TSTP Solution File: COL091-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL091-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 17:48:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COL091-2 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 11:59:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(member_type, type, (
% 0.20/0.44 member: ( $i * $i ) > $o)).
% 0.20/0.44 tff(contract_type, type, (
% 0.20/0.44 contract: $i)).
% 0.20/0.44 tff(pair_type, type, (
% 0.20/0.44 pair: ( $i * $i ) > $i)).
% 0.20/0.44 tff(ap_contractE_sk2q_type, type, (
% 0.20/0.44 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(r_type, type, (
% 0.20/0.44 r: $i)).
% 0.20/0.44 tff(p_type, type, (
% 0.20/0.44 p: $i)).
% 0.20/0.44 tff(combK_type, type, (
% 0.20/0.44 combK: $i)).
% 0.20/0.44 tff(ap_contractE_c3_type, type, (
% 0.20/0.44 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(ap_contractE_c4_type, type, (
% 0.20/0.44 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(ap_contractE_sk3q_type, type, (
% 0.20/0.44 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(comb_app_type, type, (
% 0.20/0.44 comb_app: ( $i * $i ) > $i)).
% 0.20/0.44 tff(ap_contractE_c2_type, type, (
% 0.20/0.44 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(ap_contractE_sk1q_type, type, (
% 0.20/0.44 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(ap_contractE_sk1p_type, type, (
% 0.20/0.44 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(combS_type, type, (
% 0.20/0.44 combS: $i)).
% 0.20/0.44 tff(ap_contractE_c1_type, type, (
% 0.20/0.44 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(1,assumption,(ap_contractE_c4(combK, p, r)), introduced(assumption)).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(5,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')).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.44 tff(7,plain,(
% 0.20/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.44 inference(skolemize,[status(sab)],[6])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (((~![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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, 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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, r)), contract))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 ((~![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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, r)), contract))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 ((~![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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))) <=> ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(16,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE15')).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.44 tff(18,plain,(
% 0.20/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[17])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | ((~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | (~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | ((~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | (~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[22, 19, 1])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (^[Q: $i] : refl(((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(27,axiom,(![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k1_contractD_c1')).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.44 tff(29,plain,(
% 0.20/0.44 ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | ((~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)))) <=> ((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | (~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 ((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | ((~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 ((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | (~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[33, 30, 23, 12])).
% 0.20/0.45 tff(35,plain,(~ap_contractE_c4(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(36,assumption,(combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))), introduced(assumption)).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (^[Q: $i, P: $i] : refl((~(combK = comb_app(P, Q))) <=> (~(combK = comb_app(P, Q))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(40,axiom,(![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_app')).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.45 tff(42,plain,(
% 0.20/0.45 ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[41])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[44, 43, 36])).
% 0.20/0.45 tff(46,plain,(~(combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(50,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')).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.45 tff(52,plain,(
% 0.20/0.45 ![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))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[51])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, 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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 ((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 ((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (~ap_contractE_c2(combK, p, r)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[56, 53, 46])).
% 0.20/0.45 tff(58,assumption,(combK = comb_app(combK, r)), introduced(assumption)).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (comb_app(combK, r) = combK),
% 0.20/0.45 inference(symmetry,[status(thm)],[58])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (comb_app(comb_app(combK, r), r) = comb_app(combK, r)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[59])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (comb_app(combK, r) = comb_app(comb_app(combK, r), r)),
% 0.20/0.45 inference(symmetry,[status(thm)],[60])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (combK = comb_app(comb_app(combK, r), r)),
% 0.20/0.45 inference(transitivity,[status(thm)],[58, 61])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combK, r), r)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (~(combK = comb_app(comb_app(combK, r), r))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[63, 43])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[64, 62])).
% 0.20/0.45 tff(66,plain,(~(combK = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(67,assumption,(ap_contractE_c1(combK, p, r)), introduced(assumption)).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(71,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')).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.45 tff(73,plain,(
% 0.20/0.45 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[72])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combK, p, r)) | (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(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combK, p, r)) | (combK = comb_app(combK, r))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[77, 74, 67, 66])).
% 0.20/0.45 tff(79,plain,(~ap_contractE_c1(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (member(pair(comb_app(combK, p), r), contract) <=> member(pair(comb_app(combK, p), r), contract)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(81,axiom,(member(pair(comb_app(combK, p), r), contract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k1_contractD_h1')).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (member(pair(comb_app(combK, p), r), contract)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.46 tff(88,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')).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.46 tff(91,plain,(
% 0.20/0.46 ![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)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[90])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~![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(combK, p), r), contract)) | ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, 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(combK, p), r), contract)) | ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 ((ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), contract))) <=> ((~member(pair(comb_app(combK, p), r), contract)) | ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (((~![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(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), 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(combK, p), r), contract)) | ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (((~![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(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), 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(combK, p), r), contract)) | ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r))),
% 0.20/0.46 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ((~![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(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), contract)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((~![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(combK, p), r), contract)) | ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 92, 82])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[99, 79])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[100, 57])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (ap_contractE_c3(combK, p, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[101, 35])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (^[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)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(106,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')).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.46 tff(108,plain,(
% 0.20/0.46 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.46 inference(skolemize,[status(sab)],[107])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (![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)],[108, 104])).
% 0.20/0.47 tff(110,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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, 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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(111,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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(112,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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[112, 109, 102])).
% 0.20/0.47 tff(114,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(115,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)],[114])).
% 0.20/0.47 tff(116,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(117,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_contractE')).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.47 tff(119,plain,(
% 0.20/0.47 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(skolemize,[status(sab)],[118])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[121, 120, 113])).
% 0.20/0.47 % SZS output end Proof
%------------------------------------------------------------------------------