 0.19/0.56 (((~(~(nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~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)))))) <=> ((nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(5,plain,
% 0.19/0.56 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(6,plain,
% 0.19/0.56 (((~(~ssList(W!49))) & ((~(~(nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~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))))))) <=> (ssList(W!49) & ((nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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)))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[5, 4])).
% 0.19/0.56 tff(7,plain,
% 0.19/0.56 (((~(~ssList(W!49))) & ((~(~(nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~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))))))) <=> (ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[6, 3])).
% 0.19/0.56 tff(8,plain,
% 0.19/0.56 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(9,plain,
% 0.19/0.56 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~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)))))))) <=> (ssList(V!48) & (ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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)))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[8, 7])).
% 0.19/0.56 tff(10,plain,
% 0.19/0.56 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~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)))))))) <=> (ssList(V!48) & ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[9, 2])).
% 0.19/0.56 tff(11,plain,
% 0.19/0.56 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(12,plain,
% 0.19/0.56 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~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))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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)))))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[11, 10])).
% 0.19/0.56 tff(13,plain,
% 0.19/0.56 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~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))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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))))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[12, 1])).
% 0.19/0.56 tff(14,plain,
% 0.19/0.56 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(15,plain,
% 0.19/0.56 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(nil = W)) | (~(V = X))) | (~(U = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U)))))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(nil = W)) | (~(V = X))) | (~(U = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = V)) & (app(Y, X1) = U)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.19/0.56 tff(17,plain,
% 0.19/0.56 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.56 tff(18,plain,
% 0.19/0.56 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.56 tff(19,plain,
% 0.19/0.56 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.56 tff(20,plain,
% 0.19/0.56 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.19/0.56 tff(21,plain,
% 0.19/0.56 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.19/0.56 tff(22,plain,
% 0.19/0.56 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.56 tff(23,plain,
% 0.19/0.56 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = V) & (app(Y, X1) = U))))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.19/0.56 tff(24,plain,
% 0.19/0.56 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (nil = W!49) & (V!48 = X!50) & (U!47 = W!49) & 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)))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.19/0.56 tff(25,plain,
% 0.19/0.56 (V!48 = X!50),
% 0.19/0.56 inference(and_elim,[status(thm)],[24])).
% 0.19/0.56 tff(26,plain,
% 0.19/0.56 (X!50 = V!48),
% 0.19/0.56 inference(symmetry,[status(thm)],[25])).
% 0.19/0.56 tff(27,plain,
% 0.19/0.56 (ssList(X!50)),
% 0.19/0.56 inference(and_elim,[status(thm)],[24])).
% 0.19/0.56 tff(28,plain,
% 0.19/0.56 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(29,plain,
% 0.19/0.56 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.56 tff(30,plain,
% 0.19/0.56 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(31,plain,
% 0.19/0.56 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(32,plain,
% 0.19/0.56 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.56 tff(33,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 0.19/0.56 tff(34,plain,
% 0.19/0.56 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.56 tff(35,plain,
% 0.19/0.56 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.56 tff(36,plain,(
% 0.19/0.56 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.19/0.56 inference(skolemize,[status(sab)],[35])).
% 0.19/0.56 tff(37,plain,
% 0.19/0.56 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.57 tff(38,plain,
% 0.19/0.57 (((~![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))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(39,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(40,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.57 tff(41,plain,
% 0.19/0.57 (app(X!50, nil) = X!50),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 0.19/0.57 tff(42,plain,
% 0.19/0.57 (nil = W!49),
% 0.19/0.57 inference(and_elim,[status(thm)],[24])).
% 0.19/0.57 tff(43,plain,
% 0.19/0.57 (W!49 = nil),
% 0.19/0.57 inference(symmetry,[status(thm)],[42])).
% 0.19/0.57 tff(44,plain,
% 0.19/0.57 (ssList(W!49)),
% 0.19/0.57 inference(and_elim,[status(thm)],[24])).
% 0.19/0.57 tff(45,plain,
% 0.19/0.57 (^[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))))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(46,plain,
% 0.19/0.57 (![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)))))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.57 tff(47,plain,
% 0.19/0.57 (^[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))))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(48,plain,
% 0.19/0.57 (![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)))))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.57 tff(49,plain,
% 0.19/0.57 (![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)))))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.57 tff(50,plain,
% 0.19/0.57 (^[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))))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(51,plain,
% 0.19/0.57 (![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)))))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.57 tff(52,plain,
% 0.19/0.57 (![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)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(53,plain,
% 0.19/0.57 (^[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)))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(54,plain,
% 0.19/0.57 (![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)))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.57 tff(55,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')).
