TSTP Solution File: SYN374+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN374+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN374+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Sep 5 03:03:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(big_p_type, type, (
% 0.12/0.38 big_p: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.38 tptp_fun_Y_3: $i)).
% 0.12/0.38 tff(tptp_fun_X_1_type, type, (
% 0.12/0.38 tptp_fun_X_1: $i)).
% 0.12/0.38 tff(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: $i)).
% 0.12/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.38 tptp_fun_Y_0: $i > $i)).
% 0.12/0.38 tff(elem_4_type, type, (
% 0.12/0.38 elem_4: $i)).
% 0.12/0.38 tff(1,assumption,(~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))) | (big_p(X!2) | (~big_p(Y!3)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (big_p(X!2) | (~big_p(Y!3))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))) | (![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,assumption,(~![Y: $i] : big_p(Y)), introduced(assumption)).
% 0.12/0.38 tff(7,assumption,(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)), introduced(assumption)).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | ![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X: $i] : (~big_p(X))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 6, 7])).
% 0.12/0.38 tff(10,assumption,(![X: $i] : (~big_p(X))), introduced(assumption)).
% 0.12/0.38 tff(11,assumption,(big_p(X!2)), introduced(assumption)).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((~![X: $i] : (~big_p(X))) | (~big_p(X!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[12, 11, 10])).
% 0.12/0.38 tff(14,plain,((~big_p(X!2)) | (~![X: $i] : (~big_p(X)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~big_p(X!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 9])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | big_p(X!2) | ![Y: $i] : big_p(Y)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (~(big_p(X!2) | ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[16, 15, 6])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~((~big_p(Y!3)) | ![X: $i] : (~big_p(X))))) | (big_p(X!2) | ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~((~big_p(Y!3)) | ![X: $i] : (~big_p(X))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~(![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) <=> ((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~((~big_p(Y!3)) | ![X: $i] : (~big_p(X)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~(![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) <=> ((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~(![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((((big_p(X!2) | ![Y: $i] : big_p(Y)) & (![X: $i] : (~big_p(X)) | (~big_p(Y!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) <=> ((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~(![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))) & (![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((big_p(X!2) | ![Y: $i] : big_p(Y)) & (![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))) <=> ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))) & (((big_p(X!2) | ![Y: $i] : big_p(Y)) & (![X: $i] : (~big_p(X)) | (~big_p(Y!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))) <=> ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))) <=> ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~(?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))) <=> ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))) <=> (?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~(?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))) <=> (~(?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[29])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~(?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))) <=> ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.12/0.38 tff(32,axiom,(~(?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2125')).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[35, 26])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 26])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~?[X: $i] : ![Y: $i] : (big_p(X) <=> big_p(Y))) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[38, 26])).
% 0.12/0.38 tff(40,plain,(
% 0.12/0.38 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))) & (![X: $i] : (~(big_p(X) <=> big_p(tptp_fun_Y_0(X)))) | ((big_p(X!2) | ![Y: $i] : big_p(Y)) & (![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[39])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))) & (((big_p(X!2) | ![Y: $i] : big_p(Y)) & (![X: $i] : (~big_p(X)) | (~big_p(Y!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 23])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (((big_p(X!2) | ![Y: $i] : big_p(Y)) & (![X: $i] : (~big_p(X)) | (~big_p(Y!3)))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.12/0.38 inference(and_elim,[status(thm)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~(![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 22])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~(![X: $i] : (~big_p(X)) | (~big_p(Y!3)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 21])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~((~big_p(Y!3)) | ![X: $i] : (~big_p(X)))))) | ![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[44, 20])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[45, 19])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))) | ((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~![X: $i] : (~big_p(X))) | (~big_p(tptp_fun_Y_0(elem!4)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (~big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[49, 9])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ((~![X: $i] : (~big_p(X))) | (~big_p(elem!4))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (~big_p(elem!4)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[51, 9])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 ((~((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4)))) | big_p(elem!4) | big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[53, 52, 50, 48])).
