%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL090-3 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:00:46 AM UTC 2025
% Result : Unsatisfiable 0.24s 0.42s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : COL090-3 : TPTP v9.0.0. Released v2.7.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 12:14:41 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.24/0.42 % SZS status Unsatisfiable
% 0.24/0.42 % SZS output start Proof
% 0.24/0.42 tff(member_type, type, (
% 0.24/0.42 member: ( $i * $i ) > $o)).
% 0.24/0.42 tff(contract_type, type, (
% 0.24/0.42 contract: $i)).
% 0.24/0.42 tff(pair_type, type, (
% 0.24/0.42 pair: ( $i * $i ) > $i)).
% 0.24/0.42 tff(ap_contractE_sk3q_type, type, (
% 0.24/0.42 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.24/0.42 tff(ap_contractE_sk2q_type, type, (
% 0.24/0.42 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.24/0.42 tff(r_type, type, (
% 0.24/0.42 r: $i)).
% 0.24/0.42 tff(combK_type, type, (
% 0.24/0.42 combK: $i)).
% 0.24/0.42 tff(comb_app_type, type, (
% 0.24/0.42 comb_app: ( $i * $i ) > $i)).
% 0.24/0.42 tff(combS_type, type, (
% 0.24/0.42 combS: $i)).
% 0.24/0.42 tff(ap_contractE_c4_type, type, (
% 0.24/0.42 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.24/0.42 tff(ap_contractE_c1_type, type, (
% 0.24/0.42 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.24/0.42 tff(ap_contractE_c2_type, type, (
% 0.24/0.42 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.24/0.42 tff(ap_contractE_sk1q_type, type, (
% 0.24/0.42 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.24/0.42 tff(ap_contractE_sk1p_type, type, (
% 0.24/0.42 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.24/0.42 tff(ap_contractE_c3_type, type, (
% 0.24/0.42 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.24/0.42 tff(1,assumption,(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.24/0.42 tff(2,plain,
% 0.24/0.42 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(3,plain,
% 0.24/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.24/0.42 tff(4,plain,
% 0.24/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(5,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_app')).
% 0.24/0.42 tff(6,plain,
% 0.24/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.24/0.42 tff(7,plain,(
% 0.24/0.42 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.24/0.42 inference(skolemize,[status(sab)],[6])).
% 0.24/0.42 tff(8,plain,
% 0.24/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.24/0.42 tff(9,plain,
% 0.24/0.42 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(10,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.24/0.42 tff(11,plain,(~(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.42 tff(12,assumption,(ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.24/0.42 tff(13,plain,
% 0.24/0.42 (^[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))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(14,plain,
% 0.24/0.42 (![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)))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.24/0.42 tff(15,plain,
% 0.24/0.42 (![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)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(16,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_contractE4')).
% 0.24/0.42 tff(17,plain,
% 0.24/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.24/0.42 tff(18,plain,(
% 0.24/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.24/0.42 inference(skolemize,[status(sab)],[17])).
% 0.24/0.42 tff(19,plain,
% 0.24/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.24/0.42 tff(20,plain,
% 0.24/0.42 (((~![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))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(21,plain,
% 0.24/0.42 ((~![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))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(22,plain,
% 0.24/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.24/0.42 tff(23,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[22, 19, 12, 11])).
% 0.24/0.42 tff(24,plain,(~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.42 tff(25,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)).
% 0.24/0.42 tff(26,plain,
% 0.24/0.42 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(27,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[26, 8, 25])).
% 0.24/0.42 tff(28,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,[]))).
% 0.24/0.42 tff(29,plain,
% 0.24/0.42 (^[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)))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(30,plain,
% 0.24/0.42 (![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))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.24/0.42 tff(31,plain,
% 0.24/0.42 (![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))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(32,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/sandbox/benchmark/theBenchmark.p','ap_contractE9')).
% 0.24/0.42 tff(33,plain,
% 0.24/0.42 (![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))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.24/0.42 tff(34,plain,(
% 0.24/0.42 ![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))))),
% 0.24/0.42 inference(skolemize,[status(sab)],[33])).
