TSTP Solution File: SYN075+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN075+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Thu Sep 29 23:53:34 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN075+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 00:59:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(tptp_fun_Z_1_type, type, (
% 0.13/0.40 tptp_fun_Z_1: $i)).
% 0.13/0.40 tff(tptp_fun_Z_3_type, type, (
% 0.13/0.40 tptp_fun_Z_3: $i > $i)).
% 0.13/0.40 tff(tptp_fun_W_0_type, type, (
% 0.13/0.40 tptp_fun_W_0: $i)).
% 0.13/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.13/0.40 tptp_fun_Y_2: $i > $i)).
% 0.13/0.40 tff(big_f_type, type, (
% 0.13/0.40 big_f: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_X_4_type, type, (
% 0.13/0.40 tptp_fun_X_4: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,assumption,(tptp_fun_Y_2(W!0) = W!0), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (W!0 = tptp_fun_Y_2(W!0)),
% 0.13/0.40 inference(symmetry,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0)) <=> big_f(tptp_fun_X_4(Z!1, W!0), W!0)),
% 0.13/0.40 inference(symmetry,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((~big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))) <=> (~big_f(tptp_fun_X_4(Z!1, W!0), W!0))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[4])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (^[W: $i] : trans(monotonicity(rewrite(((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) <=> ((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))), rewrite(((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))) <=> ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z)))), ((((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z)))) <=> (((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z)))))), rewrite((((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z)))) <=> (~((~((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))) | (~((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))))))), ((((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z)))) <=> (~((~((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))) | (~((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![W: $i] : (((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z)))) <=> ![W: $i] : (~((~((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))) | (~((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (^[W: $i] : rewrite(((![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))) | (tptp_fun_Y_2(W) = W)) & (![Z: $i] : (~(big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W)) <=> (tptp_fun_X_4(Z, W) = Z))) | (~(tptp_fun_Y_2(W) = W)))) <=> (((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![W: $i] : ((![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))) | (tptp_fun_Y_2(W) = W)) & (![Z: $i] : (~(big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W)) <=> (tptp_fun_X_4(Z, W) = Z))) | (~(tptp_fun_Y_2(W) = W)))) <=> ![W: $i] : (((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 ((~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))) <=> (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(11,axiom,(~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel52')).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (~?[W: $i] : ![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (^[W: $i] : trans(sk($oeq((~![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))), (~(?[Z: $i] : ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = Z)) <=> (tptp_fun_Y_2(W) = W))))), nnf_neg(trans(sk($oeq(?[Z: $i] : ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = Z)), ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))), nnf_pos(proof_bind(^[X: $i] : refl($oeq((big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))), (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))))), $oeq(![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))), ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))), $oeq(?[Z: $i] : ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = Z)), ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))), nnf_neg(proof_bind(^[Z: $i] : sk($oeq((~![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = Z))), (~(big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W)) <=> (tptp_fun_X_4(Z, W) = Z)))))), $oeq((~?[Z: $i] : ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = Z))), ![Z: $i] : (~(big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W)) <=> (tptp_fun_X_4(Z, W) = Z))))), refl($oeq((tptp_fun_Y_2(W) = W), (tptp_fun_Y_2(W) = W))), refl($oeq((~(tptp_fun_Y_2(W) = W)), (~(tptp_fun_Y_2(W) = W)))), $oeq((~(?[Z: $i] : ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = Z)) <=> (tptp_fun_Y_2(W) = W))), ((![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))) | (tptp_fun_Y_2(W) = W)) & (![Z: $i] : (~(big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W)) <=> (tptp_fun_X_4(Z, W) = Z))) | (~(tptp_fun_Y_2(W) = W)))))), $oeq((~![Y: $i] : (?[Z: $i] : ![X: $i] : (big_f(X, Y) <=> (X = Z)) <=> (Y = W))), ((![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))) | (tptp_fun_Y_2(W) = W)) & (![Z: $i] : (~(big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W)) <=> (tptp_fun_X_4(Z, W) = Z))) | (~(tptp_fun_Y_2(W) = W))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(20,plain,(
% 0.13/0.41 ![W: $i] : ((![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))) | (tptp_fun_Y_2(W) = W)) & (![Z: $i] : (~(big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W)) <=> (tptp_fun_X_4(Z, W) = Z))) | (~(tptp_fun_Y_2(W) = W))))),
% 0.13/0.41 inference(nnf-neg,[status(sab)],[18, 19])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (![W: $i] : (((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W)))) & ((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 9])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (![W: $i] : (~((~((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))) | (~((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[21, 7])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ((~![W: $i] : (~((~((tptp_fun_Y_2(W) = W) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W)) <=> (X = tptp_fun_Z_3(W))))) | (~((~(tptp_fun_Y_2(W) = W)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W), tptp_fun_Y_2(W))) <=> (tptp_fun_X_4(Z, W) = Z))))))) | (~((~((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0))))) | (~((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (~((~((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0))))) | (~((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z)))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (((~((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0))))) | (~((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))))) | ((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 ((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 ((~((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z)))) | (~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 ((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[28, 1])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 ((~![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))) | ((~big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 ((~big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.13/0.41 tff(32,assumption,(~(tptp_fun_X_4(Z!1, W!0) = Z!1)), introduced(assumption)).