%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL094-2 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:00:47 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL094-2 : TPTP v9.0.0. Released v2.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 12:15:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 tff(member_type, type, (
% 0.21/0.51 member: ( $i * $i ) > $o)).
% 0.21/0.51 tff(parcontract_type, type, (
% 0.21/0.51 parcontract: $i)).
% 0.21/0.51 tff(pair_type, type, (
% 0.21/0.51 pair: ( $i * $i ) > $i)).
% 0.21/0.51 tff(p_type, type, (
% 0.21/0.51 p: $i)).
% 0.21/0.51 tff(comb_type, type, (
% 0.21/0.51 comb: $i)).
% 0.21/0.51 tff(ap_parcontractE_c4_type, type, (
% 0.21/0.51 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(comb_app_type, type, (
% 0.21/0.51 comb_app: ( $i * $i ) > $i)).
% 0.21/0.51 tff(ap_parcontractE_sk2s_type, type, (
% 0.21/0.51 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.21/0.51 tff(r_type, type, (
% 0.21/0.51 r: $i)).
% 0.21/0.51 tff(q_type, type, (
% 0.21/0.51 q: $i)).
% 0.21/0.51 tff(combS_type, type, (
% 0.21/0.51 combS: $i)).
% 0.21/0.51 tff(ap_parcontractE_sk2q_type, type, (
% 0.21/0.51 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.21/0.51 tff(ap_parcontractE_c1_type, type, (
% 0.21/0.51 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(ap_parcontractE_c3_type, type, (
% 0.21/0.51 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(ap_parcontractE_sk1q_type, type, (
% 0.21/0.51 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.21/0.51 tff(ap_parcontractE_sk1p_type, type, (
% 0.21/0.51 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.21/0.51 tff(ap_parcontractE_c2_type, type, (
% 0.21/0.51 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(combK_type, type, (
% 0.21/0.51 combK: $i)).
% 0.21/0.51 tff(1,assumption,(~member(p, comb)), introduced(assumption)).
% 0.21/0.51 tff(2,plain,
% 0.21/0.51 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(Q, comb)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(3,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.51 tff(4,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(5,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_E2')).
% 0.21/0.51 tff(6,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.51 tff(7,plain,(
% 0.21/0.51 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.51 inference(skolemize,[status(sab)],[6])).
% 0.21/0.51 tff(8,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.51 tff(9,plain,
% 0.21/0.51 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(10,plain,
% 0.21/0.51 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(11,plain,
% 0.21/0.51 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.51 tff(12,plain,
% 0.21/0.51 ((~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.21/0.51 tff(13,plain,
% 0.21/0.51 (~member(comb_app(combS, p), comb)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[12, 1])).
% 0.21/0.51 tff(14,plain,
% 0.21/0.51 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(P, comb)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(15,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.51 tff(16,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(17,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_E1')).
% 0.21/0.51 tff(18,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.51 tff(19,plain,(
% 0.21/0.51 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.51 inference(skolemize,[status(sab)],[18])).
% 0.21/0.51 tff(20,plain,
% 0.21/0.51 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.51 tff(21,plain,
% 0.21/0.51 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(22,plain,
% 0.21/0.51 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(23,plain,
% 0.21/0.51 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.51 tff(24,plain,
% 0.21/0.51 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.21/0.51 tff(25,plain,
% 0.21/0.51 (~member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[24, 13])).
% 0.21/0.51 tff(26,assumption,(~member(comb_app(comb_app(combS, p), q), comb)), introduced(assumption)).
% 0.21/0.51 tff(27,assumption,(ap_parcontractE_c1(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.51 tff(28,plain,
% 0.21/0.51 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(29,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.51 tff(30,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(31,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE2')).
% 0.21/0.51 tff(32,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.51 tff(33,plain,(
% 0.21/0.51 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.51 inference(skolemize,[status(sab)],[32])).