% 0.12/0.38 tff(55,plain,(![Y: $i] : big_p(Y) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![Y: $i] : big_p(Y)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 5])).
% 0.12/0.38 tff(57,assumption,(![Y: $i] : big_p(Y)), introduced(assumption)).
% 0.12/0.38 tff(58,assumption,(~big_p(Y!3)), introduced(assumption)).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 ((~![Y: $i] : big_p(Y)) | big_p(Y!3)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[59, 58, 57])).
% 0.12/0.38 tff(61,plain,(big_p(Y!3) | (~![Y: $i] : big_p(Y))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (big_p(Y!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[61, 56])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 ((~(big_p(X!2) | (~big_p(Y!3)))) | big_p(X!2) | (~big_p(Y!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 (big_p(X!2)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[63, 62, 3])).
% 0.12/0.38 tff(65,assumption,(~((~big_p(Y!3)) | ![X: $i] : (~big_p(X)))), introduced(assumption)).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~((~big_p(Y!3)) | ![X: $i] : (~big_p(X))))) | ((~big_p(Y!3)) | ![X: $i] : (~big_p(X)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 ((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~((~big_p(Y!3)) | ![X: $i] : (~big_p(X))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[45, 67])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 ((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[47, 68])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 (((~big_p(Y!3)) | ![X: $i] : (~big_p(X))) | (~![X: $i] : (~big_p(X)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 (~![X: $i] : (~big_p(X))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[70, 65])).
% 0.12/0.38 tff(72,plain,
% 0.12/0.38 (![Y: $i] : big_p(Y)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 71, 7])).
% 0.12/0.38 tff(73,plain,
% 0.12/0.38 ((~![Y: $i] : big_p(Y)) | big_p(elem!4)),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (big_p(elem!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 ((~![Y: $i] : big_p(Y)) | big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4)))) | (~big_p(elem!4)) | (~big_p(tptp_fun_Y_0(elem!4)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 76, 74, 69])).
% 0.12/0.39 tff(79,plain,(((~big_p(Y!3)) | ![X: $i] : (~big_p(X))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 ((~big_p(Y!3)) | ![X: $i] : (~big_p(X))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[79, 5])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 ((~((~big_p(Y!3)) | ![X: $i] : (~big_p(X)))) | (~big_p(Y!3)) | ![X: $i] : (~big_p(X))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (![X: $i] : (~big_p(X))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[81, 62, 80])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[14, 82, 64])).
% 0.12/0.39 tff(84,plain,((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))))) <=> (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 ((~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3)))))) <=> (~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))) <=> (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[86])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))) <=> (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[87, 85])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))) <=> (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))) <=> (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3)))) <=> (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) <=> (![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3)))) <=> ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[92])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 (((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3)))) <=> (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[93, 91])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))) <=> (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3)))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[94])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 ((![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))) <=> (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[95, 90])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!3))))),
% 0.12/0.39 inference(and_elim,[status(thm)],[41])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!3))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[98, 89])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 (![Y: $i] : (big_p(X!1) <=> big_p(Y)) | (~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[99, 88])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 (![Y: $i] : (big_p(X!1) <=> big_p(Y))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[100, 84])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(Y!3))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 (big_p(X!1) <=> big_p(Y!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(X!2))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (big_p(X!1) <=> big_p(X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(elem!4))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 (big_p(X!1) <=> big_p(elem!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[106, 101])).
% 0.12/0.39 tff(108,assumption,((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4))), introduced(assumption)).
% 0.12/0.39 tff(109,assumption,(~big_p(tptp_fun_Y_0(elem!4))), introduced(assumption)).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 (big_p(elem!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[53, 109, 108])).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 ((~![Y: $i] : (big_p(X!1) <=> big_p(Y))) | (big_p(X!1) <=> big_p(tptp_fun_Y_0(elem!4)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 (big_p(X!1) <=> big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[111, 101])).
