TSTP Solution File: SYN078+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 23:53:37 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.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 01:48:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(big_p_type, type, (
% 0.20/0.39 big_p: $i > $o)).
% 0.20/0.39 tff(tptp_fun_U_2_type, type, (
% 0.20/0.39 tptp_fun_U_2: $i)).
% 0.20/0.39 tff(f_type, type, (
% 0.20/0.39 f: $i > $i)).
% 0.20/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.39 tptp_fun_Y_1: $i)).
% 0.20/0.39 tff(tptp_fun_X_0_type, type, (
% 0.20/0.39 tptp_fun_X_0: $i)).
% 0.20/0.39 tff(1,assumption,(~(big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1))))), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))) | (X!0 = f(Y!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (X!0 = f(Y!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 ((big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))) | (~big_p(X!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (~big_p(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.39 tff(6,assumption,(X!0 = f(Y!1)), introduced(assumption)).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (f(Y!1) = X!0),
% 0.20/0.39 inference(symmetry,[status(thm)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (big_p(f(Y!1)) <=> big_p(X!0)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[7])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (big_p(X!0) <=> big_p(f(Y!1))),
% 0.20/0.39 inference(symmetry,[status(thm)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((~big_p(X!0)) <=> (~big_p(f(Y!1)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.39 tff(11,assumption,(~big_p(X!0)), introduced(assumption)).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~big_p(f(Y!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.39 tff(13,assumption,(big_p(f(Y!1))), introduced(assumption)).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.39 tff(15,plain,((~big_p(f(Y!1))) | big_p(X!0) | (~(X!0 = f(Y!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (~big_p(f(Y!1))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[15, 5, 3])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))) | big_p(Y!1)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (big_p(Y!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[17, 1])).
% 0.20/0.39 tff(19,assumption,(~big_p(f(Y!1))), introduced(assumption)).
% 0.20/0.39 tff(20,assumption,(big_p(Y!1)), introduced(assumption)).
% 0.20/0.39 tff(21,assumption,(![U: $i] : (big_p(f(U)) | (~big_p(U)))), introduced(assumption)).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (big_p(f(Y!1)) | (~big_p(Y!1)))) <=> ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | big_p(f(Y!1)) | (~big_p(Y!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (big_p(f(Y!1)) | (~big_p(Y!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | big_p(f(Y!1)) | (~big_p(Y!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[24, 21, 20, 19])).
% 0.20/0.39 tff(26,plain,((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (~big_p(Y!1)) | big_p(f(Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 18, 16])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 ((![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) <=> (![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y)))))) <=> (![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (((![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y))))) | ![U: $i] : (big_p(f(U)) | (~big_p(U)))) & (((~big_p(X!0)) & (big_p(Y!1) & (X!0 = f(Y!1)))) | (~(big_p(f(U!2)) | (~big_p(U!2)))))) <=> ((![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y)))))) & ((~(big_p(f(U!2)) | (~big_p(U!2)))) | ((~big_p(X!0)) & big_p(Y!1) & (X!0 = f(Y!1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))) <=> ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))) <=> ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U)))) <=> (![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~(![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U))))) <=> (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~(![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U))))) <=> ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.39 tff(36,axiom,(~(![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel56')).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 31])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y)))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 31])).
