TSTP Solution File: SYN063+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN063+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 23:53:28 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN063+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.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 01:38:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.33 Usage: tptp [options] [-file:]file
% 0.19/0.33 -h, -? prints this message.
% 0.19/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.33 -m, -model generate model.
% 0.19/0.33 -p, -proof generate proof.
% 0.19/0.33 -c, -core generate unsat core of named formulas.
% 0.19/0.33 -st, -statistics display statistics.
% 0.19/0.33 -t:timeout set timeout (in second).
% 0.19/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.33 -<param>:<value> configuration parameter and value.
% 0.19/0.33 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(big_p_type, type, (
% 0.19/0.38 big_p: $i > $o)).
% 0.19/0.38 tff(tptp_fun_X_0_type, type, (
% 0.19/0.38 tptp_fun_X_0: $i)).
% 0.19/0.38 tff(b_type, type, (
% 0.19/0.38 b: $i)).
% 0.19/0.38 tff(c_type, type, (
% 0.19/0.38 c: $i)).
% 0.19/0.38 tff(a_type, type, (
% 0.19/0.38 a: $i)).
% 0.19/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.19/0.38 tptp_fun_X1_1: $i)).
% 0.19/0.38 tff(1,assumption,(~big_p(c)), introduced(assumption)).
% 0.19/0.38 tff(2,assumption,(~big_p(a)), introduced(assumption)).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))) | big_p(a)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (((~big_p(a)) | big_p(c) | (~big_p(b))) | big_p(a)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 ((~big_p(a)) | big_p(c) | (~big_p(b))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (((~big_p(a)) | big_p(c) | big_p(X1!1)) | big_p(a)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~big_p(a)) | big_p(c) | big_p(X1!1)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[7, 2])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (((~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))) | ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> ((~((~big_p(a)) | big_p(c) | (~big_p(b)))) | (~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ((~(~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))) <=> (~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (((~big_p(a)) | big_p(c) | (~big_p(b))) <=> ((~big_p(a)) | big_p(c) | (~big_p(b)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (((~big_p(a)) | big_p(c) | big_p(X1!1)) <=> ((~big_p(a)) | big_p(c) | big_p(X1!1))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))) <=> (((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[13, 12])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))) <=> (~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[14, 11])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 ((~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) <=> (~(~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 ((~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) <=> ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[16, 10])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) <=> (~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> ((~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))) | ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[18, 17])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> ((~((~big_p(a)) | big_p(c) | (~big_p(b)))) | (~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[19, 9])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (((![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) & ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> ((![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) & ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) <=> ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 ((![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c)))) <=> (![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c))))) <=> (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c))))) <=> ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.19/0.38 tff(27,axiom,(~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel33')).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 22])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X))))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 22])).
% 0.19/0.38 tff(35,plain,(
% 0.19/0.38 (![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) & ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[34])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 ((![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) & ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[35, 21])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.19/0.38 inference(and_elim,[status(thm)],[36])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 ((~((~big_p(a)) | big_p(c) | (~big_p(b)))) | (~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 20])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[38, 8, 6, 4])).
% 0.19/0.38 tff(40,plain,(big_p(a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 ((~((~big_p(a)) | big_p(c))) | (~big_p(a)) | big_p(c)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (~((~big_p(a)) | big_p(c))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[41, 40, 1])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))) | ((~big_p(a)) | big_p(c))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 ((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((big_p(b) | (~big_p(c))) | big_p(c)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (big_p(b) | (~big_p(c))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[45, 1])).
% 0.19/0.38 tff(47,assumption,(![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X)))))), introduced(assumption)).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (((~![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X)))))) | ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(c)))))) <=> ((~![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X)))))) | (~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(c)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X)))))) | ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(c)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 ((~![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X)))))) | (~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(c))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[50, 47, 40, 1, 46])).
% 0.19/0.39 tff(52,plain,((~![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X)))))) | big_p(c)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (~![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[52, 1])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> (![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) <=> (![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.19/0.39 inference(and_elim,[status(thm)],[36])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![X: $i] : ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 53])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> ((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~((~((~big_p(a)) | big_p(c) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> (~((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> ((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> ((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ((~![X1: $i] : (~((~((~big_p(a)) | big_p(c) | big_p(X1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) | (~((~((~big_p(a)) | big_p(c))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[65, 59, 44])).
% 0.19/0.39 tff(67,plain,(big_p(c)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))) | (~big_p(c))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (((~big_p(a)) | big_p(c) | (~big_p(b))) | (~big_p(c))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 ((~big_p(a)) | big_p(c) | (~big_p(b))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (((~big_p(a)) | big_p(c) | big_p(X1!1)) | (~big_p(c))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~big_p(a)) | big_p(c) | big_p(X1!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[72, 67])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[38, 73, 71, 69])).
% 0.19/0.39 % SZS output end Proof
%------------------------------------------------------------------------------