TSTP Solution File: SWC094+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC094+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:55:13 EDT 2022
% Result : Theorem 0.19s 0.58s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC094+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 21:43:51 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.
% 0.19/0.58 % SZS status Theorem
% 0.19/0.58 % SZS output start Proof
% 0.19/0.58 tff(tptp_fun_U_47_type, type, (
% 0.19/0.58 tptp_fun_U_47: $i)).
% 0.19/0.58 tff(app_type, type, (
% 0.19/0.58 app: ( $i * $i ) > $i)).
% 0.19/0.58 tff(tptp_fun_W_5_type, type, (
% 0.19/0.58 tptp_fun_W_5: ( $i * $i ) > $i)).
% 0.19/0.58 tff(tptp_fun_W_49_type, type, (
% 0.19/0.58 tptp_fun_W_49: $i)).
% 0.19/0.58 tff(nil_type, type, (
% 0.19/0.58 nil: $i)).
% 0.19/0.58 tff(tptp_fun_V_48_type, type, (
% 0.19/0.58 tptp_fun_V_48: $i)).
% 0.19/0.58 tff(ssList_type, type, (
% 0.19/0.58 ssList: $i > $o)).
% 0.19/0.58 tff(tptp_fun_X_50_type, type, (
% 0.19/0.58 tptp_fun_X_50: $i)).
% 0.19/0.58 tff(frontsegP_type, type, (
% 0.19/0.58 frontsegP: ( $i * $i ) > $o)).
% 0.19/0.58 tff(1,plain,
% 0.19/0.58 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(2,plain,
% 0.19/0.58 ((ssList(V!48) & (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))) <=> (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(3,plain,
% 0.19/0.58 ((ssList(W!49) & ((X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))) <=> (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(4,plain,
% 0.19/0.58 (((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))) <=> ((X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(5,plain,
% 0.19/0.58 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(6,plain,
% 0.19/0.58 (((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))) <=> (ssList(W!49) & ((X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[5, 4])).
% 0.19/0.58 tff(7,plain,
% 0.19/0.58 (((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))) <=> (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[6, 3])).
% 0.19/0.58 tff(8,plain,
% 0.19/0.58 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(9,plain,
% 0.19/0.58 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))))) <=> (ssList(V!48) & (ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))))),
% 0.54/0.58 inference(monotonicity,[status(thm)],[8, 7])).
% 0.54/0.58 tff(10,plain,
% 0.54/0.58 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))))) <=> (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))),
% 0.54/0.58 inference(transitivity,[status(thm)],[9, 2])).
% 0.54/0.58 tff(11,plain,
% 0.54/0.58 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(12,plain,
% 0.54/0.58 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))))),
% 0.54/0.58 inference(monotonicity,[status(thm)],[11, 10])).
% 0.54/0.58 tff(13,plain,
% 0.54/0.58 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(~(X!50 = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))))),
% 0.54/0.58 inference(transitivity,[status(thm)],[12, 1])).
% 0.54/0.58 tff(14,plain,
% 0.54/0.58 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V)))))))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(15,plain,
% 0.54/0.58 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = U)) & (app(Y, X1) = V)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V)))))))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~(X = W))) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Y, Z), X1) = U)) & (app(Y, X1) = V)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.54/0.58 tff(17,plain,
% 0.54/0.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.54/0.58 tff(18,plain,
% 0.54/0.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.54/0.58 tff(19,plain,
% 0.54/0.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.54/0.58 tff(20,plain,
% 0.54/0.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.54/0.58 tff(21,plain,
% 0.54/0.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.54/0.58 tff(22,plain,
% 0.54/0.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.54/0.58 tff(23,plain,
% 0.54/0.58 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~(X = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | ?[Y: $i] : (ssList(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Y, Z), X1) = U) & (app(Y, X1) = V))))))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.54/0.58 tff(24,plain,
% 0.54/0.58 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (X!50 = W!49) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.54/0.58 tff(25,plain,
% 0.54/0.58 (U!47 = W!49),
% 0.54/0.58 inference(and_elim,[status(thm)],[24])).