% 0.19/0.57 tff(56,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.57 tff(57,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.57 tff(58,plain,(
% 0.19/0.57 ![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)))))))),
% 0.19/0.57 inference(skolemize,[status(sab)],[57])).
% 0.19/0.57 tff(59,plain,
% 0.19/0.57 (![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)))))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.57 tff(60,plain,
% 0.19/0.57 (![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)))))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.19/0.57 tff(61,plain,
% 0.19/0.57 (((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49)))))))))) <=> ((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49)))))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(62,plain,
% 0.19/0.57 ((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49)))))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(63,plain,
% 0.19/0.57 ((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49))))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.57 tff(64,plain,
% 0.19/0.57 (![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49))))))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[63, 60, 44])).
% 0.19/0.57 tff(65,plain,
% 0.19/0.57 (((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49))))))))) | ((~ssList(W!49)) | (~((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~(frontsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = W!49))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49))))))))) | (~ssList(W!49)) | (~((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~(frontsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = W!49))))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(66,plain,
% 0.19/0.57 ((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49))))))))) | ((~ssList(W!49)) | (~((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~(frontsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = W!49))))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(67,plain,
% 0.19/0.57 ((~![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(W!49, V)) | (~((~ssList(tptp_fun_W_5(V, W!49))) | (~(app(V, tptp_fun_W_5(V, W!49)) = W!49)))))) | (~(frontsegP(W!49, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = W!49))))))))) | (~ssList(W!49)) | (~((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~(frontsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = W!49)))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.57 tff(68,plain,
% 0.19/0.57 (~((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~(frontsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = W!49))))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[67, 44, 64])).
% 0.19/0.57 tff(69,plain,
% 0.19/0.57 (((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~(frontsegP(W!49, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W!49, W) = W!49)))))) | ((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(70,plain,
% 0.19/0.57 ((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.57 tff(71,plain,
% 0.19/0.57 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(72,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.57 tff(73,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(74,plain,
% 0.19/0.57 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(75,plain,
% 0.19/0.57 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.57 tff(76,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax42')).
% 0.19/0.57 tff(77,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.57 tff(78,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.57 tff(79,plain,(
% 0.19/0.57 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.19/0.57 inference(skolemize,[status(sab)],[78])).
% 0.19/0.57 tff(80,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.19/0.57 tff(81,plain,
% 0.19/0.57 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(82,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(W!49)) | frontsegP(W!49, W!49))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(83,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(W!49)) | frontsegP(W!49, W!49)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.57 tff(84,plain,
% 0.19/0.57 (frontsegP(W!49, W!49)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[83, 80, 44])).
% 0.19/0.57 tff(85,plain,
% 0.19/0.57 ((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49))))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(86,plain,
% 0.19/0.57 ((~((~frontsegP(W!49, W!49)) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))))) | (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.57 tff(87,plain,
% 0.19/0.57 (~((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[86, 70])).
% 0.19/0.57 tff(88,plain,
% 0.19/0.57 (((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49))) | (app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49)),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(89,plain,
% 0.19/0.57 (app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.57 tff(90,plain,
% 0.19/0.57 (app(W!49, tptp_fun_W_5(W!49, W!49)) = nil),
% 0.19/0.57 inference(transitivity,[status(thm)],[89, 43])).
% 0.19/0.57 tff(91,plain,
% 0.19/0.57 (app(X!50, app(W!49, tptp_fun_W_5(W!49, W!49))) = app(X!50, nil)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.57 tff(92,plain,
% 0.19/0.57 (((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = W!49))) | ssList(tptp_fun_W_5(W!49, W!49))),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(93,plain,
% 0.19/0.57 (ssList(tptp_fun_W_5(W!49, W!49))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[92, 87])).
% 0.19/0.57 tff(94,plain,
% 0.19/0.57 (^[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)))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(95,plain,
% 0.19/0.57 (![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))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.57 tff(96,plain,
% 0.19/0.57 (^[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)))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(97,plain,
% 0.19/0.57 (![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))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.57 tff(98,plain,
% 0.19/0.57 (![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))))))),
% 0.19/0.57 inference(transitivity,[status(thm)],[97, 95])).
% 0.19/0.57 tff(99,plain,
% 0.19/0.57 (![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))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(100,plain,
% 0.19/0.57 (^[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))))))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(101,plain,
% 0.19/0.57 (![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))))))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.57 tff(102,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/sandbox2/benchmark/Axioms/SWC001+0.ax','ax82')).