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 ((~((~big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))) | big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0)) | (tptp_fun_X_4(Z!1, W!0) = Z!1)),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[33, 32, 31])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (big_f(tptp_fun_X_4(Z!1, W!0), W!0)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[34, 4])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : refl((big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0))))) <=> (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0))))) <=> ![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : rewrite((big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))) <=> (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))) <=> ![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W))) <=> ?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,axiom,(?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel52_1')).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.41 tff(43,plain,(
% 0.20/0.41 $oeq(![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))), ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))))),
% 0.20/0.41 inference(transitivity,[status(sab)],[42])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))) <=> ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (~((~(tptp_fun_X_4(Z!1, W!0) = Z!1)) | (~(W!0 = W!0))))) <=> (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (~((~(tptp_fun_X_4(Z!1, W!0) = Z!1)) | (~(W!0 = W!0)))))) <=> ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (~((~(tptp_fun_X_4(Z!1, W!0) = Z!1)) | (~(W!0 = W!0)))))) <=> ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (~((~(tptp_fun_X_4(Z!1, W!0) = Z!1)) | (~(W!0 = W!0)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[51, 45])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((~(big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))) | (~big_f(tptp_fun_X_4(Z!1, W!0), W!0)) | (tptp_fun_X_4(Z!1, W!0) = Z!1)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (~big_f(tptp_fun_X_4(Z!1, W!0), W!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[53, 32, 52])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[54, 35])).
% 0.20/0.41 tff(56,plain,((tptp_fun_X_4(Z!1, W!0) = Z!1) | (~(tptp_fun_Y_2(W!0) = W!0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (tptp_fun_X_4(Z!1, W!0) = Z!1),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[56, 1])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~((~big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))) | (~big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))) | (~(tptp_fun_X_4(Z!1, W!0) = Z!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (~big_f(tptp_fun_X_4(Z!1, W!0), tptp_fun_Y_2(W!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 57, 31])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (~big_f(tptp_fun_X_4(Z!1, W!0), W!0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 5])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~(big_f(tptp_fun_X_4(Z!1, W!0), W!0) <=> (tptp_fun_X_4(Z!1, W!0) = Z!1))) | big_f(tptp_fun_X_4(Z!1, W!0), W!0) | (~(tptp_fun_X_4(Z!1, W!0) = Z!1))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (big_f(tptp_fun_X_4(Z!1, W!0), W!0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 57, 52])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[62, 60])).
% 0.20/0.42 tff(64,plain,(~(tptp_fun_Y_2(W!0) = W!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1))) | (tptp_fun_Y_2(W!0) = W!0)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (((~((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0))))) | (~((~(tptp_fun_Y_2(W!0) = W!0)) | ![Z: $i] : ((~big_f(tptp_fun_X_4(Z, W!0), tptp_fun_Y_2(W!0))) <=> (tptp_fun_X_4(Z, W!0) = Z))))) | ((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 ((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[67, 24])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((~((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0))))) | (tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 ((tptp_fun_Y_2(W!0) = W!0) | ![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0))) <=> ((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> $true) <=> big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ((tptp_fun_Z_3(W!0) = tptp_fun_Z_3(W!0)) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (tptp_fun_Z_3(W!0) = tptp_fun_Z_3(W!0))) <=> (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> $true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (tptp_fun_Z_3(W!0) = tptp_fun_Z_3(W!0))) <=> big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0))),
% 0.20/0.42 inference(transitivity,[status(thm)],[75, 73])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (tptp_fun_Z_3(W!0) = tptp_fun_Z_3(W!0)))) <=> ((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (tptp_fun_Z_3(W!0) = tptp_fun_Z_3(W!0)))) <=> ((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[77, 72])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (tptp_fun_Z_3(W!0) = tptp_fun_Z_3(W!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~![X: $i] : (big_f(X, tptp_fun_Y_2(W!0)) <=> (X = tptp_fun_Z_3(W!0)))) | big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[80, 71])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((~(big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1)))))) | (~big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0))) | (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~(big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[82, 81, 66])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1)))))) <=> ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Z_3(W!0) = Z!1)) | (~(tptp_fun_Y_2(W!0) = W!0))))) <=> (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Z_3(W!0) = Z!1)) | (~(tptp_fun_Y_2(W!0) = W!0)))))) <=> ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Z_3(W!0) = Z!1)) | (~(tptp_fun_Y_2(W!0) = W!0)))))) <=> ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Z_3(W!0) = Z!1)) | (~(tptp_fun_Y_2(W!0) = W!0)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0)))))) | (big_f(tptp_fun_Z_3(W!0), tptp_fun_Y_2(W!0)) <=> (~((~(tptp_fun_Y_2(W!0) = W!0)) | (~(tptp_fun_Z_3(W!0) = Z!1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 45, 83])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------