% 0.54/0.58 tff(26,plain,
% 0.54/0.58 (W!49 = U!47),
% 0.54/0.58 inference(symmetry,[status(thm)],[25])).
% 0.54/0.58 tff(27,plain,
% 0.54/0.58 (ssList(W!49)),
% 0.54/0.58 inference(and_elim,[status(thm)],[24])).
% 0.54/0.58 tff(28,plain,
% 0.54/0.58 (^[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))))))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(29,plain,
% 0.54/0.58 (![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)))))))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[28])).
% 0.54/0.58 tff(30,plain,
% 0.54/0.58 (^[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))))))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(31,plain,
% 0.54/0.58 (![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)))))))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[30])).
% 0.54/0.58 tff(32,plain,
% 0.54/0.58 (![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)))))))))),
% 0.54/0.58 inference(transitivity,[status(thm)],[31, 29])).
% 0.54/0.58 tff(33,plain,
% 0.54/0.58 (^[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))))))))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(34,plain,
% 0.54/0.58 (![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)))))))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[33])).
% 0.54/0.58 tff(35,plain,
% 0.54/0.58 (![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)))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(36,plain,
% 0.54/0.58 (^[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)))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(37,plain,
% 0.54/0.59 (![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)))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[36])).
% 0.54/0.59 tff(38,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax5')).
% 0.54/0.59 tff(39,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.54/0.59 tff(40,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.54/0.59 tff(41,plain,(
% 0.54/0.59 ![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)))))))),
% 0.54/0.59 inference(skolemize,[status(sab)],[40])).
% 0.54/0.59 tff(42,plain,
% 0.54/0.59 (![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)))))))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.54/0.59 tff(43,plain,
% 0.54/0.59 (![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)))))))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.54/0.59 tff(44,plain,
% 0.54/0.59 (((~![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)))))))))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(45,plain,
% 0.54/0.59 ((~![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)))))))))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(46,plain,
% 0.54/0.59 ((~![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))))))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.54/0.59 tff(47,plain,
% 0.54/0.59 (![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))))))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[46, 43, 27])).
% 0.54/0.59 tff(48,plain,
% 0.54/0.59 (ssList(nil) <=> ssList(nil)),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(49,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.54/0.59 tff(50,plain,
% 0.54/0.59 (ssList(nil)),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.54/0.59 tff(51,plain,
% 0.54/0.59 (((~![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(nil)) | (~((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~(frontsegP(W!49, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, 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(nil)) | (~((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~(frontsegP(W!49, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = W!49))))))))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(52,plain,
% 0.54/0.59 ((~![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(nil)) | (~((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~(frontsegP(W!49, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = W!49))))))))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(53,plain,
% 0.54/0.59 ((~![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(nil)) | (~((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~(frontsegP(W!49, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = W!49)))))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.54/0.59 tff(54,plain,
% 0.54/0.59 (~((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~(frontsegP(W!49, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = W!49))))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[53, 50, 47])).
% 0.54/0.59 tff(55,plain,
% 0.54/0.59 (((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~(frontsegP(W!49, nil) | ![W: $i] : ((~ssList(W)) | (~(app(nil, W) = W!49)))))) | ((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(56,plain,
% 0.54/0.59 ((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.54/0.59 tff(57,plain,
% 0.54/0.59 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(58,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[57])).
% 0.54/0.59 tff(59,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(60,plain,
% 0.54/0.59 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(61,plain,
% 0.54/0.59 (![U: $i] : (ssList(U) => frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[60])).
% 0.54/0.59 tff(62,axiom,(![U: $i] : (ssList(U) => frontsegP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax45')).
% 0.54/0.59 tff(63,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.54/0.59 tff(64,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.54/0.59 tff(65,plain,(
% 0.54/0.59 ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.54/0.59 inference(skolemize,[status(sab)],[64])).