% 0.24/0.42 tff(35,plain,
% 0.24/0.42 (![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))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.24/0.42 tff(36,plain,
% 0.24/0.42 (((~![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)))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(37,plain,
% 0.24/0.42 ((~![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)))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(38,plain,
% 0.24/0.42 ((~![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))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.24/0.42 tff(39,plain,
% 0.24/0.42 (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.24/0.42 tff(40,assumption,(member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), introduced(assumption)).
% 0.24/0.42 tff(41,plain,
% 0.24/0.42 (^[R: $i] : refl((~member(pair(combK, R), contract)) <=> (~member(pair(combK, R), contract)))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(42,plain,
% 0.24/0.42 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.24/0.42 tff(43,plain,
% 0.24/0.42 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(44,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_contractE')).
% 0.24/0.42 tff(45,plain,
% 0.24/0.42 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.24/0.42 tff(46,plain,(
% 0.24/0.42 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.24/0.42 inference(skolemize,[status(sab)],[45])).
% 0.24/0.42 tff(47,plain,
% 0.24/0.42 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.24/0.42 tff(48,plain,
% 0.24/0.42 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(49,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[48, 47, 40])).
% 0.24/0.42 tff(50,plain,(~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.42 tff(51,plain,
% 0.24/0.42 (^[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)))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(52,plain,
% 0.24/0.42 (![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))),
% 0.24/0.43 inference(quant_intro,[status(thm)],[51])).
% 0.24/0.43 tff(53,plain,
% 0.24/0.43 (![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))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(54,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/sandbox/benchmark/theBenchmark.p','ap_contractE13')).
% 0.24/0.43 tff(55,plain,
% 0.24/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.24/0.43 tff(56,plain,(
% 0.24/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.24/0.43 inference(skolemize,[status(sab)],[55])).
% 0.24/0.43 tff(57,plain,
% 0.24/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.24/0.43 tff(58,plain,
% 0.24/0.43 (((~![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))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(59,plain,
% 0.24/0.43 ((~![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))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(60,plain,
% 0.24/0.43 ((~![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)),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.24/0.43 tff(61,plain,
% 0.24/0.43 (~ap_contractE_c4(comb_app(combS, combK), combK, r)),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[60, 57, 50])).
% 0.24/0.43 tff(62,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)).
% 0.24/0.43 tff(63,assumption,(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.24/0.43 tff(64,plain,
% 0.24/0.43 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(65,plain,
% 0.24/0.43 ($false),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[64, 8, 63])).
% 0.24/0.43 tff(66,plain,(~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.43 tff(67,plain,
% 0.24/0.43 (^[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)))),
% 0.24/0.43 inference(bind,[status(th)],[])).
% 0.24/0.43 tff(68,plain,
% 0.24/0.43 (![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))),
% 0.24/0.43 inference(quant_intro,[status(thm)],[67])).
% 0.24/0.43 tff(69,plain,
% 0.24/0.43 (![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))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(70,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','app_app1')).
% 0.24/0.43 tff(71,plain,
% 0.24/0.43 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.24/0.43 tff(72,plain,(
% 0.24/0.43 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.24/0.43 inference(skolemize,[status(sab)],[71])).
% 0.24/0.43 tff(73,plain,
% 0.24/0.43 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.24/0.43 tff(74,plain,
% 0.24/0.43 (((~![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))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(75,plain,
% 0.24/0.43 ((~![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))))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(76,plain,
% 0.24/0.43 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.24/0.43 tff(77,plain,
% 0.24/0.43 ($false),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[76, 73, 66, 62])).
% 0.24/0.43 tff(78,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,[]))).
% 0.24/0.43 tff(79,plain,
% 0.24/0.43 (((~![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))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(80,plain,
% 0.24/0.43 ((~![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))))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(81,plain,
% 0.24/0.43 ((~![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)))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.24/0.43 tff(82,plain,
% 0.24/0.43 ((~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)))),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[81, 35])).
% 0.24/0.43 tff(83,plain,
% 0.24/0.43 (~ap_contractE_c2(comb_app(combS, combK), combK, r)),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[82, 78])).
% 0.24/0.43 tff(84,assumption,(comb_app(combS, combK) = comb_app(combK, r)), introduced(assumption)).
