TSTP Solution File: SYN084+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:53:40 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n014.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 01:43:02 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.
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 tff(big_p_type, type, (
% 0.14/0.39 big_p: $i > $o)).
% 0.14/0.39 tff(tptp_fun_X1_1_type, type, (
% 0.14/0.39 tptp_fun_X1_1: $i)).
% 0.14/0.39 tff(f_type, type, (
% 0.14/0.39 f: $i > $i)).
% 0.14/0.39 tff(a_type, type, (
% 0.14/0.39 a: $i)).
% 0.14/0.39 tff(tptp_fun_X_0_type, type, (
% 0.14/0.39 tptp_fun_X_0: $i)).
% 0.14/0.39 tff(1,assumption,(~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))), introduced(assumption)).
% 0.14/0.39 tff(2,plain,
% 0.14/0.39 (((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))) | big_p(f(X1!1))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(3,plain,
% 0.14/0.39 (big_p(f(X1!1))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.14/0.39 tff(4,plain,
% 0.14/0.39 ((big_p(f(X1!1)) | (~big_p(X1!1))) | (~big_p(f(X1!1)))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(5,plain,
% 0.14/0.39 (big_p(f(X1!1)) | (~big_p(X1!1))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.14/0.39 tff(6,plain,
% 0.14/0.39 (((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))) | (~big_p(f(f(X1!1))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(7,plain,
% 0.14/0.39 (~big_p(f(f(X1!1)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.14/0.39 tff(8,assumption,(~big_p(a)), introduced(assumption)).
% 0.14/0.39 tff(9,plain,
% 0.14/0.39 (((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) | big_p(a)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(10,plain,
% 0.14/0.39 ((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.14/0.39 tff(11,plain,
% 0.14/0.39 (((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))) | big_p(a)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(12,plain,
% 0.14/0.39 ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.14/0.39 tff(13,assumption,(~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))), introduced(assumption)).
% 0.14/0.39 tff(14,plain,
% 0.14/0.39 (((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))) | (big_p(f(X!0)) | (~big_p(X!0)))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(15,plain,
% 0.14/0.39 (big_p(f(X!0)) | (~big_p(X!0))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.14/0.39 tff(16,plain,
% 0.14/0.39 (((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))) | (~big_p(f(f(X!0))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(17,plain,
% 0.14/0.39 (~big_p(f(f(X!0)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.14/0.39 tff(18,plain,
% 0.14/0.39 (((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))) | big_p(a)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(19,plain,
% 0.14/0.39 (big_p(a)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[18, 13])).
% 0.14/0.39 tff(20,assumption,(big_p(f(X!0)) | (~big_p(X!0))), introduced(assumption)).
% 0.14/0.39 tff(21,assumption,(~big_p(f(f(X!0)))), introduced(assumption)).
% 0.14/0.39 tff(22,assumption,(big_p(a)), introduced(assumption)).
% 0.14/0.39 tff(23,assumption,(![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))), introduced(assumption)).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | ((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))) <=> ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | ((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[26, 23, 22, 21, 20])).
% 0.14/0.39 tff(28,plain,((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 (~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[28, 19, 17, 15])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 ((![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))) <=> (![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 ((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) <=> (![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) & ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))) <=> ((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) & ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) <=> ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 ((~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))) <=> ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 ((![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1)))))) <=> (![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(36,plain,
% 0.14/0.39 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1))))))) <=> (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.14/0.39 inference(monotonicity,[status(thm)],[35])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1))))))) <=> ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.14/0.39 inference(transitivity,[status(thm)],[36, 34])).
% 0.14/0.39 tff(38,axiom,(~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62')).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[42, 33])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 ((~![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[44, 33])).
% 0.14/0.40 tff(46,plain,(
% 0.14/0.40 (![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) & ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[45])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 ((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) & ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[46, 32])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))),
% 0.14/0.40 inference(and_elim,[status(thm)],[47])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[48, 31])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[49, 30])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[50, 29])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 ((~![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))) | (~((~((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0))) | (~((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0)))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (~((~((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0))) | (~((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0))))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (((~((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0))) | (~((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0)))))) | ((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 ((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.14/0.40 tff(56,plain,
% 0.14/0.40 ((~((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0))) | (~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0)),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 ((~((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0))) | big_p(X!0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[56, 19, 17])).
% 0.14/0.40 tff(58,plain,
% 0.14/0.40 (big_p(X!0)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[57, 55])).
% 0.14/0.40 tff(59,plain,
% 0.14/0.40 (((~((~big_p(a)) | big_p(f(f(X!0))) | big_p(X!0))) | (~((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0)))))) | ((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 ((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[59, 53])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 ((~((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0))))) | (~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(62,plain,
% 0.14/0.40 ((~((~big_p(a)) | big_p(f(f(X!0))) | (~big_p(f(X!0))))) | (~big_p(f(X!0)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[61, 19, 17])).
