%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL090-2 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL090-2 : TPTP v9.0.0. Released v2.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n015.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Thu Jun 19 12:15:40 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(comb_app_type, type, (
% 0.21/0.47 comb_app: ( $i * $i ) > $i)).
% 0.21/0.47 tff(ap_contractE_sk2q_type, type, (
% 0.21/0.47 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(r_type, type, (
% 0.21/0.47 r: $i)).
% 0.21/0.47 tff(combK_type, type, (
% 0.21/0.47 combK: $i)).
% 0.21/0.47 tff(combS_type, type, (
% 0.21/0.47 combS: $i)).
% 0.21/0.47 tff(ap_contractE_c1_type, type, (
% 0.21/0.47 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.21/0.47 tff(member_type, type, (
% 0.21/0.47 member: ( $i * $i ) > $o)).
% 0.21/0.47 tff(contract_type, type, (
% 0.21/0.47 contract: $i)).
% 0.21/0.47 tff(pair_type, type, (
% 0.21/0.47 pair: ( $i * $i ) > $i)).
% 0.21/0.47 tff(ap_contractE_c3_type, type, (
% 0.21/0.47 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.21/0.47 tff(ap_contractE_c2_type, type, (
% 0.21/0.47 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.21/0.47 tff(ap_contractE_sk1q_type, type, (
% 0.21/0.47 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(ap_contractE_sk1p_type, type, (
% 0.21/0.47 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(ap_contractE_c4_type, type, (
% 0.21/0.47 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.21/0.47 tff(ap_contractE_sk3q_type, type, (
% 0.21/0.47 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.21/0.47 tff(1,assumption,(comb_app(combS, combK) = comb_app(combK, r)), introduced(assumption)).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 ((combS = combK) <=> (combK = combS)),
% 0.21/0.47 inference(commutativity,[status(thm)],[])).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 ((combK = combS) <=> (combS = combK)),
% 0.21/0.47 inference(symmetry,[status(thm)],[2])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 ((~(combK = combS)) <=> (~(combS = combK))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(6,axiom,(~(combK = combS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_s')).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (~(combK = combS)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (~(combS = combK)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (^[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)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (![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))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(12,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')).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.47 tff(14,plain,(
% 0.21/0.47 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.47 inference(skolemize,[status(sab)],[13])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(combK, r))) | (combS = combK))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(combK, r))) | (combS = combK)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[18, 15, 8, 1])).
% 0.21/0.47 tff(20,plain,(~(comb_app(combS, combK) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(21,assumption,(ap_contractE_c1(comb_app(combS, combK), combK, r)), introduced(assumption)).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[22])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(25,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')).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.47 tff(27,plain,(
% 0.21/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[26])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.47 tff(29,plain,
% 0.21/0.47 (((~![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 ((~![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)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[31, 28, 21, 20])).
% 0.21/0.47 tff(33,plain,(~ap_contractE_c1(comb_app(combS, combK), combK, r)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(34,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)).
% 0.21/0.47 tff(35,assumption,(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(37,plain,
% 0.21/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(39,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_app')).
% 0.21/0.47 tff(40,plain,
% 0.21/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.47 tff(41,plain,(
% 0.21/0.47 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[40])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[43, 42, 35])).
% 0.21/0.47 tff(45,plain,(~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (((~![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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(47,plain,
% 0.21/0.47 ((~![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))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(48,plain,
% 0.21/0.47 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.47 tff(49,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[48, 15, 45, 34])).
% 0.21/0.47 tff(50,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,[]))).
% 0.21/0.47 tff(51,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(52,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.47 tff(53,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(54,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')).
% 0.21/0.47 tff(55,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.21/0.47 tff(56,plain,(
% 0.21/0.47 ![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))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[55])).
% 0.21/0.47 tff(57,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.48 tff(58,plain,
% 0.21/0.48 (((~![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))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(59,plain,
% 0.21/0.48 ((~![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))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 ((~![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)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 ((~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)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.21/0.48 tff(62,plain,
% 0.21/0.48 (~ap_contractE_c2(comb_app(combS, combK), combK, r)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[61, 50])).
