TSTP Solution File: COL094-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL094-1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Tue Sep 6 17:48:32 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL094-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 12:08:10 EDT 2022
% 0.14/0.35 % 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.
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(comb_app_type, type, (
% 0.21/0.45 comb_app: ( $i * $i ) > $i)).
% 0.21/0.45 tff(ap_parcontractE_sk2s_type, type, (
% 0.21/0.45 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(r_type, type, (
% 0.21/0.45 r: $i)).
% 0.21/0.45 tff(q_type, type, (
% 0.21/0.45 q: $i)).
% 0.21/0.45 tff(p_type, type, (
% 0.21/0.45 p: $i)).
% 0.21/0.45 tff(combS_type, type, (
% 0.21/0.45 combS: $i)).
% 0.21/0.45 tff(ap_parcontractE_sk2q_type, type, (
% 0.21/0.45 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(ap_parcontractE_c1_type, type, (
% 0.21/0.45 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.21/0.45 tff(ap_parcontractE_c2_type, type, (
% 0.21/0.45 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.21/0.45 tff(combK_type, type, (
% 0.21/0.45 combK: $i)).
% 0.21/0.45 tff(ap_parcontractE_c3_type, type, (
% 0.21/0.45 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.21/0.45 tff(ap_parcontractE_sk1q_type, type, (
% 0.21/0.45 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(ap_parcontractE_sk1p_type, type, (
% 0.21/0.45 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.21/0.45 tff(member_type, type, (
% 0.21/0.45 member: ( $i * $i ) > $o)).
% 0.21/0.45 tff(parcontract_type, type, (
% 0.21/0.45 parcontract: $i)).
% 0.21/0.45 tff(pair_type, type, (
% 0.21/0.45 pair: ( $i * $i ) > $i)).
% 0.21/0.45 tff(ap_parcontractE_c4_type, type, (
% 0.21/0.45 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.21/0.45 tff(comb_type, type, (
% 0.21/0.45 comb: $i)).
% 0.21/0.45 tff(1,assumption,(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(5,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_app')).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.45 tff(7,plain,(
% 0.21/0.45 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[6])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.45 tff(11,plain,(~(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(12,assumption,(ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(16,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.45 tff(18,plain,(
% 0.21/0.45 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[17])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[22, 19, 12, 11])).
% 0.21/0.46 tff(24,plain,(~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(25,assumption,(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))), introduced(assumption)).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[26, 8, 25])).
% 0.21/0.46 tff(28,plain,(~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(32,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.46 tff(34,plain,(
% 0.21/0.46 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[33])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.46 tff(36,plain,
% 0.21/0.46 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(37,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(38,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.46 tff(39,plain,
% 0.21/0.46 (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.21/0.46 tff(40,assumption,(ap_parcontractE_c1(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.46 tff(41,plain,
% 0.21/0.46 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(42,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.46 tff(43,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(44,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE2')).
% 0.21/0.46 tff(45,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.46 tff(46,plain,(
% 0.21/0.46 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.46 inference(skolemize,[status(sab)],[45])).
% 0.21/0.46 tff(47,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.21/0.46 tff(48,plain,
% 0.21/0.46 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(49,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(50,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.46 tff(51,plain,
% 0.21/0.46 (member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[50, 47, 40])).
% 0.21/0.46 tff(52,assumption,(~member(p, comb)), introduced(assumption)).
% 0.21/0.46 tff(53,assumption,(ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.46 tff(56,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(57,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE9')).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.46 tff(59,plain,(
% 0.21/0.46 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.46 inference(skolemize,[status(sab)],[58])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[63, 60, 52, 53])).
% 0.21/0.46 tff(65,plain,((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[65, 52])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(Q, comb)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(68,plain,
% 0.21/0.46 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.46 tff(69,plain,
% 0.21/0.46 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(70,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E2')).
% 0.21/0.47 tff(71,plain,
% 0.21/0.47 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.47 tff(72,plain,(
% 0.21/0.47 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.47 inference(skolemize,[status(sab)],[71])).
% 0.21/0.47 tff(73,plain,
% 0.21/0.47 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.47 tff(74,plain,
% 0.21/0.47 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(75,plain,
% 0.21/0.47 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(76,plain,
% 0.21/0.47 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.47 tff(77,plain,
% 0.21/0.47 ((~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.21/0.47 tff(78,plain,
% 0.21/0.47 (~member(comb_app(combS, p), comb)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[77, 52])).