% 0.24/0.43 tff(85,plain,
% 0.24/0.43 (comb_app(combK, r) = comb_app(combS, combK)),
% 0.24/0.43 inference(symmetry,[status(thm)],[84])).
% 0.24/0.43 tff(86,assumption,(comb_app(combK, r) = comb_app(combS, combK)), introduced(assumption)).
% 0.24/0.43 tff(87,plain,
% 0.24/0.43 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(88,axiom,(~(combK = combS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_s')).
% 0.24/0.43 tff(89,plain,
% 0.24/0.43 (~(combK = combS)),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.24/0.43 tff(90,plain,
% 0.24/0.43 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(91,plain,
% 0.24/0.43 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(92,plain,
% 0.24/0.43 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS)),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.24/0.43 tff(93,plain,
% 0.24/0.43 ($false),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[92, 89, 73, 86])).
% 0.24/0.43 tff(94,plain,(~(comb_app(combK, r) = comb_app(combS, combK))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.43 tff(95,plain,
% 0.24/0.43 ($false),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[94, 85])).
% 0.24/0.43 tff(96,plain,(~(comb_app(combS, combK) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.43 tff(97,assumption,(ap_contractE_c1(comb_app(combS, combK), combK, r)), introduced(assumption)).
% 0.24/0.43 tff(98,plain,
% 0.24/0.43 (((~![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)))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(99,plain,
% 0.24/0.43 ((~![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)))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(100,plain,
% 0.24/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.24/0.43 tff(101,plain,
% 0.24/0.43 ($false),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[100, 19, 97, 96])).
% 0.24/0.43 tff(102,plain,(~ap_contractE_c1(comb_app(combS, combK), combK, r)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.43 tff(103,plain,
% 0.24/0.43 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract) <=> member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(104,axiom,(member(pair(comb_app(comb_app(combS, combK), combK), r), contract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_contract_E')).
% 0.24/0.43 tff(105,plain,
% 0.24/0.43 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.24/0.43 tff(106,plain,
% 0.24/0.43 (^[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))))),
% 0.24/0.43 inference(bind,[status(th)],[])).
% 0.24/0.43 tff(107,plain,
% 0.24/0.43 (![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)))),
% 0.24/0.43 inference(quant_intro,[status(thm)],[106])).
% 0.24/0.43 tff(108,plain,
% 0.24/0.43 (![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)))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(109,plain,
% 0.24/0.43 (^[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)))))),
% 0.24/0.43 inference(bind,[status(th)],[])).
% 0.24/0.43 tff(110,plain,
% 0.24/0.43 (![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)))),
% 0.24/0.43 inference(quant_intro,[status(thm)],[109])).
% 0.24/0.43 tff(111,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/sandbox/benchmark/theBenchmark.p','ap_contractE1')).
% 0.24/0.44 tff(112,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.24/0.44 tff(113,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.24/0.44 tff(114,plain,(
% 0.24/0.44 ![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)))),
% 0.24/0.44 inference(skolemize,[status(sab)],[113])).
% 0.24/0.44 tff(115,plain,
% 0.24/0.44 (![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)))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.24/0.44 tff(116,plain,
% 0.24/0.44 (((~![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)))) | 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)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(117,plain,
% 0.24/0.44 ((~![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)))),
% 0.24/0.44 inference(quant_inst,[status(thm)],[])).
% 0.24/0.44 tff(118,plain,
% 0.24/0.44 ((~![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))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.24/0.44 tff(119,plain,
% 0.24/0.44 (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)),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[118, 115, 105])).
% 0.24/0.44 tff(120,plain,
% 0.24/0.44 (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)),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[119, 102])).
% 0.24/0.44 tff(121,plain,
% 0.24/0.44 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[120, 83])).
% 0.24/0.44 tff(122,plain,
% 0.24/0.44 (ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[121, 61])).
% 0.24/0.44 tff(123,plain,
% 0.24/0.44 (^[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)))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(124,plain,
% 0.24/0.44 (![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))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[123])).
% 0.24/0.44 tff(125,plain,
% 0.24/0.44 (![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))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(126,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/sandbox/benchmark/theBenchmark.p','ap_contractE10')).