% 0.21/0.48 tff(63,assumption,(member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), introduced(assumption)).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (^[R: $i] : refl((~member(pair(combK, R), contract)) <=> (~member(pair(combK, R), contract)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(67,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_contractE')).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.48 tff(69,plain,(
% 0.21/0.48 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.21/0.48 inference(skolemize,[status(sab)],[68])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.48 tff(71,plain,
% 0.21/0.48 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[71, 70, 63])).
% 0.21/0.48 tff(73,plain,(~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (^[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)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(77,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')).
% 0.21/0.48 tff(78,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.48 tff(79,plain,(
% 0.21/0.48 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.21/0.48 inference(skolemize,[status(sab)],[78])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 ((~![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))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 ((~![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)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (~ap_contractE_c4(comb_app(combS, combK), combK, r)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[83, 80, 73])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract) <=> member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(86,axiom,(member(pair(comb_app(comb_app(combS, combK), combK), r), contract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','i_contract_E')).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (^[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))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.48 tff(93,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')).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.21/0.48 tff(96,plain,(
% 0.21/0.48 ![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)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[95])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 ((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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 (((~![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)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[99])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(transitivity,[status(thm)],[100, 98])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 ((~![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)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(103,plain,
% 0.21/0.48 ((~![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)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (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)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[103, 97, 87])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 (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)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[104, 84])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[105, 62])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[106, 33])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 (^[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)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(111,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')).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.48 tff(113,plain,(
% 0.21/0.48 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.21/0.48 inference(skolemize,[status(sab)],[112])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.48 tff(115,plain,
% 0.21/0.48 (((~![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 ((~![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))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.49 tff(118,plain,
% 0.21/0.49 ((~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)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.21/0.49 tff(119,plain,
% 0.21/0.49 (member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[118, 107])).
% 0.21/0.49 tff(120,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)).
% 0.21/0.49 tff(121,plain,
% 0.21/0.49 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(122,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[121, 42, 120])).
% 0.21/0.49 tff(123,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,[]))).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 (((~![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)))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(125,plain,
% 0.21/0.49 ((~![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)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 ((~![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))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.49 tff(127,plain,
% 0.21/0.49 (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[126, 57, 123])).
% 0.21/0.49 tff(128,assumption,(member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 (^[R: $i] : refl((~member(pair(combS, R), contract)) <=> (~member(pair(combS, R), contract)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(130,plain,
% 0.21/0.49 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.49 tff(131,plain,
% 0.21/0.49 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(132,axiom,(![R: $i] : (~member(pair(combS, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_contractE')).
% 0.21/0.49 tff(133,plain,
% 0.21/0.49 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.49 tff(134,plain,(
% 0.21/0.49 ![R: $i] : (~member(pair(combS, R), contract))),
% 0.21/0.49 inference(skolemize,[status(sab)],[133])).
% 0.21/0.49 tff(135,plain,
% 0.21/0.49 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.21/0.49 tff(136,plain,
% 0.21/0.49 ((~![R: $i] : (~member(pair(combS, R), contract))) | (~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(137,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[136, 135, 128])).
% 0.21/0.49 tff(138,plain,(~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(139,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(140,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.49 tff(142,plain,
% 0.21/0.49 (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[141, 114, 138])).
% 0.21/0.49 tff(143,assumption,(member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.21/0.49 tff(144,plain,
% 0.21/0.49 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[144, 70, 143])).
% 0.21/0.49 tff(146,plain,(~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(147,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(148,plain,
% 0.21/0.49 ((~![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))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(149,plain,
% 0.21/0.49 ((~![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)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[149, 80, 146])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 (((~![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_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)) | 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)))) | (~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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 ((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_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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 (((~![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_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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[152])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 (((~![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_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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[153, 151])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 ((~![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)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 ((~![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_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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 ((~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[156, 97, 150])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 ((~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[157, 142])).
% 0.21/0.50 tff(159,plain,
% 0.21/0.50 ((~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[158, 127])).
% 0.21/0.50 tff(160,plain,
% 0.21/0.50 (ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[159, 119])).
% 0.21/0.50 tff(161,plain,
% 0.21/0.50 (((~![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))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(162,plain,
% 0.21/0.50 ((~![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))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(163,plain,
% 0.21/0.50 ((~![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)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.50 tff(164,plain,
% 0.21/0.50 (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[163, 28, 160])).
% 0.21/0.50 tff(165,plain,
% 0.21/0.50 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(166,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[165, 42, 164])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------