% 0.19/0.57 tff(103,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.57 tff(104,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.57 tff(105,plain,(
% 0.19/0.57 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.19/0.57 inference(skolemize,[status(sab)],[104])).
% 0.19/0.57 tff(106,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.19/0.57 tff(107,plain,
% 0.19/0.57 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(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(X!50)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(108,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W))))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(109,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(U, V), W) = app(U, app(V, W))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W)))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.57 tff(110,plain,
% 0.19/0.57 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W)))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[109, 106, 27])).
% 0.19/0.57 tff(111,plain,
% 0.19/0.57 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(112,plain,
% 0.19/0.57 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(113,plain,
% 0.19/0.57 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, V), W) = app(X!50, app(V, W)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.57 tff(114,plain,
% 0.19/0.57 (![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[113, 44, 110])).
% 0.19/0.57 tff(115,plain,
% 0.19/0.57 (((~![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W))))) | ((~ssList(tptp_fun_W_5(W!49, W!49))) | (app(app(X!50, W!49), tptp_fun_W_5(W!49, W!49)) = app(X!50, app(W!49, tptp_fun_W_5(W!49, W!49)))))) <=> ((~![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W))))) | (~ssList(tptp_fun_W_5(W!49, W!49))) | (app(app(X!50, W!49), tptp_fun_W_5(W!49, W!49)) = app(X!50, app(W!49, tptp_fun_W_5(W!49, W!49)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(116,plain,
% 0.19/0.57 ((~![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W))))) | ((~ssList(tptp_fun_W_5(W!49, W!49))) | (app(app(X!50, W!49), tptp_fun_W_5(W!49, W!49)) = app(X!50, app(W!49, tptp_fun_W_5(W!49, W!49)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(117,plain,
% 0.19/0.57 ((~![W: $i] : ((~ssList(W)) | (app(app(X!50, W!49), W) = app(X!50, app(W!49, W))))) | (~ssList(tptp_fun_W_5(W!49, W!49))) | (app(app(X!50, W!49), tptp_fun_W_5(W!49, W!49)) = app(X!50, app(W!49, tptp_fun_W_5(W!49, W!49))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.57 tff(118,plain,
% 0.19/0.57 (app(app(X!50, W!49), tptp_fun_W_5(W!49, W!49)) = app(X!50, app(W!49, tptp_fun_W_5(W!49, W!49)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[117, 114, 93])).
% 0.19/0.57 tff(119,plain,
% 0.19/0.57 (app(X!50, W!49) = app(X!50, nil)),
% 0.19/0.57 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.57 tff(120,plain,
% 0.19/0.57 (app(X!50, nil) = app(X!50, W!49)),
% 0.19/0.57 inference(symmetry,[status(thm)],[119])).
% 0.19/0.57 tff(121,plain,
% 0.19/0.57 (X!50 = app(X!50, nil)),
% 0.19/0.57 inference(symmetry,[status(thm)],[41])).
% 0.19/0.57 tff(122,plain,
% 0.19/0.57 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(123,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.57 tff(124,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(125,plain,
% 0.19/0.57 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(126,plain,
% 0.19/0.57 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.57 tff(127,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax28')).
% 0.19/0.57 tff(128,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.19/0.57 tff(129,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.19/0.57 tff(130,plain,(
% 0.19/0.57 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.19/0.57 inference(skolemize,[status(sab)],[129])).
% 0.19/0.57 tff(131,plain,
% 0.19/0.57 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.19/0.57 tff(132,plain,
% 0.19/0.57 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(X!50)) | (app(nil, X!50) = X!50))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(X!50)) | (app(nil, X!50) = X!50))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(133,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(X!50)) | (app(nil, X!50) = X!50))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(134,plain,
% 0.19/0.57 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(X!50)) | (app(nil, X!50) = X!50)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.58 tff(135,plain,
% 0.19/0.58 (app(nil, X!50) = X!50),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[134, 131, 27])).
% 0.19/0.58 tff(136,plain,
% 0.19/0.58 (app(W!49, X!50) = app(nil, X!50)),
% 0.19/0.58 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.58 tff(137,plain,
% 0.19/0.58 (app(W!49, X!50) = app(X!50, W!49)),
% 0.19/0.58 inference(transitivity,[status(thm)],[136, 135, 121, 120])).
% 0.19/0.58 tff(138,plain,
% 0.19/0.58 (app(app(W!49, X!50), tptp_fun_W_5(W!49, W!49)) = app(app(X!50, W!49), tptp_fun_W_5(W!49, W!49))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[137])).