% 0.21/0.51 tff(34,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.51 tff(35,plain,
% 0.21/0.51 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(36,plain,
% 0.21/0.51 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(37,plain,
% 0.21/0.51 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.51 tff(38,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[37, 34, 27, 26])).
% 0.21/0.51 tff(39,plain,((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(40,plain,
% 0.21/0.51 (~ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[39, 25])).
% 0.21/0.51 tff(41,assumption,(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.51 tff(42,assumption,(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.51 tff(43,plain,
% 0.21/0.51 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(44,plain,
% 0.21/0.51 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.51 tff(45,plain,
% 0.21/0.51 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(46,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_app')).
% 0.21/0.51 tff(47,plain,
% 0.21/0.51 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.51 tff(48,plain,(
% 0.21/0.51 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[47])).
% 0.21/0.51 tff(49,plain,
% 0.21/0.51 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.51 tff(50,plain,
% 0.21/0.51 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(51,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.21/0.51 tff(52,plain,(~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(53,plain,
% 0.21/0.51 (^[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)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(54,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.51 tff(55,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(56,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')).
% 0.21/0.51 tff(57,plain,
% 0.21/0.51 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.51 tff(58,plain,(
% 0.21/0.51 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.51 inference(skolemize,[status(sab)],[57])).
% 0.21/0.51 tff(59,plain,
% 0.21/0.51 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.21/0.51 tff(60,plain,
% 0.21/0.51 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(61,plain,
% 0.21/0.51 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(62,plain,
% 0.21/0.51 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.51 tff(63,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[62, 59, 52, 41])).
% 0.21/0.51 tff(64,plain,(~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(65,plain,
% 0.21/0.51 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(66,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.51 tff(67,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(68,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.21/0.51 tff(69,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.51 tff(70,plain,(
% 0.21/0.51 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[69])).
% 0.21/0.51 tff(71,plain,
% 0.21/0.51 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.21/0.51 tff(72,plain,
% 0.21/0.51 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(73,plain,
% 0.21/0.51 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(74,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.52 tff(75,plain,
% 0.21/0.52 ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.21/0.52 tff(76,plain,
% 0.21/0.52 (~ap_parcontractE_c3(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[75, 64])).
% 0.21/0.52 tff(77,assumption,(comb_app(combS, p) = comb_app(combK, r)), introduced(assumption)).
% 0.21/0.52 tff(78,plain,
% 0.21/0.52 ((combS = combK) <=> (combK = combS)),
% 0.21/0.52 inference(commutativity,[status(thm)],[])).
% 0.21/0.52 tff(79,plain,
% 0.21/0.52 ((combK = combS) <=> (combS = combK)),
% 0.21/0.52 inference(symmetry,[status(thm)],[78])).
% 0.21/0.52 tff(80,plain,
% 0.21/0.52 ((~(combK = combS)) <=> (~(combS = combK))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[79])).
% 0.21/0.52 tff(81,plain,
% 0.21/0.52 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(82,axiom,(~(combK = combS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_s')).
% 0.21/0.52 tff(83,plain,
% 0.21/0.52 (~(combK = combS)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.52 tff(84,plain,
% 0.21/0.52 (~(combS = combK)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.21/0.52 tff(85,plain,
% 0.21/0.52 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = 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, p) = comb_app(combK, r))) | (combS = combK))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(86,plain,
% 0.21/0.52 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(combK, r))) | (combS = combK))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(87,plain,
% 0.21/0.52 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(combK, r))) | (combS = combK)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.52 tff(88,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[87, 59, 84, 77])).
% 0.21/0.52 tff(89,plain,(~(comb_app(combS, p) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(90,assumption,(ap_parcontractE_c2(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.52 tff(91,plain,
% 0.21/0.52 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(92,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.52 tff(93,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(94,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.21/0.52 tff(95,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.52 tff(96,plain,(
% 0.21/0.52 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[95])).
% 0.21/0.52 tff(97,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.21/0.52 tff(98,plain,
% 0.21/0.52 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(99,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(100,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.52 tff(101,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[100, 97, 90, 89])).
