%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN084-2 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Sat Jun 21 05:38:12 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN084-2 : TPTP v9.0.0. Released v1.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:27:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(big_p_type, type, (
% 0.19/0.37 big_p: $i > $o)).
% 0.19/0.37 tff(sk2_type, type, (
% 0.19/0.37 sk2: $i)).
% 0.19/0.37 tff(f_type, type, (
% 0.19/0.37 f: $i > $i)).
% 0.19/0.37 tff(sk1_type, type, (
% 0.19/0.37 sk1: $i)).
% 0.19/0.37 tff(a_type, type, (
% 0.19/0.37 a: $i)).
% 0.19/0.37 tff(1,assumption,(big_p(f(f(sk2)))), introduced(assumption)).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (((~big_p(f(f(sk1)))) | (~big_p(f(f(sk2))))) <=> ((~big_p(f(f(sk1)))) | (~big_p(f(f(sk2)))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,axiom,((~big_p(f(f(sk1)))) | (~big_p(f(f(sk2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62_4')).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 ((~big_p(f(f(sk1)))) | (~big_p(f(f(sk2))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (~big_p(f(f(sk1)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (^[A: $i] : refl(((~big_p(a)) | big_p(A) | big_p(f(f(A)))) <=> ((~big_p(a)) | big_p(A) | big_p(f(f(A)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A)))) <=> ![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A)))) <=> ![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (^[A: $i] : trans(monotonicity(rewrite((big_p(f(f(A))) | big_p(A)) <=> (big_p(A) | big_p(f(f(A))))), (((big_p(f(f(A))) | big_p(A)) | (~big_p(a))) <=> ((big_p(A) | big_p(f(f(A)))) | (~big_p(a))))), rewrite(((big_p(A) | big_p(f(f(A)))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(A) | big_p(f(f(A))))), (((big_p(f(f(A))) | big_p(A)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(A) | big_p(f(f(A))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![A: $i] : ((big_p(f(f(A))) | big_p(A)) | (~big_p(a))) <=> ![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.37 tff(11,axiom,(![A: $i] : ((big_p(f(f(A))) | big_p(A)) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62_2')).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.37 tff(14,plain,(
% 0.19/0.37 ![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[13])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (big_p(a) <=> big_p(a)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(17,axiom,(big_p(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62_1')).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (big_p(a)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | (big_p(f(f(sk1))) | (~big_p(a)) | big_p(sk1))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | big_p(f(f(sk1))) | (~big_p(a)) | big_p(sk1))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (((~big_p(a)) | big_p(sk1) | big_p(f(f(sk1)))) <=> (big_p(f(f(sk1))) | (~big_p(a)) | big_p(sk1))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(sk1) | big_p(f(f(sk1))))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | (big_p(f(f(sk1))) | (~big_p(a)) | big_p(sk1)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(sk1) | big_p(f(f(sk1))))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | big_p(f(f(sk1))) | (~big_p(a)) | big_p(sk1))),
% 0.19/0.37 inference(transitivity,[status(thm)],[21, 19])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(sk1) | big_p(f(f(sk1))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | big_p(f(f(sk1))) | (~big_p(a)) | big_p(sk1)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (big_p(sk1)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[24, 18, 15, 5])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (^[A: $i] : refl(((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A)))) <=> ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A)))) <=> ![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A)))) <=> ![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (^[A: $i] : rewrite(((big_p(f(f(A))) | (~big_p(f(A)))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (![A: $i] : ((big_p(f(f(A))) | (~big_p(f(A)))) | (~big_p(a))) <=> ![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.37 tff(31,axiom,(![A: $i] : ((big_p(f(f(A))) | (~big_p(f(A)))) | (~big_p(a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62_3')).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.37 tff(34,plain,(
% 0.19/0.37 ![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[33])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | ((~big_p(a)) | big_p(f(f(sk1))) | (~big_p(f(sk1))))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | (~big_p(a)) | big_p(f(f(sk1))) | (~big_p(f(sk1))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | ((~big_p(a)) | big_p(f(f(sk1))) | (~big_p(f(sk1))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | (~big_p(a)) | big_p(f(f(sk1))) | (~big_p(f(sk1)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (~big_p(f(sk1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[38, 18, 35, 5])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1))) <=> ((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (((big_p(f(sk1)) | (~big_p(sk1))) | (~big_p(f(f(sk2))))) <=> ((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(42,axiom,((big_p(f(sk1)) | (~big_p(sk1))) | (~big_p(f(f(sk2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62_6')).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 ((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 ((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 ((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 ((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 ((~big_p(f(f(sk2)))) | big_p(f(sk1)) | (~big_p(sk1))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[47, 39, 25, 1])).
