TSTP Solution File: SYN082+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Thu Sep 29 23:53:39 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 01:56:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(big_f_type, type, (
% 0.21/0.39 big_f: ( $i * $i ) > $o)).
% 0.21/0.39 tff(f_type, type, (
% 0.21/0.39 f: $i > $i)).
% 0.21/0.39 tff(tptp_fun_X_0_type, type, (
% 0.21/0.39 tptp_fun_X_0: $i)).
% 0.21/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.39 tptp_fun_Y_1: $i)).
% 0.21/0.39 tff(tptp_fun_Z_2_type, type, (
% 0.21/0.39 tptp_fun_Z_2: $i > $i)).
% 0.21/0.39 tff(1,assumption,(big_f(X!0, f(X!0))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) <=> ((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) <=> ((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 ((![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1)) <=> (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 ((big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))) <=> (big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (((big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))) & ((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y))))) <=> ((big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))) & ((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[5, 3])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 ((~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))) <=> (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : (big_f(Z, Y) => big_f(Z, f(X))) & big_f(X, Y)))) <=> (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(9,axiom,(~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : (big_f(Z, Y) => big_f(Z, f(X))) & big_f(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel60')).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (~![X: $i] : (big_f(X, f(X)) <=> ?[Y: $i] : (![Z: $i] : ((~big_f(Z, Y)) | big_f(Z, f(X))) & big_f(X, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ((big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))) & ((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 ((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))),
% 0.21/0.39 inference(and_elim,[status(thm)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 ((~big_f(X!0, f(X!0))) | ![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[19, 1])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | (~big_f(X!0, f(X!0)))) <=> ((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | (~big_f(X!0, f(X!0))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (($false | (~big_f(X!0, f(X!0)))) <=> (~big_f(X!0, f(X!0)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 ((~$true) <=> $false),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) <=> $true),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0)))) <=> (~$true)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 ((~((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0)))) <=> $false),
% 0.21/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (((~((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0)))) | (~big_f(X!0, f(X!0)))) <=> ($false | (~big_f(X!0, f(X!0))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (((~((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0)))) | (~big_f(X!0, f(X!0)))) <=> (~big_f(X!0, f(X!0)))),
% 0.21/0.39 inference(transitivity,[status(thm)],[27, 22])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | ((~((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0)))) | (~big_f(X!0, f(X!0))))) <=> ((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | (~big_f(X!0, f(X!0))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | ((~((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0)))) | (~big_f(X!0, f(X!0))))) <=> ((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | (~big_f(X!0, f(X!0))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[29, 21])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 ((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | ((~((~big_f(tptp_fun_Z_2(f(X!0)), f(X!0))) | big_f(tptp_fun_Z_2(f(X!0)), f(X!0)))) | (~big_f(X!0, f(X!0))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 ((~![Y: $i] : ((~((~big_f(tptp_fun_Z_2(Y), Y)) | big_f(tptp_fun_Z_2(Y), f(X!0)))) | (~big_f(X!0, Y)))) | (~big_f(X!0, f(X!0)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[32, 1, 20])).
% 0.21/0.39 tff(34,plain,(~big_f(X!0, f(X!0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((big_f(X!0, f(X!0)) | (~((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))))))) <=> (big_f(X!0, f(X!0)) | (~((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 ((~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1)))) <=> (~((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 ((big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1))))) <=> (big_f(X!0, f(X!0)) | (~((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 ((big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1))))) <=> (big_f(X!0, f(X!0)) | (~((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[37, 35])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 ((big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1))))) <=> (big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 ((big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1))))) <=> (big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 ((![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1)) <=> (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 ((big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))) <=> (big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 ((big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))) <=> (big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1)))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 (big_f(X!0, f(X!0)) | (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))) & big_f(X!0, Y!1))),
% 0.21/0.40 inference(and_elim,[status(thm)],[17])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 (big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.40 tff(46,plain,
% 0.21/0.40 (big_f(X!0, f(X!0)) | (~((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[45, 39])).
% 0.21/0.40 tff(47,plain,
% 0.21/0.40 (big_f(X!0, f(X!0)) | (~((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (~((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[47, 34])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 (((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))))) | ![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (((~big_f(X!0, Y!1)) | (~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0))))) | big_f(X!0, Y!1)),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (big_f(X!0, Y!1)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | ((~big_f(X!0, Y!1)) | big_f(X!0, f(X!0)))) <=> ((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1)) | big_f(X!0, f(X!0)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 ((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | ((~big_f(X!0, Y!1)) | big_f(X!0, f(X!0)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 ((~![Z: $i] : ((~big_f(Z, Y!1)) | big_f(Z, f(X!0)))) | (~big_f(X!0, Y!1)) | big_f(X!0, f(X!0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[55, 34, 52, 50])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------