% 0.21/0.52 tff(102,plain,(~ap_parcontractE_c2(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.52 tff(103,plain,
% 0.21/0.52 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract) <=> member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(104,axiom,(member(pair(comb_app(comb_app(combS, p), q), r), parcontract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s2_parcontractD_h1')).
% 0.21/0.52 tff(105,plain,
% 0.21/0.52 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.52 tff(106,plain,
% 0.21/0.52 (^[R: $i, Q: $i, P: $i] : refl((ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(107,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.52 tff(108,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(109,plain,
% 0.21/0.52 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) <=> (ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> ((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)))), rewrite(((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)))), rewrite(((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(110,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.52 tff(111,axiom,(![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.21/0.52 tff(112,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.52 tff(113,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.52 tff(114,plain,(
% 0.21/0.52 ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[113])).
% 0.21/0.52 tff(115,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.21/0.52 tff(116,plain,
% 0.21/0.52 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(117,plain,
% 0.21/0.52 ((ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract))) <=> ((~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(118,plain,
% 0.21/0.52 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.52 tff(119,plain,
% 0.21/0.52 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.52 tff(120,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(121,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.52 tff(122,plain,
% 0.21/0.52 (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[121, 115, 105])).
% 0.21/0.52 tff(123,plain,
% 0.21/0.52 (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[122, 102])).
% 0.21/0.52 tff(124,plain,
% 0.21/0.52 (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[123, 76])).
% 0.21/0.52 tff(125,plain,
% 0.21/0.52 (ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[124, 40])).
% 0.21/0.52 tff(126,plain,
% 0.21/0.52 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(127,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.52 tff(128,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(129,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.21/0.52 tff(130,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.52 tff(131,plain,(
% 0.21/0.52 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.52 inference(skolemize,[status(sab)],[130])).
% 0.21/0.52 tff(132,plain,
% 0.21/0.52 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.21/0.52 tff(133,plain,
% 0.21/0.52 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(134,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(135,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.52 tff(136,plain,
% 0.21/0.52 ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.21/0.52 tff(137,plain,
% 0.21/0.52 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[136, 125])).
% 0.21/0.52 tff(138,plain,
% 0.21/0.52 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = r),
% 0.21/0.52 inference(symmetry,[status(thm)],[137])).
% 0.21/0.52 tff(139,plain,
% 0.21/0.52 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) <=> ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (ap_parcontractE_c4(comb_app(combS, p), q, r) <=> ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.52 inference(symmetry,[status(thm)],[139])).
% 0.21/0.52 tff(141,plain,
% 0.21/0.52 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[125, 140])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) = ap_parcontractE_sk2s(comb_app(combS, p), q, r)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) = pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.52 tff(144,plain,
% 0.21/0.52 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.21/0.52 inference(symmetry,[status(thm)],[144])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) <=> (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[145])).
% 0.21/0.52 tff(147,assumption,(ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.52 tff(148,assumption,(~member(comb_app(combS, p), comb)), introduced(assumption)).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(151,plain,
% 0.21/0.52 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[151, 34, 148, 147])).
% 0.21/0.52 tff(153,plain,((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(154,plain,
% 0.21/0.53 (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[153, 13])).
% 0.21/0.53 tff(155,plain,
% 0.21/0.53 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(156,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.53 tff(157,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(158,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.21/0.53 tff(159,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.53 tff(160,plain,(
% 0.21/0.53 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.53 inference(skolemize,[status(sab)],[159])).
% 0.21/0.53 tff(161,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.21/0.53 tff(162,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(163,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(164,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.53 tff(165,plain,
% 0.21/0.53 ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[164, 161])).
% 0.21/0.53 tff(166,plain,
% 0.21/0.53 (member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[165, 125])).
% 0.21/0.53 tff(167,assumption,(~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.53 tff(168,assumption,(~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.53 tff(169,assumption,(ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.53 tff(170,plain,
% 0.21/0.53 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(171,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.53 tff(172,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(173,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE5')).