% 0.20/0.39 tff(44,plain,(
% 0.20/0.39 (![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y))))) | ![U: $i] : (big_p(f(U)) | (~big_p(U)))) & (((~big_p(X!0)) & (big_p(Y!1) & (X!0 = f(Y!1)))) | (~(big_p(f(U!2)) | (~big_p(U!2)))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[43])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y)))))) & ((~(big_p(f(U!2)) | (~big_p(U!2)))) | ((~big_p(X!0)) & big_p(Y!1) & (X!0 = f(Y!1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 30])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y)))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[45])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 29])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 28])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 27])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | (big_p(f(Y!1)) | ![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y)))))) <=> ((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | big_p(f(Y!1)) | ![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | (big_p(f(Y!1)) | ![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | big_p(f(Y!1)) | ![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[52, 49, 16])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | (~big_p(Y!1))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | (~big_p(Y!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (((~big_p(Y!1)) | $false) <=> (~big_p(Y!1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 ((~$true) <=> $false),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((f(Y!1) = f(Y!1)) <=> $true),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 ((~(f(Y!1) = f(Y!1))) <=> (~$true)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~(f(Y!1) = f(Y!1))) <=> $false),
% 0.20/0.39 inference(transitivity,[status(thm)],[58, 56])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (((~big_p(Y!1)) | (~(f(Y!1) = f(Y!1)))) <=> ((~big_p(Y!1)) | $false)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~big_p(Y!1)) | (~(f(Y!1) = f(Y!1)))) <=> (~big_p(Y!1))),
% 0.20/0.39 inference(transitivity,[status(thm)],[60, 55])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | ((~big_p(Y!1)) | (~(f(Y!1) = f(Y!1))))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | (~big_p(Y!1)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | ((~big_p(Y!1)) | (~(f(Y!1) = f(Y!1))))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | (~big_p(Y!1)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[62, 54])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | ((~big_p(Y!1)) | (~(f(Y!1) = f(Y!1))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~![Y: $i] : ((~big_p(Y)) | (~(f(Y!1) = f(Y))))) | (~big_p(Y!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[65, 18, 53])).
% 0.20/0.39 tff(67,plain,(big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (((~(big_p(f(U!2)) | (~big_p(U!2)))) | ((~big_p(X!0)) & big_p(Y!1) & (X!0 = f(Y!1)))) <=> ((~(big_p(f(U!2)) | (~big_p(U!2)))) | (~(big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ((~(big_p(f(U!2)) | (~big_p(U!2)))) | ((~big_p(X!0)) & big_p(Y!1) & (X!0 = f(Y!1)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[45])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ((~(big_p(f(U!2)) | (~big_p(U!2)))) | (~(big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (~(big_p(f(U!2)) | (~big_p(U!2)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 ((big_p(f(U!2)) | (~big_p(U!2))) | big_p(U!2)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (big_p(U!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 ((big_p(f(U!2)) | (~big_p(U!2))) | (~big_p(f(U!2)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (~big_p(f(U!2))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.20/0.39 tff(76,assumption,(![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))), introduced(assumption)).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | (~big_p(U!2))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | (~big_p(U!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (((~big_p(U!2)) | $false) <=> (~big_p(U!2))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 ((f(U!2) = f(U!2)) <=> $true),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ((~(f(U!2) = f(U!2))) <=> (~$true)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ((~(f(U!2) = f(U!2))) <=> $false),
% 0.20/0.40 inference(transitivity,[status(thm)],[80, 56])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (((~big_p(U!2)) | (~(f(U!2) = f(U!2)))) <=> ((~big_p(U!2)) | $false)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (((~big_p(U!2)) | (~(f(U!2) = f(U!2)))) <=> (~big_p(U!2))),
% 0.20/0.40 inference(transitivity,[status(thm)],[82, 78])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | ((~big_p(U!2)) | (~(f(U!2) = f(U!2))))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | (~big_p(U!2)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | ((~big_p(U!2)) | (~(f(U!2) = f(U!2))))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | (~big_p(U!2)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[84, 77])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | ((~big_p(U!2)) | (~(f(U!2) = f(U!2))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 ((~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))) | (~big_p(U!2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[87, 73, 76])).
% 0.20/0.40 tff(89,plain,(~![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(90,assumption,(![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))), introduced(assumption)).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | (big_p(f(U!2)) | ![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y)))))) <=> ((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | big_p(f(U!2)) | ![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 ((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | (big_p(f(U!2)) | ![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 ((~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) | big_p(f(U!2)) | ![Y: $i] : ((~big_p(Y)) | (~(f(U!2) = f(Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[93, 90, 75, 89])).
% 0.20/0.40 tff(95,plain,(~![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 95])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (big_p(f(U!2)) | (~big_p(U!2)))) <=> ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | big_p(f(U!2)) | (~big_p(U!2)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (big_p(f(U!2)) | (~big_p(U!2)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | big_p(f(U!2)) | (~big_p(U!2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[99, 96, 75, 73])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------