% 0.21/0.47 tff(79,assumption,(ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.47 tff(80,assumption,(~member(comb_app(combS, p), comb)), introduced(assumption)).
% 0.21/0.47 tff(81,plain,
% 0.21/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(82,plain,
% 0.21/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(83,plain,
% 0.21/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.47 tff(84,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[83, 47, 80, 79])).
% 0.21/0.47 tff(85,plain,((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(86,plain,
% 0.21/0.47 (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[85, 78])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.47 tff(89,plain,
% 0.21/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(90,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE5')).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.48 tff(92,plain,(
% 0.21/0.48 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.48 inference(skolemize,[status(sab)],[91])).
% 0.21/0.48 tff(93,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(96,plain,
% 0.21/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[96, 93, 52, 12])).
% 0.21/0.48 tff(98,plain,((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[98, 52])).
% 0.21/0.48 tff(100,assumption,(ap_parcontractE_c4(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(104,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.48 tff(106,plain,(
% 0.21/0.48 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[105])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.48 tff(111,plain,
% 0.21/0.48 ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[110, 107])).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[111, 100])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = r),
% 0.21/0.48 inference(symmetry,[status(thm)],[112])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) <=> ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[113])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (ap_parcontractE_c4(comb_app(combS, p), q, r) <=> ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.48 inference(symmetry,[status(thm)],[114])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[100, 115])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) = ap_parcontractE_sk2s(comb_app(combS, p), q, r)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[113])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) = pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.21/0.48 inference(symmetry,[status(thm)],[119])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) <=> (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.49 tff(122,plain,
% 0.21/0.49 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(123,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(125,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.49 tff(127,plain,(
% 0.21/0.49 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.49 inference(skolemize,[status(sab)],[126])).
% 0.21/0.49 tff(128,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(130,plain,
% 0.21/0.49 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(131,plain,
% 0.21/0.49 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.49 tff(132,plain,
% 0.21/0.49 ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[131, 128])).
% 0.21/0.49 tff(133,plain,
% 0.21/0.49 (member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[132, 100])).
% 0.21/0.49 tff(134,assumption,(~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.49 tff(135,assumption,(~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.49 tff(136,assumption,(~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.49 tff(137,plain,
% 0.21/0.49 (^[R: $i, Q: $i, P: $i] : refl((ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(138,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.49 tff(139,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(140,plain,
% 0.21/0.49 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) <=> (ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> ((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)))), rewrite(((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)))), rewrite(((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[140])).
% 0.21/0.49 tff(142,axiom,(![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.21/0.50 tff(143,plain,
% 0.21/0.50 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.50 tff(144,plain,
% 0.21/0.50 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.21/0.50 tff(145,plain,(
% 0.21/0.50 ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[144])).
% 0.21/0.50 tff(146,plain,
% 0.21/0.50 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.21/0.50 tff(147,plain,
% 0.21/0.50 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(148,plain,
% 0.21/0.50 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(149,plain,
% 0.21/0.50 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.50 tff(150,plain,
% 0.21/0.50 (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[149, 146, 136, 135, 134])).
% 0.21/0.50 tff(151,plain,
% 0.21/0.50 (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[150, 133])).
% 0.21/0.51 tff(152,assumption,(ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.51 tff(153,plain,
% 0.21/0.51 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(154,plain,
% 0.21/0.51 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(155,plain,
% 0.21/0.51 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.51 tff(156,plain,
% 0.21/0.51 (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[155, 107, 152])).
% 0.21/0.51 tff(157,plain,
% 0.21/0.51 (comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.21/0.51 inference(symmetry,[status(thm)],[156])).
% 0.21/0.51 tff(158,plain,
% 0.21/0.51 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(159,plain,
% 0.21/0.51 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(160,plain,
% 0.21/0.51 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.21/0.51 tff(161,plain,
% 0.21/0.51 (member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[160, 128, 152])).
% 0.21/0.51 tff(162,plain,
% 0.21/0.51 (^[R: $i] : refl(((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ((~member(pair(combS, R), parcontract)) | (R = combS)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(163,plain,
% 0.21/0.51 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.51 tff(164,plain,
% 0.21/0.51 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(165,axiom,(![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_parcontractE2')).
% 0.21/0.51 tff(166,plain,
% 0.21/0.51 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.21/0.51 tff(167,plain,(
% 0.21/0.51 ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.51 inference(skolemize,[status(sab)],[166])).