% 0.54/0.59 tff(66,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.54/0.59 tff(67,plain,
% 0.54/0.59 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(W!49)) | frontsegP(W!49, nil))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(W!49)) | frontsegP(W!49, nil))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(68,plain,
% 0.54/0.59 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(W!49)) | frontsegP(W!49, nil))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(69,plain,
% 0.54/0.59 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(W!49)) | frontsegP(W!49, nil)),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.54/0.59 tff(70,plain,
% 0.54/0.59 (frontsegP(W!49, nil)),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[69, 66, 27])).
% 0.54/0.59 tff(71,plain,
% 0.54/0.59 ((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49))))),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(72,plain,
% 0.54/0.59 ((~((~frontsegP(W!49, nil)) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))))) | (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.54/0.59 tff(73,plain,
% 0.54/0.59 (~((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49)))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[72, 56])).
% 0.54/0.59 tff(74,plain,
% 0.54/0.59 (((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49))) | (app(nil, tptp_fun_W_5(nil, W!49)) = W!49)),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(75,plain,
% 0.54/0.59 (app(nil, tptp_fun_W_5(nil, W!49)) = W!49),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.54/0.59 tff(76,plain,
% 0.54/0.59 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(77,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[76])).
% 0.54/0.59 tff(78,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(79,plain,
% 0.54/0.59 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(80,plain,
% 0.54/0.59 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[79])).
% 0.54/0.59 tff(81,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 0.54/0.59 tff(82,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.54/0.59 tff(83,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.54/0.59 tff(84,plain,(
% 0.54/0.59 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.54/0.59 inference(skolemize,[status(sab)],[83])).
% 0.54/0.59 tff(85,plain,
% 0.54/0.59 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.54/0.59 tff(86,plain,
% 0.54/0.59 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(87,plain,
% 0.54/0.59 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(nil)) | (app(nil, nil) = nil))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(88,plain,
% 0.54/0.59 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(nil)) | (app(nil, nil) = nil)),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.54/0.59 tff(89,plain,
% 0.54/0.59 (app(nil, nil) = nil),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[88, 50, 85])).
% 0.54/0.59 tff(90,plain,
% 0.54/0.59 (app(app(nil, nil), tptp_fun_W_5(nil, W!49)) = app(nil, tptp_fun_W_5(nil, W!49))),
% 0.54/0.59 inference(monotonicity,[status(thm)],[89])).
% 0.54/0.59 tff(91,plain,
% 0.54/0.59 (app(app(nil, nil), tptp_fun_W_5(nil, W!49)) = U!47),
% 0.54/0.59 inference(transitivity,[status(thm)],[90, 75, 26])).
% 0.54/0.59 tff(92,plain,
% 0.54/0.59 (V!48 = X!50),
% 0.54/0.59 inference(and_elim,[status(thm)],[24])).
% 0.54/0.59 tff(93,plain,
% 0.54/0.59 (X!50 = V!48),
% 0.54/0.59 inference(symmetry,[status(thm)],[92])).
% 0.54/0.59 tff(94,plain,
% 0.54/0.59 (X!50 = W!49),
% 0.54/0.59 inference(and_elim,[status(thm)],[24])).
% 0.54/0.59 tff(95,plain,
% 0.54/0.59 (W!49 = X!50),
% 0.54/0.59 inference(symmetry,[status(thm)],[94])).
% 0.54/0.59 tff(96,plain,
% 0.54/0.59 (app(nil, tptp_fun_W_5(nil, W!49)) = V!48),
% 0.54/0.59 inference(transitivity,[status(thm)],[75, 95, 93])).
% 0.54/0.59 tff(97,plain,
% 0.54/0.59 (((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = W!49))) | ssList(tptp_fun_W_5(nil, W!49))),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(98,plain,
% 0.54/0.59 (ssList(tptp_fun_W_5(nil, W!49))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[97, 73])).
% 0.54/0.59 tff(99,plain,
% 0.54/0.59 (^[Y: $i] : refl(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(100,plain,
% 0.54/0.59 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[99])).