% 0.19/0.58 tff(139,plain,
% 0.19/0.58 (app(app(W!49, X!50), tptp_fun_W_5(W!49, W!49)) = V!48),
% 0.19/0.58 inference(transitivity,[status(thm)],[138, 118, 91, 41, 26])).
% 0.19/0.58 tff(140,plain,
% 0.19/0.58 (U!47 = W!49),
% 0.19/0.58 inference(and_elim,[status(thm)],[24])).
% 0.19/0.58 tff(141,plain,
% 0.19/0.58 (W!49 = U!47),
% 0.19/0.58 inference(symmetry,[status(thm)],[140])).
% 0.19/0.58 tff(142,plain,
% 0.19/0.58 (app(W!49, tptp_fun_W_5(W!49, W!49)) = U!47),
% 0.19/0.58 inference(transitivity,[status(thm)],[89, 141])).
% 0.19/0.58 tff(143,plain,
% 0.19/0.58 (^[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))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(144,plain,
% 0.19/0.58 (![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)))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.58 tff(145,plain,
% 0.19/0.58 (^[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))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(146,plain,
% 0.19/0.58 (![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)))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[145])).
% 0.19/0.58 tff(147,plain,
% 0.19/0.58 (![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)))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[146, 144])).
% 0.19/0.58 tff(148,plain,
% 0.19/0.58 (^[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))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(149,plain,
% 0.19/0.58 (![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)))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.58 tff(150,plain,
% 0.19/0.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = V!48) & (app(Y, X1) = U!47)))))),
% 0.19/0.58 inference(and_elim,[status(thm)],[24])).
% 0.19/0.58 tff(151,plain,
% 0.19/0.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.58 tff(152,plain,
% 0.19/0.58 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = V!48)) | (~(app(Y, X1) = U!47)))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.19/0.58 tff(153,plain,
% 0.19/0.58 (((~![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)))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(154,plain,
% 0.19/0.58 ((~![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)))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(155,plain,
% 0.19/0.58 ((~![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))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.58 tff(156,plain,
% 0.19/0.58 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[155, 44, 152])).
% 0.19/0.58 tff(157,plain,
% 0.19/0.58 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(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(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(158,plain,
% 0.19/0.58 (((~ssList(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, X!50), X1) = V!48)) | (~(app(W!49, X1) = U!47)))) <=> ((~ssList(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(159,plain,
% 0.19/0.58 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(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(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48)))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[158])).
% 0.19/0.58 tff(160,plain,
% 0.19/0.58 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(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(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[159, 157])).
% 0.19/0.58 tff(161,plain,
% 0.19/0.58 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | ((~ssList(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, X!50), X1) = V!48)) | (~(app(W!49, X1) = U!47))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(162,plain,
% 0.19/0.58 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(W!49, Z), X1) = V!48)) | (~(app(W!49, X1) = U!47))))) | (~ssList(X!50)) | ![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.59 tff(163,plain,
% 0.19/0.59 (![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48)))),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[162, 27, 156])).
% 0.19/0.59 tff(164,plain,
% 0.19/0.59 (((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48)))) | ((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = U!47)) | (~(app(app(W!49, X!50), tptp_fun_W_5(W!49, W!49)) = V!48)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48)))) | (~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = U!47)) | (~(app(app(W!49, X!50), tptp_fun_W_5(W!49, W!49)) = V!48)))),
% 0.19/0.59 inference(rewrite,[status(thm)],[])).
% 0.19/0.59 tff(165,plain,
% 0.19/0.59 ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48)))) | ((~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = U!47)) | (~(app(app(W!49, X!50), tptp_fun_W_5(W!49, W!49)) = V!48)))),
% 0.19/0.59 inference(quant_inst,[status(thm)],[])).
% 0.19/0.59 tff(166,plain,
% 0.19/0.59 ((~![X1: $i] : ((~ssList(X1)) | (~(app(W!49, X1) = U!47)) | (~(app(app(W!49, X!50), X1) = V!48)))) | (~ssList(tptp_fun_W_5(W!49, W!49))) | (~(app(W!49, tptp_fun_W_5(W!49, W!49)) = U!47)) | (~(app(app(W!49, X!50), tptp_fun_W_5(W!49, W!49)) = V!48))),
% 0.19/0.59 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.59 tff(167,plain,
% 0.19/0.59 (~(app(app(W!49, X!50), tptp_fun_W_5(W!49, W!49)) = V!48)),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[166, 163, 93, 142])).
% 0.19/0.59 tff(168,plain,
% 0.19/0.59 ($false),
% 0.19/0.59 inference(unit_resolution,[status(thm)],[167, 139])).
% 0.19/0.59 % SZS output end Proof
%------------------------------------------------------------------------------