% 0.21/0.51 tff(168,plain,
% 0.21/0.51 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.21/0.51 tff(169,plain,
% 0.21/0.51 (((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))) <=> ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(170,plain,
% 0.21/0.51 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(171,plain,
% 0.21/0.51 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.51 tff(172,plain,
% 0.21/0.51 (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[171, 168, 161])).
% 0.21/0.51 tff(173,plain,
% 0.21/0.51 (combS = ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.51 inference(symmetry,[status(thm)],[172])).
% 0.21/0.51 tff(174,plain,
% 0.21/0.51 (comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[173])).
% 0.21/0.51 tff(175,plain,
% 0.21/0.51 (comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.21/0.51 inference(transitivity,[status(thm)],[174, 157])).
% 0.21/0.51 tff(176,plain,
% 0.21/0.51 (comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[175])).
% 0.21/0.52 tff(177,plain,
% 0.21/0.52 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(symmetry,[status(thm)],[176])).
% 0.21/0.52 tff(178,assumption,(r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.52 tff(179,plain,
% 0.21/0.52 (r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(transitivity,[status(thm)],[178, 177])).
% 0.21/0.52 tff(180,plain,
% 0.21/0.52 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(181,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[180])).
% 0.21/0.52 tff(182,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(183,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.21/0.52 tff(184,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.52 tff(185,plain,(
% 0.21/0.52 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.52 inference(skolemize,[status(sab)],[184])).
% 0.21/0.52 tff(186,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.21/0.52 tff(187,plain,
% 0.21/0.52 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(188,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(189,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.21/0.52 tff(190,plain,
% 0.21/0.52 (member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[189, 186, 152])).
% 0.21/0.52 tff(191,assumption,(member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)), introduced(assumption)).
% 0.21/0.52 tff(192,plain,
% 0.21/0.52 (^[QP: $i, PP: $i] : refl(((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(193,plain,
% 0.21/0.52 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.52 tff(194,plain,
% 0.21/0.52 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(195,plain,
% 0.21/0.52 (^[QP: $i, PP: $i] : trans(monotonicity(rewrite(((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) <=> ((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))), ((((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> (((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) | (~member(pair(q, QP), parcontract))))), rewrite((((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) | (~member(pair(q, QP), parcontract))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))), ((((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(196,plain,
% 0.21/0.52 (![QP: $i, PP: $i] : (((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[195])).
% 0.21/0.52 tff(197,axiom,(![QP: $i, PP: $i] : (((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s2_parcontractD_c1')).
% 0.21/0.52 tff(198,plain,
% 0.21/0.52 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.52 tff(199,plain,
% 0.21/0.52 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.21/0.52 tff(200,plain,(
% 0.21/0.52 ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[199])).
% 0.21/0.52 tff(201,plain,
% 0.21/0.52 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.21/0.52 tff(202,plain,
% 0.21/0.52 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(203,plain,
% 0.21/0.53 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(204,plain,
% 0.21/0.53 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.53 tff(205,plain,
% 0.21/0.53 (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[204, 201, 191, 190])).
% 0.21/0.53 tff(206,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[205, 179])).
% 0.21/0.53 tff(207,plain,((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (~(r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(208,plain,
% 0.21/0.53 (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[207, 151, 112])).
% 0.21/0.53 tff(209,plain,
% 0.21/0.53 (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[208, 121])).
% 0.21/0.53 tff(210,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(211,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.41/0.53 inference(quant_inst,[status(thm)],[])).
% 0.41/0.53 tff(212,plain,
% 0.41/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.41/0.53 tff(213,plain,
% 0.41/0.53 ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[212, 186])).
% 0.41/0.53 tff(214,plain,
% 0.41/0.53 ($false),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[213, 209, 116])).
% 0.41/0.53 tff(215,plain,((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.53 tff(216,plain,
% 0.41/0.53 (~ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[215, 99, 86, 66])).
% 0.41/0.53 tff(217,assumption,(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.41/0.53 tff(218,assumption,(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.41/0.53 tff(219,plain,
% 0.41/0.53 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.41/0.53 inference(quant_inst,[status(thm)],[])).
% 0.41/0.53 tff(220,plain,
% 0.41/0.53 ($false),
% 0.41/0.53 inference(unit_resolution,[status(thm)],[219, 8, 218])).