% 0.24/0.44 tff(127,plain,
% 0.24/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.24/0.44 tff(128,plain,(
% 0.24/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.24/0.44 inference(skolemize,[status(sab)],[127])).
% 0.24/0.44 tff(129,plain,
% 0.24/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.24/0.44 tff(130,plain,
% 0.24/0.44 (((~![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))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(131,plain,
% 0.24/0.44 ((~![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))),
% 0.24/0.44 inference(quant_inst,[status(thm)],[])).
% 0.24/0.44 tff(132,plain,
% 0.24/0.44 ((~![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)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.24/0.44 tff(133,plain,
% 0.24/0.44 ((~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)),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[132, 129])).
% 0.24/0.44 tff(134,plain,
% 0.24/0.44 (member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[133, 122])).
% 0.24/0.44 tff(135,assumption,(member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.24/0.44 tff(136,plain,
% 0.24/0.44 (^[R: $i] : refl((~member(pair(combS, R), contract)) <=> (~member(pair(combS, R), contract)))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(137,plain,
% 0.24/0.44 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[136])).
% 0.24/0.44 tff(138,plain,
% 0.24/0.44 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(139,axiom,(![R: $i] : (~member(pair(combS, R), contract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_contractE')).
% 0.24/0.44 tff(140,plain,
% 0.24/0.44 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.24/0.44 tff(141,plain,(
% 0.24/0.44 ![R: $i] : (~member(pair(combS, R), contract))),
% 0.24/0.44 inference(skolemize,[status(sab)],[140])).
% 0.24/0.44 tff(142,plain,
% 0.24/0.44 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.24/0.44 tff(143,plain,
% 0.24/0.44 ((~![R: $i] : (~member(pair(combS, R), contract))) | (~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.24/0.44 inference(quant_inst,[status(thm)],[])).
% 0.24/0.44 tff(144,plain,
% 0.24/0.44 ($false),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[143, 142, 135])).
% 0.24/0.44 tff(145,plain,(~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.44 tff(146,plain,
% 0.24/0.44 (((~![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))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(147,plain,
% 0.24/0.44 ((~![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))),
% 0.24/0.44 inference(quant_inst,[status(thm)],[])).
% 0.24/0.44 tff(148,plain,
% 0.24/0.44 ((~![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)),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.24/0.44 tff(149,plain,
% 0.24/0.44 (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[148, 129, 145])).
% 0.24/0.44 tff(150,plain,
% 0.24/0.44 (((~![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_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)) | ap_contractE_c2(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)))) | 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)) | (~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)))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(151,plain,
% 0.24/0.44 ((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))) <=> (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)) | (~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)))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(152,plain,
% 0.24/0.45 (((~![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)))) | (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)))) | (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)) | (~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))))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[151])).
% 0.24/0.45 tff(153,plain,
% 0.24/0.45 (((~![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)))) | (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)))) | 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)) | (~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)))),
% 0.24/0.45 inference(transitivity,[status(thm)],[152, 150])).
% 0.24/0.45 tff(154,plain,
% 0.24/0.45 ((~![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)))) | (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)))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(155,plain,
% 0.24/0.45 ((~![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)))) | 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)) | (~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))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.24/0.45 tff(156,plain,
% 0.24/0.45 (ap_contractE_c4(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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[155, 115, 149])).
% 0.24/0.45 tff(157,plain,
% 0.24/0.45 (ap_contractE_c4(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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[156, 134])).
% 0.24/0.45 tff(158,plain,
% 0.24/0.45 (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[157, 39, 24])).
% 0.24/0.45 tff(159,plain,
% 0.24/0.45 (((~![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))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(160,plain,
% 0.24/0.45 ((~![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))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(161,plain,
% 0.24/0.45 ((~![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)),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.24/0.45 tff(162,plain,
% 0.24/0.45 (member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[161, 57, 158])).
% 0.24/0.45 tff(163,plain,
% 0.24/0.45 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(164,plain,
% 0.24/0.45 ($false),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[163, 47, 162])).
% 0.24/0.45 % SZS output end Proof
% 0.24/0.46 % E exiting
%------------------------------------------------------------------------------