% 0.19/0.37 tff(49,plain,(~big_p(f(f(sk2)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(50,assumption,(~big_p(sk2)), introduced(assumption)).
% 0.19/0.37 tff(51,assumption,(~big_p(f(f(sk2)))), introduced(assumption)).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(f(f(sk2))) | big_p(sk2))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | (~big_p(a)) | big_p(f(f(sk2))) | big_p(sk2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (((~big_p(a)) | big_p(sk2) | big_p(f(f(sk2)))) <=> ((~big_p(a)) | big_p(f(f(sk2))) | big_p(sk2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(sk2) | big_p(f(f(sk2))))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(f(f(sk2))) | big_p(sk2)))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(sk2) | big_p(f(f(sk2))))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | (~big_p(a)) | big_p(f(f(sk2))) | big_p(sk2))),
% 0.19/0.37 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | ((~big_p(a)) | big_p(sk2) | big_p(f(f(sk2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(57,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(A) | big_p(f(f(A))))) | (~big_p(a)) | big_p(f(f(sk2))) | big_p(sk2)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.37 tff(58,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[57, 18, 15, 51, 50])).
% 0.19/0.37 tff(59,plain,(big_p(f(f(sk2))) | big_p(sk2)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(60,plain,
% 0.19/0.37 (big_p(sk2)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[59, 49])).
% 0.19/0.37 tff(61,plain,
% 0.19/0.37 (((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | ((~big_p(a)) | big_p(f(f(sk2))) | (~big_p(f(sk2))))) <=> ((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | (~big_p(a)) | big_p(f(f(sk2))) | (~big_p(f(sk2))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(62,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | ((~big_p(a)) | big_p(f(f(sk2))) | (~big_p(f(sk2))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(63,plain,
% 0.19/0.37 ((~![A: $i] : ((~big_p(a)) | big_p(f(f(A))) | (~big_p(f(A))))) | (~big_p(a)) | big_p(f(f(sk2))) | (~big_p(f(sk2)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.37 tff(64,plain,
% 0.19/0.37 (~big_p(f(sk2))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[63, 18, 35, 49])).
% 0.19/0.37 tff(65,plain,
% 0.19/0.37 (((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2))) <=> ((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(66,plain,
% 0.19/0.37 (((big_p(f(sk2)) | (~big_p(sk2))) | (~big_p(f(f(sk1))))) <=> ((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(67,axiom,((big_p(f(sk2)) | (~big_p(sk2))) | (~big_p(f(f(sk1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62_7')).
% 0.19/0.37 tff(68,plain,
% 0.19/0.37 ((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.37 tff(69,plain,
% 0.19/0.37 ((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.19/0.37 tff(70,plain,
% 0.19/0.37 ((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.19/0.37 tff(71,plain,
% 0.19/0.37 ((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[70, 65])).
% 0.19/0.37 tff(72,plain,
% 0.19/0.37 ((~big_p(f(f(sk1)))) | big_p(f(sk2)) | (~big_p(sk2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[71, 65])).
% 0.19/0.37 tff(73,plain,
% 0.19/0.37 (~big_p(f(f(sk1)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[72, 64, 60])).
% 0.19/0.37 tff(74,plain,
% 0.19/0.37 (big_p(sk1)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[24, 18, 15, 73])).
% 0.19/0.37 tff(75,plain,
% 0.19/0.37 (~big_p(f(sk1))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[38, 18, 35, 73])).
% 0.19/0.37 tff(76,plain,
% 0.19/0.37 ((big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1)) | (~big_p(sk2))) <=> (big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1)) | (~big_p(sk2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(77,plain,
% 0.19/0.37 (((big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1))) | (~big_p(sk2))) <=> (big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1)) | (~big_p(sk2)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(78,plain,
% 0.19/0.37 (((big_p(f(sk1)) | big_p(f(sk2))) | (~big_p(sk1))) <=> (big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 ((((big_p(f(sk1)) | big_p(f(sk2))) | (~big_p(sk1))) | (~big_p(sk2))) <=> ((big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1))) | (~big_p(sk2)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 ((((big_p(f(sk1)) | big_p(f(sk2))) | (~big_p(sk1))) | (~big_p(sk2))) <=> (big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1)) | (~big_p(sk2)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[79, 77])).
% 0.19/0.38 tff(81,axiom,(((big_p(f(sk1)) | big_p(f(sk2))) | (~big_p(sk1))) | (~big_p(sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel62_5')).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 (big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1)) | (~big_p(sk2))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (big_p(f(sk1)) | big_p(f(sk2)) | (~big_p(sk1)) | (~big_p(sk2))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[82, 76])).
% 0.19/0.38 tff(84,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[83, 75, 74, 64, 60])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------