% 0.41/0.53 tff(221,plain,(~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.53 tff(222,plain,
% 0.41/0.53 (^[P2: $i, Q2: $i, Q1: $i, P1: $i] : refl(((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)) <=> ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)))),
% 0.41/0.53 inference(bind,[status(th)],[])).
% 0.41/0.53 tff(223,plain,
% 0.41/0.53 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)) <=> ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.41/0.53 inference(quant_intro,[status(thm)],[222])).
% 0.41/0.53 tff(224,plain,
% 0.41/0.53 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)) <=> ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.41/0.53 inference(rewrite,[status(thm)],[])).
% 0.41/0.53 tff(225,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','app_app1')).
% 0.41/0.53 tff(226,plain,
% 0.41/0.53 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.41/0.53 tff(227,plain,(
% 0.41/0.53 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.41/0.53 inference(skolemize,[status(sab)],[226])).
% 0.41/0.53 tff(228,plain,
% 0.41/0.53 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.41/0.53 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.41/0.53 tff(229,plain,
% 0.41/0.53 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(230,plain,
% 0.41/0.54 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.41/0.54 inference(quant_inst,[status(thm)],[])).
% 0.41/0.54 tff(231,plain,
% 0.41/0.54 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))),
% 0.41/0.54 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.41/0.54 tff(232,plain,
% 0.41/0.54 ($false),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[231, 228, 221, 217])).
% 0.41/0.54 tff(233,plain,(~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.54 tff(234,plain,
% 0.41/0.54 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(235,plain,
% 0.41/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))),
% 0.41/0.54 inference(quant_inst,[status(thm)],[])).
% 0.41/0.54 tff(236,plain,
% 0.41/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))),
% 0.41/0.54 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.41/0.54 tff(237,plain,
% 0.41/0.54 ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[236, 35])).
% 0.41/0.54 tff(238,plain,
% 0.41/0.54 (~ap_parcontractE_c3(comb_app(combS, p), q, r)),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[237, 233])).
% 0.41/0.54 tff(239,assumption,(comb_app(combS, p) = comb_app(combK, r)), introduced(assumption)).
% 0.41/0.54 tff(240,plain,
% 0.41/0.54 (comb_app(combK, r) = comb_app(combS, p)),
% 0.41/0.54 inference(symmetry,[status(thm)],[239])).
% 0.41/0.54 tff(241,assumption,(comb_app(combK, r) = comb_app(combS, p)), introduced(assumption)).
% 0.41/0.54 tff(242,plain,
% 0.41/0.54 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(243,axiom,(~(combK = combS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_s')).
% 0.41/0.54 tff(244,plain,
% 0.41/0.54 (~(combK = combS)),
% 0.41/0.54 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.41/0.54 tff(245,plain,
% 0.41/0.54 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(246,plain,
% 0.41/0.54 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS))),
% 0.41/0.54 inference(quant_inst,[status(thm)],[])).
% 0.41/0.54 tff(247,plain,
% 0.41/0.54 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS)),
% 0.41/0.54 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.41/0.54 tff(248,plain,
% 0.41/0.54 ($false),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[247, 244, 228, 241])).
% 0.41/0.54 tff(249,plain,(~(comb_app(combK, r) = comb_app(combS, p))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.54 tff(250,plain,
% 0.41/0.54 ($false),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[249, 240])).
% 0.41/0.54 tff(251,plain,(~(comb_app(combS, p) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.54 tff(252,assumption,(ap_parcontractE_c2(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.41/0.54 tff(253,plain,
% 0.41/0.54 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(254,plain,
% 0.41/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))),
% 0.41/0.54 inference(quant_inst,[status(thm)],[])).
% 0.41/0.54 tff(255,plain,
% 0.41/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r))),
% 0.41/0.54 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.41/0.54 tff(256,plain,
% 0.41/0.54 ($false),
% 0.41/0.54 inference(unit_resolution,[status(thm)],[255, 19, 252, 251])).
% 0.41/0.54 tff(257,plain,(~ap_parcontractE_c2(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.54 tff(258,plain,
% 0.41/0.54 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract) <=> member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(259,axiom,(member(pair(comb_app(comb_app(combS, p), q), r), parcontract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s2_parcontractD_h1')).
% 0.41/0.54 tff(260,plain,
% 0.41/0.54 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.41/0.54 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.41/0.54 tff(261,plain,
% 0.41/0.54 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(262,plain,
% 0.41/0.55 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))),
% 0.41/0.55 inference(quant_inst,[status(thm)],[])).