% 0.21/0.53 tff(174,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.53 tff(175,plain,(
% 0.21/0.53 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(skolemize,[status(sab)],[174])).
% 0.21/0.53 tff(176,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.21/0.53 tff(177,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(178,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(179,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.53 tff(180,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[179, 176, 1, 169])).
% 0.21/0.53 tff(181,plain,((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(182,plain,
% 0.21/0.53 (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[181, 1])).
% 0.21/0.53 tff(183,assumption,(member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)), introduced(assumption)).
% 0.21/0.53 tff(184,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(185,plain,
% 0.21/0.53 ((ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))) <=> ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(186,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[185])).
% 0.21/0.53 tff(187,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[186, 184])).
% 0.21/0.53 tff(188,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(189,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.21/0.53 tff(190,plain,
% 0.21/0.53 (ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[189, 115, 183])).
% 0.21/0.53 tff(191,plain,
% 0.21/0.53 (ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[190, 182, 168, 167])).
% 0.21/0.53 tff(192,plain,
% 0.21/0.53 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(193,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.53 tff(194,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(195,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE9')).
% 0.21/0.53 tff(196,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.53 tff(197,plain,(
% 0.21/0.53 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(skolemize,[status(sab)],[196])).
% 0.21/0.53 tff(198,plain,
% 0.21/0.53 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.21/0.53 tff(199,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(200,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(201,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.21/0.53 tff(202,plain,
% 0.21/0.53 ($false),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[201, 198, 1, 191])).
% 0.21/0.53 tff(203,plain,(member(p, comb) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.53 tff(204,plain,
% 0.21/0.53 (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[203, 166, 1, 154])).
% 0.21/0.53 tff(205,assumption,(ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.53 tff(206,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(207,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(208,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.21/0.53 tff(209,plain,
% 0.21/0.53 (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[208, 132, 205])).
% 0.21/0.53 tff(210,plain,
% 0.21/0.53 (comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.21/0.53 inference(symmetry,[status(thm)],[209])).
% 0.21/0.53 tff(211,plain,
% 0.21/0.53 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(212,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(213,plain,
% 0.21/0.53 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.21/0.54 tff(214,plain,
% 0.21/0.54 (member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[213, 161, 205])).
% 0.21/0.54 tff(215,plain,
% 0.21/0.54 (^[R: $i] : refl(((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ((~member(pair(combS, R), parcontract)) | (R = combS)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(216,plain,
% 0.21/0.54 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[215])).
% 0.21/0.54 tff(217,plain,
% 0.21/0.54 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(218,axiom,(![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_parcontractE2')).
% 0.21/0.54 tff(219,plain,
% 0.21/0.54 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.21/0.54 tff(220,plain,(
% 0.21/0.54 ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.54 inference(skolemize,[status(sab)],[219])).
% 0.21/0.54 tff(221,plain,
% 0.21/0.54 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.21/0.54 tff(222,plain,
% 0.21/0.54 (((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))) <=> ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(223,plain,
% 0.21/0.54 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(224,plain,
% 0.21/0.54 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.54 tff(225,plain,
% 0.21/0.54 (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[224, 221, 214])).
% 0.21/0.54 tff(226,plain,
% 0.21/0.54 (combS = ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.54 inference(symmetry,[status(thm)],[225])).
% 0.21/0.54 tff(227,plain,
% 0.21/0.54 (comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[226])).
% 0.21/0.54 tff(228,plain,
% 0.21/0.54 (comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.21/0.54 inference(transitivity,[status(thm)],[227, 210])).
% 0.21/0.54 tff(229,plain,
% 0.21/0.54 (comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[228])).
% 0.21/0.54 tff(230,plain,
% 0.21/0.54 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.54 inference(symmetry,[status(thm)],[229])).
% 0.21/0.54 tff(231,assumption,(r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.54 tff(232,plain,
% 0.21/0.54 (r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.54 inference(transitivity,[status(thm)],[231, 230])).
