TSTP Solution File: COL090-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL090-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 17:48:29 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL090-2 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 12:00:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(comb_app_type, type, (
% 0.20/0.46 comb_app: ( $i * $i ) > $i)).
% 0.20/0.46 tff(ap_contractE_sk2q_type, type, (
% 0.20/0.46 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(r_type, type, (
% 0.20/0.46 r: $i)).
% 0.20/0.46 tff(combK_type, type, (
% 0.20/0.46 combK: $i)).
% 0.20/0.46 tff(combS_type, type, (
% 0.20/0.46 combS: $i)).
% 0.20/0.46 tff(ap_contractE_c1_type, type, (
% 0.20/0.46 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(ap_contractE_c2_type, type, (
% 0.20/0.46 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(ap_contractE_sk1q_type, type, (
% 0.20/0.46 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(ap_contractE_sk1p_type, type, (
% 0.20/0.46 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.20/0.46 tff(ap_contractE_c3_type, type, (
% 0.20/0.46 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(member_type, type, (
% 0.20/0.46 member: ( $i * $i ) > $o)).
% 0.20/0.46 tff(contract_type, type, (
% 0.20/0.46 contract: $i)).
% 0.20/0.46 tff(pair_type, type, (
% 0.20/0.46 pair: ( $i * $i ) > $i)).
% 0.20/0.46 tff(ap_contractE_c4_type, type, (
% 0.20/0.46 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.20/0.46 tff(ap_contractE_sk3q_type, type, (
% 0.20/0.46 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(1,assumption,(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))), introduced(assumption)).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(5,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_app')).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.47 tff(7,plain,(
% 0.20/0.47 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[6])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.47 tff(11,plain,(~(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))) <=> ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(15,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE9')).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.47 tff(17,plain,(
% 0.20/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[16])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.20/0.47 tff(23,assumption,(member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (^[R: $i] : refl((~member(pair(combS, R), contract)) <=> (~member(pair(combS, R), contract)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(27,axiom,(![R: $i] : (~member(pair(combS, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_contractE')).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.47 tff(29,plain,(
% 0.20/0.47 ![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.47 inference(skolemize,[status(sab)],[28])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 ((~![R: $i] : (~member(pair(combS, R), contract))) | (~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.20/0.47 tff(33,plain,(~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)) <=> ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(37,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE10')).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.47 tff(39,plain,(
% 0.20/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.47 inference(skolemize,[status(sab)],[38])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.20/0.47 tff(45,assumption,(member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (^[R: $i] : refl((~member(pair(combK, R), contract)) <=> (~member(pair(combK, R), contract)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(49,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_contractE')).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.47 tff(51,plain,(
% 0.20/0.47 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(skolemize,[status(sab)],[50])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[53, 52, 45])).
% 0.20/0.47 tff(55,plain,(~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)) <=> ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(59,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE13')).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.47 tff(61,plain,(
% 0.20/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.47 inference(skolemize,[status(sab)],[60])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[65, 62, 55])).
% 0.20/0.47 tff(67,assumption,(member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), introduced(assumption)).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[68, 52, 67])).
% 0.20/0.47 tff(70,plain,(~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (~ap_contractE_c4(comb_app(combS, combK), combK, r)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[73, 62, 70])).
% 0.20/0.47 tff(75,assumption,(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.20/0.47 tff(76,assumption,(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[77, 8, 76])).
% 0.20/0.47 tff(79,plain,(~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (^[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)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (![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))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(83,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','app_app1')).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.47 tff(85,plain,(
% 0.20/0.47 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.20/0.47 inference(skolemize,[status(sab)],[84])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[89, 86, 79, 75])).
% 0.20/0.47 tff(91,plain,(~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(94,plain,
% 0.20/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 ((~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[94, 18])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (~ap_contractE_c2(comb_app(combS, combK), combK, r)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[95, 91])).
% 0.20/0.47 tff(97,assumption,(comb_app(combS, combK) = comb_app(combK, r)), introduced(assumption)).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 ((combS = combK) <=> (combK = combS)),
% 0.20/0.47 inference(commutativity,[status(thm)],[])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 ((combK = combS) <=> (combS = combK)),
% 0.20/0.47 inference(symmetry,[status(thm)],[98])).
% 0.20/0.47 tff(100,plain,
% 0.20/0.47 ((~(combK = combS)) <=> (~(combS = combK))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.47 tff(101,plain,
% 0.20/0.47 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(102,axiom,(~(combK = combS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_s')).
% 0.20/0.47 tff(103,plain,
% 0.20/0.47 (~(combK = combS)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.47 tff(104,plain,
% 0.20/0.47 (~(combS = combK)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[103, 100])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(combK, r))) | (combS = combK))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(combK, r))) | (combS = combK))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(combK, r))) | (combS = combK))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(combK, r))) | (combS = combK)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[107, 86, 104, 97])).
% 0.20/0.48 tff(109,plain,(~(comb_app(combS, combK) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(110,assumption,(ap_contractE_c1(comb_app(combS, combK), combK, r)), introduced(assumption)).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))) <=> ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(114,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE4')).
% 0.20/0.48 tff(115,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.48 tff(116,plain,(
% 0.20/0.48 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[115])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[120, 117, 110, 109])).
% 0.20/0.48 tff(122,plain,(~ap_contractE_c1(comb_app(combS, combK), combK, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract) <=> member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(124,axiom,(member(pair(comb_app(comb_app(combS, combK), combK), r), contract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','i_contract_E')).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 (^[R: $i, Q: $i, P: $i] : refl((ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) <=> (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) <=> ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) <=> ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) <=> (ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))), (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) <=> ((ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c3(P, Q, R)))), rewrite(((ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c3(P, Q, R)) <=> (ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))), (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) <=> (ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))))), ((((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R)) <=> ((ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c4(P, Q, R)))), rewrite(((ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c4(P, Q, R)) <=> (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))), ((((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R)) <=> (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R)) <=> ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.48 tff(131,axiom,(![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE1')).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.20/0.48 tff(134,plain,(
% 0.20/0.48 ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[133])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ((~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 ((ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract))) <=> ((~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ((~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r))),
% 0.20/0.48 inference(transitivity,[status(thm)],[138, 136])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[141, 135, 125])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[142, 122])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[143, 96])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[144, 74])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(148,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[148, 40, 145])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ((~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(151,plain,
% 0.20/0.48 ((ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))) <=> ((~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ((~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[151])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[152, 150])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 (ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[155, 135, 149])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 66])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[157, 44, 22])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[161, 117, 158])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[163, 8, 162])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------