% 0.41/0.55 tff(263,plain,
% 0.41/0.55 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.41/0.55 tff(264,plain,
% 0.41/0.55 (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[263, 146, 260])).
% 0.41/0.55 tff(265,plain,
% 0.41/0.55 (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[264, 257, 238])).
% 0.41/0.55 tff(266,plain,
% 0.41/0.55 (ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[265, 216])).
% 0.41/0.55 tff(267,plain,
% 0.41/0.55 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(P, comb)))),
% 0.41/0.55 inference(bind,[status(th)],[])).
% 0.41/0.55 tff(268,plain,
% 0.41/0.55 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.41/0.55 inference(quant_intro,[status(thm)],[267])).
% 0.41/0.55 tff(269,plain,
% 0.41/0.55 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(270,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E1')).
% 0.41/0.55 tff(271,plain,
% 0.41/0.55 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.41/0.55 tff(272,plain,(
% 0.41/0.55 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.41/0.55 inference(skolemize,[status(sab)],[271])).
% 0.41/0.55 tff(273,plain,
% 0.41/0.55 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[272, 268])).
% 0.41/0.55 tff(274,plain,
% 0.41/0.55 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(275,plain,
% 0.41/0.55 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))),
% 0.41/0.55 inference(quant_inst,[status(thm)],[])).
% 0.41/0.55 tff(276,plain,
% 0.41/0.55 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.41/0.55 tff(277,plain,
% 0.41/0.55 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[276, 273])).
% 0.41/0.55 tff(278,plain,
% 0.41/0.55 (~member(comb_app(comb_app(combS, p), q), comb)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[277, 78])).
% 0.41/0.55 tff(279,plain,
% 0.41/0.55 ($false),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[50, 47, 278, 266])).
% 0.41/0.55 tff(280,plain,(member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.41/0.55 tff(281,plain,
% 0.41/0.55 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.41/0.55 inference(bind,[status(th)],[])).
% 0.41/0.55 tff(282,plain,
% 0.41/0.55 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.41/0.55 inference(quant_intro,[status(thm)],[281])).
% 0.41/0.55 tff(283,plain,
% 0.41/0.55 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(284,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.41/0.55 tff(285,plain,
% 0.41/0.55 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.41/0.55 tff(286,plain,(
% 0.41/0.55 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.41/0.55 inference(skolemize,[status(sab)],[285])).
% 0.41/0.55 tff(287,plain,
% 0.41/0.55 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.41/0.55 tff(288,plain,
% 0.41/0.55 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(289,plain,
% 0.41/0.55 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.41/0.55 inference(quant_inst,[status(thm)],[])).
% 0.41/0.55 tff(290,plain,
% 0.41/0.55 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.41/0.55 tff(291,plain,
% 0.41/0.55 (member(pair(p, p), parcontract)),
% 0.41/0.55 inference(unit_resolution,[status(thm)],[290, 287, 280])).
% 0.41/0.55 tff(292,assumption,(~(r = comb_app(comb_app(combS, p), q))), introduced(assumption)).
% 0.41/0.55 tff(293,plain,
% 0.41/0.55 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))))),
% 0.41/0.55 inference(bind,[status(th)],[])).
% 0.41/0.55 tff(294,plain,
% 0.41/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.41/0.55 inference(quant_intro,[status(thm)],[293])).
% 0.41/0.55 tff(295,plain,
% 0.41/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(296,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.41/0.55 tff(297,plain,
% 0.41/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.41/0.55 tff(298,plain,(
% 0.41/0.55 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.41/0.55 inference(skolemize,[status(sab)],[297])).
% 0.41/0.55 tff(299,plain,
% 0.41/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.41/0.55 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.41/0.55 tff(300,plain,
% 0.41/0.55 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(301,plain,
% 0.41/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(302,plain,
% 0.43/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.43/0.55 tff(303,plain,
% 0.43/0.55 ($false),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[302, 299, 292, 40])).
% 0.43/0.55 tff(304,plain,((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q))), inference(lemma,lemma(discharge,[]))).
% 0.43/0.55 tff(305,plain,
% 0.43/0.55 (r = comb_app(comb_app(combS, p), q)),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[304, 40])).
% 0.43/0.55 tff(306,plain,
% 0.43/0.55 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(307,plain,
% 0.43/0.55 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(308,plain,
% 0.43/0.55 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.43/0.55 tff(309,plain,
% 0.43/0.55 ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[308, 201])).