% 0.21/0.54 tff(233,plain,
% 0.21/0.54 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(234,plain,
% 0.21/0.54 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[233])).
% 0.21/0.54 tff(235,plain,
% 0.21/0.54 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(236,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.21/0.54 tff(237,plain,
% 0.21/0.54 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.21/0.54 tff(238,plain,(
% 0.21/0.54 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.54 inference(skolemize,[status(sab)],[237])).
% 0.21/0.54 tff(239,plain,
% 0.21/0.54 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[238, 234])).
% 0.21/0.54 tff(240,plain,
% 0.21/0.54 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(241,plain,
% 0.21/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(242,plain,
% 0.21/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.21/0.54 tff(243,plain,
% 0.21/0.54 (member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[242, 239, 205])).
% 0.21/0.54 tff(244,assumption,(member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)), introduced(assumption)).
% 0.21/0.54 tff(245,plain,
% 0.21/0.54 (^[QP: $i, PP: $i] : refl(((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(246,plain,
% 0.21/0.54 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[245])).
% 0.21/0.54 tff(247,plain,
% 0.21/0.54 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(248,plain,
% 0.21/0.54 (^[QP: $i, PP: $i] : trans(monotonicity(rewrite(((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) <=> ((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))), ((((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> (((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) | (~member(pair(q, QP), parcontract))))), rewrite((((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) | (~member(pair(q, QP), parcontract))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))), ((((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(249,plain,
% 0.21/0.54 (![QP: $i, PP: $i] : (((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[248])).
% 0.21/0.54 tff(250,axiom,(![QP: $i, PP: $i] : (((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s2_parcontractD_c1')).
% 0.21/0.54 tff(251,plain,
% 0.21/0.54 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.21/0.54 tff(252,plain,
% 0.21/0.54 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.21/0.54 tff(253,plain,(
% 0.21/0.54 ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.54 inference(skolemize,[status(sab)],[252])).
% 0.21/0.54 tff(254,plain,
% 0.21/0.54 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.21/0.54 tff(255,plain,
% 0.21/0.54 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(256,plain,
% 0.21/0.54 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(257,plain,
% 0.21/0.54 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.21/0.54 tff(258,plain,
% 0.21/0.54 (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[257, 254, 244, 243])).
% 0.21/0.54 tff(259,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[258, 232])).
% 0.21/0.54 tff(260,plain,((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (~(r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(261,plain,
% 0.21/0.54 (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[260, 204, 137])).
% 0.21/0.54 tff(262,plain,
% 0.21/0.54 (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[261, 146])).
% 0.21/0.54 tff(263,plain,
% 0.21/0.54 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(264,plain,
% 0.21/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(265,plain,
% 0.21/0.54 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.21/0.54 tff(266,plain,
% 0.21/0.54 ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[265, 239])).
% 0.21/0.54 tff(267,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[266, 262, 141])).
% 0.21/0.54 tff(268,plain,(member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(269,plain,
% 0.21/0.54 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(270,plain,
% 0.21/0.54 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[269])).
% 0.21/0.54 tff(271,plain,
% 0.21/0.54 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(272,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.21/0.54 tff(273,plain,
% 0.21/0.54 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.21/0.54 tff(274,plain,(
% 0.21/0.54 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.54 inference(skolemize,[status(sab)],[273])).
% 0.21/0.54 tff(275,plain,
% 0.21/0.54 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.21/0.54 tff(276,plain,
% 0.21/0.54 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(277,plain,
% 0.21/0.54 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(278,plain,
% 0.21/0.54 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.21/0.54 tff(279,plain,
% 0.21/0.54 (member(pair(p, p), parcontract)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[278, 275, 268])).
% 0.21/0.54 tff(280,assumption,(ap_parcontractE_c4(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.54 tff(281,plain,
% 0.21/0.54 (member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[165, 280])).