% 0.12/0.39 tff(113,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(elem!4)))) | (~big_p(X!1)) | big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 (~big_p(X!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[113, 109, 112])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(elem!4))) | big_p(X!1) | (~big_p(elem!4))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(116,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[115, 114, 110, 107])).
% 0.12/0.39 tff(117,plain,(big_p(tptp_fun_Y_0(elem!4)) | (~((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(118,plain,
% 0.12/0.39 (big_p(tptp_fun_Y_0(elem!4))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[117, 108])).
% 0.12/0.39 tff(119,plain,
% 0.12/0.39 (~big_p(elem!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 118, 108])).
% 0.12/0.39 tff(120,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(tptp_fun_Y_0(elem!4)))) | big_p(X!1) | (~big_p(tptp_fun_Y_0(elem!4)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(121,plain,
% 0.12/0.39 (big_p(X!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[120, 118, 112])).
% 0.12/0.39 tff(122,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(elem!4))) | (~big_p(X!1)) | big_p(elem!4)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(123,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[122, 121, 119, 107])).
% 0.12/0.39 tff(124,plain,(~((~big_p(elem!4)) <=> big_p(tptp_fun_Y_0(elem!4)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(125,plain,
% 0.12/0.39 (~![X: $i] : ((~big_p(X)) <=> big_p(tptp_fun_Y_0(X)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[47, 124])).
% 0.12/0.39 tff(126,plain,
% 0.12/0.39 (~((~(big_p(X!2) | ![Y: $i] : big_p(Y))) | (~((~big_p(Y!3)) | ![X: $i] : (~big_p(X)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[45, 125])).
% 0.12/0.39 tff(127,plain,
% 0.12/0.39 (big_p(X!2) | ![Y: $i] : big_p(Y)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[18, 126])).
% 0.12/0.39 tff(128,plain,
% 0.12/0.39 (big_p(X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[16, 6, 127])).
% 0.12/0.39 tff(129,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(X!2))) | big_p(X!1) | (~big_p(X!2))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(130,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(X!2))) | big_p(X!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.12/0.39 tff(131,plain,
% 0.12/0.39 (big_p(X!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[130, 105])).
% 0.12/0.39 tff(132,plain,
% 0.12/0.39 ((~big_p(Y!3)) | ![X: $i] : (~big_p(X))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 126])).
% 0.12/0.39 tff(133,plain,
% 0.12/0.39 (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[55, 6])).
% 0.12/0.39 tff(134,plain,
% 0.12/0.39 ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) | (~![X: $i] : (~big_p(X)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(135,plain,
% 0.12/0.39 (~![X: $i] : (~big_p(X))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.12/0.39 tff(136,plain,
% 0.12/0.39 (~big_p(Y!3)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[81, 135, 132])).
% 0.12/0.39 tff(137,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(Y!3))) | (~big_p(X!1)) | big_p(Y!3)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(138,plain,
% 0.12/0.39 ((~(big_p(X!1) <=> big_p(Y!3))) | (~big_p(X!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.12/0.39 tff(139,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[138, 131, 103])).
% 0.12/0.39 tff(140,plain,(![Y: $i] : big_p(Y)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(141,plain,
% 0.12/0.39 ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) | (~![Y: $i] : big_p(Y))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(142,plain,
% 0.12/0.39 (![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.12/0.39 tff(143,plain,
% 0.12/0.39 ((~((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))) | (~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(144,plain,
% 0.12/0.39 ((~(big_p(X!2) | (~big_p(Y!3)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[143, 84])).
% 0.12/0.39 tff(145,plain,
% 0.12/0.39 (~(big_p(X!2) | (~big_p(Y!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[144, 142])).
% 0.12/0.39 tff(146,plain,
% 0.12/0.39 ((big_p(X!2) | (~big_p(Y!3))) | (~big_p(X!2))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(147,plain,
% 0.12/0.39 (~big_p(X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.12/0.39 tff(148,plain,
% 0.12/0.39 ((~![Y: $i] : big_p(Y)) | big_p(X!2)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(149,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[148, 147, 140])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------