% 0.14/0.40 tff(63,plain,
% 0.14/0.40 (~big_p(f(X!0))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[62, 60])).
% 0.14/0.40 tff(64,plain,
% 0.14/0.40 ((~(big_p(f(X!0)) | (~big_p(X!0)))) | big_p(f(X!0)) | (~big_p(X!0))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(65,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[64, 63, 58, 15])).
% 0.14/0.40 tff(66,plain,((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(67,plain,
% 0.14/0.40 (((~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))) | ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))) <=> ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))) | (~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(68,plain,
% 0.14/0.40 ((~(~((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))) <=> ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(69,plain,
% 0.14/0.40 ((((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))) <=> (~((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(70,plain,
% 0.14/0.40 (((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) <=> ((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(71,plain,
% 0.14/0.40 ((((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))) <=> (((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.14/0.40 tff(72,plain,
% 0.14/0.40 ((((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))) <=> (~((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[71, 69])).
% 0.14/0.40 tff(73,plain,
% 0.14/0.40 ((~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))) <=> (~(~((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.14/0.40 tff(74,plain,
% 0.14/0.40 ((~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))) <=> ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[73, 68])).
% 0.14/0.40 tff(75,plain,
% 0.14/0.40 ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) <=> (~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(76,plain,
% 0.14/0.40 (((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))) <=> ((~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))) | ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[75, 74])).
% 0.14/0.40 tff(77,plain,
% 0.14/0.40 (((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))) <=> ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))) | (~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[76, 67])).
% 0.14/0.40 tff(78,plain,
% 0.14/0.40 ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))),
% 0.14/0.40 inference(and_elim,[status(thm)],[47])).
% 0.14/0.40 tff(79,plain,
% 0.14/0.40 ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))) | (~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.14/0.40 tff(80,plain,
% 0.14/0.40 ((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[79, 66])).
% 0.14/0.40 tff(81,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[80, 12, 10])).
% 0.14/0.40 tff(82,plain,(big_p(a)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(83,assumption,(~((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))), introduced(assumption)).
% 0.14/0.40 tff(84,plain,
% 0.14/0.40 (((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))) | ((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(85,plain,
% 0.14/0.40 ((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.14/0.40 tff(86,plain,
% 0.14/0.40 (((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))) | ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(87,plain,
% 0.14/0.40 ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.14/0.40 tff(88,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[80, 87, 85])).
% 0.14/0.40 tff(89,plain,((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(90,assumption,((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))), introduced(assumption)).
% 0.14/0.40 tff(91,assumption,(![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))), introduced(assumption)).
% 0.14/0.40 tff(92,plain,
% 0.14/0.40 ((~![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))) | (~((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(93,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[92, 91, 90])).
% 0.14/0.41 tff(94,plain,((~((~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))) | (~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))) | (~![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(95,plain,
% 0.14/0.41 (~![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[94, 89])).
% 0.14/0.41 tff(96,plain,
% 0.14/0.41 (![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[50, 95])).
% 0.14/0.41 tff(97,plain,
% 0.14/0.41 (((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | ((~big_p(a)) | big_p(f(f(X1!1))) | (~(big_p(f(X1!1)) | (~big_p(X1!1)))))) <=> ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X1!1))) | (~(big_p(f(X1!1)) | (~big_p(X1!1)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(98,plain,
% 0.14/0.41 ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | ((~big_p(a)) | big_p(f(f(X1!1))) | (~(big_p(f(X1!1)) | (~big_p(X1!1)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(99,plain,
% 0.14/0.41 ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X1!1))) | (~(big_p(f(X1!1)) | (~big_p(X1!1))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.14/0.41 tff(100,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[99, 96, 82, 7, 5])).
% 0.14/0.41 tff(101,plain,((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(102,plain,
% 0.14/0.41 (~((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[80, 101])).
% 0.14/0.41 tff(103,plain,
% 0.14/0.41 (((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) | (~big_p(X1!1))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(104,plain,
% 0.14/0.41 (~big_p(X1!1)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.14/0.41 tff(105,plain,
% 0.14/0.41 ((big_p(f(X1!1)) | (~big_p(X1!1))) | big_p(X1!1)),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(106,plain,
% 0.14/0.41 (big_p(f(X1!1)) | (~big_p(X1!1))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.14/0.41 tff(107,plain,
% 0.14/0.41 (((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) | (~big_p(f(f(X1!1))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(108,plain,
% 0.14/0.41 (~big_p(f(f(X1!1)))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[107, 102])).
% 0.14/0.41 tff(109,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[99, 96, 82, 108, 106])).
% 0.14/0.41 % SZS output end Proof
%------------------------------------------------------------------------------