% 0.54/0.59 tff(101,plain,
% 0.54/0.59 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(102,plain,
% 0.54/0.59 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[101])).
% 0.54/0.59 tff(103,plain,
% 0.54/0.59 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))),
% 0.54/0.59 inference(transitivity,[status(thm)],[102, 100])).
% 0.54/0.59 tff(104,plain,
% 0.54/0.59 (^[Y: $i] : rewrite(((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))) <=> ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(105,plain,
% 0.54/0.59 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48))))) <=> ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[104])).
% 0.54/0.59 tff(106,plain,
% 0.54/0.59 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Y, Z), X1) = U!47) & (app(Y, X1) = V!48)))))),
% 0.54/0.59 inference(and_elim,[status(thm)],[24])).
% 0.54/0.59 tff(107,plain,
% 0.54/0.59 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.54/0.59 tff(108,plain,
% 0.54/0.59 (![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.54/0.59 tff(109,plain,
% 0.54/0.59 (((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))) | ((~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48)))))) <=> ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))) | (~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48)))))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(110,plain,
% 0.54/0.59 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))) | ((~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48)))))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(111,plain,
% 0.54/0.59 ((~![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Y, Z), X1) = U!47)) | (~(app(Y, X1) = V!48)))))) | (~ssList(nil)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.54/0.59 tff(112,plain,
% 0.54/0.59 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[111, 50, 108])).
% 0.54/0.59 tff(113,plain,
% 0.54/0.59 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47))))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(114,plain,
% 0.54/0.59 (((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!47)) | (~(app(nil, X1) = V!48)))) <=> ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47))))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(115,plain,
% 0.54/0.59 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!47)) | (~(app(nil, X1) = V!48))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47)))))),
% 0.54/0.59 inference(monotonicity,[status(thm)],[114])).
% 0.54/0.59 tff(116,plain,
% 0.54/0.59 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!47)) | (~(app(nil, X1) = V!48))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47))))),
% 0.54/0.59 inference(transitivity,[status(thm)],[115, 113])).
% 0.54/0.59 tff(117,plain,
% 0.54/0.59 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | ((~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, nil), X1) = U!47)) | (~(app(nil, X1) = V!48))))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(118,plain,
% 0.56/0.60 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(nil, Z), X1) = U!47)) | (~(app(nil, X1) = V!48))))) | (~ssList(nil)) | ![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47)))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.56/0.60 tff(119,plain,
% 0.56/0.60 (![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47)))),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[118, 50, 112])).
% 0.56/0.60 tff(120,plain,
% 0.56/0.60 (((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47)))) | ((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = V!48)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, W!49)) = U!47)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47)))) | (~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = V!48)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, W!49)) = U!47)))),
% 0.56/0.60 inference(rewrite,[status(thm)],[])).
% 0.56/0.60 tff(121,plain,
% 0.56/0.60 ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47)))) | ((~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = V!48)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, W!49)) = U!47)))),
% 0.56/0.60 inference(quant_inst,[status(thm)],[])).
% 0.56/0.60 tff(122,plain,
% 0.56/0.60 ((~![X1: $i] : ((~ssList(X1)) | (~(app(nil, X1) = V!48)) | (~(app(app(nil, nil), X1) = U!47)))) | (~ssList(tptp_fun_W_5(nil, W!49))) | (~(app(nil, tptp_fun_W_5(nil, W!49)) = V!48)) | (~(app(app(nil, nil), tptp_fun_W_5(nil, W!49)) = U!47))),
% 0.56/0.60 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.56/0.60 tff(123,plain,
% 0.56/0.60 (~(app(app(nil, nil), tptp_fun_W_5(nil, W!49)) = U!47)),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[122, 119, 98, 96])).
% 0.56/0.60 tff(124,plain,
% 0.56/0.60 ($false),
% 0.56/0.60 inference(unit_resolution,[status(thm)],[123, 91])).
% 0.56/0.60 % SZS output end Proof
%------------------------------------------------------------------------------