% 0.43/0.55 tff(310,plain,
% 0.43/0.55 (~member(pair(q, q), parcontract)),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[309, 305, 291])).
% 0.43/0.55 tff(311,plain,
% 0.43/0.55 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(q, comb)) | member(pair(q, q), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(q, comb)) | member(pair(q, q), parcontract))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(312,plain,
% 0.43/0.55 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(q, comb)) | member(pair(q, q), parcontract))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(313,plain,
% 0.43/0.55 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(q, comb)) | member(pair(q, q), parcontract)),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.43/0.55 tff(314,plain,
% 0.43/0.55 (~member(q, comb)),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[313, 287, 310])).
% 0.43/0.55 tff(315,plain,
% 0.43/0.55 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))),
% 0.43/0.55 inference(rewrite,[status(thm)],[])).
% 0.43/0.55 tff(316,plain,
% 0.43/0.55 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))),
% 0.43/0.55 inference(quant_inst,[status(thm)],[])).
% 0.43/0.55 tff(317,plain,
% 0.43/0.55 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.43/0.55 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.43/0.55 tff(318,plain,
% 0.43/0.55 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.43/0.55 inference(unit_resolution,[status(thm)],[317, 73])).
% 0.43/0.55 tff(319,plain,
% 0.43/0.55 ($false),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[318, 314, 51])).
% 0.43/0.56 tff(320,plain,(~ap_parcontractE_c1(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.56 tff(321,plain,
% 0.43/0.56 (ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[265, 320])).
% 0.43/0.56 tff(322,plain,
% 0.43/0.56 (member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[131, 128, 321])).
% 0.43/0.56 tff(323,plain,
% 0.43/0.56 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[110, 107, 321])).
% 0.43/0.56 tff(324,plain,
% 0.43/0.56 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(325,plain,
% 0.43/0.56 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))),
% 0.43/0.56 inference(quant_inst,[status(thm)],[])).
% 0.43/0.56 tff(326,plain,
% 0.43/0.56 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.43/0.56 tff(327,plain,
% 0.43/0.56 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[326, 186, 321])).
% 0.43/0.56 tff(328,plain,
% 0.43/0.56 (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[207, 327, 323])).
% 0.43/0.56 tff(329,plain,
% 0.43/0.56 (ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[149, 146, 328, 322])).
% 0.43/0.56 tff(330,plain,
% 0.43/0.56 (ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[329, 39, 24])).
% 0.43/0.56 tff(331,plain,
% 0.43/0.56 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(332,plain,
% 0.43/0.56 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))),
% 0.43/0.56 inference(quant_inst,[status(thm)],[])).
% 0.43/0.56 tff(333,plain,
% 0.43/0.56 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))),
% 0.43/0.56 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.43/0.56 tff(334,plain,
% 0.43/0.56 (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)),
% 0.43/0.56 inference(unit_resolution,[status(thm)],[333, 299, 330])).
% 0.43/0.56 tff(335,plain,
% 0.43/0.56 (comb_app(combS, p) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.43/0.56 inference(symmetry,[status(thm)],[334])).
% 0.43/0.56 tff(336,plain,
% 0.43/0.56 (comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[335])).
% 0.43/0.56 tff(337,plain,
% 0.43/0.56 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.43/0.56 inference(symmetry,[status(thm)],[336])).
% 0.43/0.56 tff(338,plain,
% 0.43/0.56 (r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.43/0.56 inference(transitivity,[status(thm)],[323, 337])).
% 0.43/0.56 tff(339,plain,
% 0.43/0.56 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(340,plain,
% 0.43/0.56 (((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))) <=> ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(341,plain,
% 0.43/0.56 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[340])).
% 0.43/0.56 tff(342,plain,
% 0.43/0.56 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.43/0.56 inference(transitivity,[status(thm)],[341, 339])).
% 0.43/0.56 tff(343,plain,
% 0.43/0.56 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.43/0.56 inference(quant_inst,[status(thm)],[])).
% 0.43/0.56 tff(344,plain,
% 0.43/0.56 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.43/0.57 tff(345,plain,
% 0.43/0.57 (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[344, 201, 291, 327])).
% 0.43/0.57 tff(346,plain,
% 0.43/0.57 ($false),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[345, 338])).
% 0.43/0.57 % SZS output end Proof
%------------------------------------------------------------------------------