TSTP Solution File: SYN375+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN375+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 23:55:02 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN375+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 02:59:44 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(big_p_type, type, (
% 0.20/0.38 big_p: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.38 tptp_fun_Y_1: $i)).
% 0.20/0.38 tff(tptp_fun_X_2_type, type, (
% 0.20/0.38 tptp_fun_X_2: $i)).
% 0.20/0.38 tff(1,assumption,(~big_p(X!0)), introduced(assumption)).
% 0.20/0.38 tff(2,assumption,(~big_p(Y!1)), introduced(assumption)).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 ((~(big_p(X!0) | big_p(Y!1))) | big_p(X!0) | big_p(Y!1)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (~(big_p(X!0) | big_p(Y!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[3, 2, 1])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y))))) | (big_p(X!0) | big_p(Y!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!1))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))) <=> ((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!1))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))) <=> ((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!1))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((((big_p(X!0) | big_p(Y!1)) & ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!1)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))) <=> ((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!1))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (((![X: $i] : (((~big_p(X)) | big_p(Y!1)) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | (((~big_p(X!2)) | big_p(Y!1)) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) & (((big_p(X!0) | big_p(Y!1)) & ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!1)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))) <=> ((![X: $i] : ((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | ((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) & (((big_p(X!0) | big_p(Y!1)) & ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!1)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[12, 11])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))) <=> ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 ((![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))) <=> (~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))) <=> ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.38 tff(19,axiom,(~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2126')).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 13])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 13])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y))) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 13])).
% 0.20/0.38 tff(27,plain,(
% 0.20/0.38 (![X: $i] : (((~big_p(X)) | big_p(Y!1)) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | (((~big_p(X!2)) | big_p(Y!1)) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) & (((big_p(X!0) | big_p(Y!1)) & ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!1)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((![X: $i] : ((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | ((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) & (((big_p(X!0) | big_p(Y!1)) & ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!1)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 10])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (((big_p(X!0) | big_p(Y!1)) & ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!1)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.38 inference(and_elim,[status(thm)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!1))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[29, 9])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 ((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!1))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[30, 8])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ((~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[31, 7])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (~((~(big_p(Y!1) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[32, 6])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (((~(big_p(Y!1) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))) | (big_p(Y!1) | ![X: $i] : big_p(X))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (big_p(Y!1) | ![X: $i] : big_p(X)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 ((~(big_p(Y!1) | ![X: $i] : big_p(X))) | big_p(Y!1) | ![X: $i] : big_p(X)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![X: $i] : big_p(X)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[36, 35, 2])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~![X: $i] : big_p(X)) | big_p(Y!1)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[38, 2, 37])).
% 0.20/0.38 tff(40,plain,(big_p(Y!1) | big_p(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (big_p(Y!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[40, 1])).
% 0.20/0.38 tff(42,assumption,(![Y: $i] : (~big_p(Y))), introduced(assumption)).
% 0.20/0.38 tff(43,assumption,(big_p(Y!1)), introduced(assumption)).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 ((~![Y: $i] : (~big_p(Y))) | (~big_p(Y!1))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[44, 43, 42])).
% 0.20/0.38 tff(46,plain,((~big_p(Y!1)) | (~![Y: $i] : (~big_p(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (~![Y: $i] : (~big_p(Y))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[46, 41])).
% 0.20/0.38 tff(48,assumption,(~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))), introduced(assumption)).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 ((![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))) | (~![Y: $i] : (~big_p(Y)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (~![Y: $i] : (~big_p(Y))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) | (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 ((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 ((![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))))) <=> (![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 ((![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))))) <=> (![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))) <=> (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 ((![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))) <=> (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))) <=> ((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))) <=> (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((big_p(X) | ![Y: $i] : (~big_p(Y))) <=> (big_p(X) | ![Y: $i] : (~big_p(Y)))), (((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) <=> ((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))))), rewrite(((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) <=> (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y))))))), (((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) <=> (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![X: $i] : ((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) <=> ![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((![X: $i] : ((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | ((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) <=> (![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[60, 58])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((![X: $i] : ((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | ((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) <=> (![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[61, 54])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![X: $i] : ((big_p(Y!1) | (~big_p(X))) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | ((big_p(Y!1) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.39 inference(and_elim,[status(thm)],[28])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[64, 53])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[65, 52])).
% 0.20/0.39 tff(67,assumption,((~(big_p(Y!1) | (~big_p(X!2)))) | (~(big_p(X!2) | ![Y: $i] : (~big_p(Y))))), introduced(assumption)).
% 0.20/0.39 tff(68,assumption,(![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y))))))), introduced(assumption)).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ((~![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y))))))) | (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(big_p(X!2) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[69, 68, 67])).
% 0.20/0.39 tff(71,plain,((~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(big_p(X!2) | ![Y: $i] : (~big_p(Y)))))) | (~![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (~((~(big_p(Y!1) | (~big_p(X!2)))) | (~(big_p(X!2) | ![Y: $i] : (~big_p(Y)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 66])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (((~(big_p(Y!1) | (~big_p(X!2)))) | (~(big_p(X!2) | ![Y: $i] : (~big_p(Y))))) | (big_p(X!2) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (big_p(X!2) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 ((~(big_p(X!2) | ![Y: $i] : (~big_p(Y)))) | big_p(X!2) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 ((~(big_p(X!2) | ![Y: $i] : (~big_p(Y)))) | big_p(X!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[75, 50])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (big_p(X!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[76, 74])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 ((~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))) | (~big_p(X!2)) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[78, 77, 50])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (((~(big_p(Y!1) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))) | ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((~(big_p(Y!1) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (~((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 81])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y))))) | ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((~big_p(X!0)) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))) | (~big_p(X!0)) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 (~big_p(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[85, 84, 50])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 ((~(big_p(X!0) | ![Y: $i] : (~big_p(Y)))) | big_p(X!0) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (~(big_p(X!0) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[87, 50, 86])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (((~(big_p(Y!1) | (~big_p(X!0)))) | (~(big_p(X!0) | ![Y: $i] : (~big_p(Y))))) | (big_p(X!0) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ((~(big_p(Y!1) | (~big_p(X!0)))) | (~(big_p(X!0) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 ((~![X: $i] : (~((~(big_p(Y!1) | (~big_p(X)))) | (~(big_p(X) | ![Y: $i] : (~big_p(Y))))))) | (~((~(big_p(Y!1) | (~big_p(X!0)))) | (~(big_p(X!0) | ![Y: $i] : (~big_p(Y))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[91, 66, 90])).
% 0.20/0.39 tff(93,plain,(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 ((~(![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y)))) | ![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (![X: $i] : big_p(X)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[95, 47])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 ((~![X: $i] : big_p(X)) | big_p(X!0)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[97, 96, 1])).
% 0.20/0.39 tff(99,plain,(big_p(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(100,assumption,(~![Y: $i] : (~big_p(Y))), introduced(assumption)).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (![X: $i] : big_p(X)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[95, 100])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[85, 100, 99])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 ((~(big_p(X!0) | big_p(Y!1))) | (~((~big_p(X!0)) | ![Y: $i] : (~big_p(Y))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[83, 102])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (~((~(big_p(Y!1) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 103])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[80, 104])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (~big_p(X!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[78, 105, 100])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 ((~![X: $i] : big_p(X)) | big_p(X!2)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[107, 106, 101])).
% 0.20/0.39 tff(109,plain,(![Y: $i] : (~big_p(Y))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 ((~![Y: $i] : (~big_p(Y))) | (~big_p(X!0))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[110, 109, 99])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------