% 0.21/0.54 tff(282,assumption,(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.54 tff(283,plain,
% 0.21/0.54 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(284,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[283, 49, 282])).
% 0.21/0.54 tff(285,plain,(~(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(286,plain,
% 0.21/0.55 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(287,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(288,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.21/0.55 tff(289,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[288, 97, 169, 285])).
% 0.21/0.55 tff(290,plain,(~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(291,plain,
% 0.21/0.55 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[136, 280])).
% 0.21/0.55 tff(292,plain,
% 0.21/0.55 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = r),
% 0.21/0.55 inference(symmetry,[status(thm)],[291])).
% 0.21/0.55 tff(293,plain,
% 0.21/0.55 (ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) = ap_parcontractE_sk2s(comb_app(combS, p), q, r)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[292])).
% 0.21/0.55 tff(294,plain,
% 0.21/0.55 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) = pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[293])).
% 0.21/0.55 tff(295,plain,
% 0.21/0.55 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[294])).
% 0.21/0.55 tff(296,plain,
% 0.21/0.55 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) <=> ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[292])).
% 0.21/0.55 tff(297,plain,
% 0.21/0.55 (ap_parcontractE_c4(comb_app(combS, p), q, r) <=> ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.55 inference(symmetry,[status(thm)],[296])).
% 0.21/0.55 tff(298,plain,
% 0.21/0.55 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[280, 297])).
% 0.21/0.55 tff(299,plain,
% 0.21/0.55 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[266, 298])).
% 0.21/0.55 tff(300,plain,
% 0.21/0.55 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[299, 295])).
% 0.21/0.55 tff(301,plain,
% 0.21/0.55 (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[260, 300, 291])).
% 0.21/0.55 tff(302,assumption,(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))), introduced(assumption)).
% 0.21/0.55 tff(303,plain,
% 0.21/0.55 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(304,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[303, 49, 302])).
% 0.21/0.55 tff(305,plain,(~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(306,plain,
% 0.21/0.55 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(307,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(308,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.21/0.55 tff(309,plain,
% 0.21/0.55 (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[308, 71, 305])).
% 0.21/0.55 tff(310,plain,
% 0.21/0.55 ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[189, 115, 309])).
% 0.21/0.55 tff(311,plain,
% 0.21/0.55 (ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[310, 301, 290, 281])).
% 0.21/0.55 tff(312,plain,
% 0.21/0.55 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(313,plain,
% 0.21/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[312])).
% 0.21/0.55 tff(314,plain,
% 0.21/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(315,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.21/0.55 tff(316,plain,
% 0.21/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.21/0.55 tff(317,plain,(
% 0.21/0.55 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[316])).
% 0.21/0.55 tff(318,plain,
% 0.21/0.55 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[317, 313])).
% 0.21/0.55 tff(319,plain,
% 0.21/0.55 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(320,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(321,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.21/0.55 tff(322,plain,
% 0.21/0.55 (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[321, 318, 311])).
% 0.21/0.55 tff(323,plain,
% 0.21/0.55 (comb_app(combS, p) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.21/0.55 inference(symmetry,[status(thm)],[322])).
% 0.21/0.55 tff(324,plain,
% 0.21/0.55 (comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[323])).
% 0.21/0.55 tff(325,plain,
% 0.21/0.55 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(symmetry,[status(thm)],[324])).
% 0.21/0.55 tff(326,plain,
% 0.21/0.55 (r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.21/0.55 inference(transitivity,[status(thm)],[291, 325])).
% 0.21/0.55 tff(327,plain,
% 0.21/0.55 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(328,plain,
% 0.21/0.55 (((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))) <=> ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(329,plain,
% 0.21/0.55 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[328])).
% 0.21/0.55 tff(330,plain,
% 0.21/0.55 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.55 inference(transitivity,[status(thm)],[329, 327])).
% 0.21/0.55 tff(331,plain,
% 0.21/0.55 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(332,plain,
% 0.21/0.55 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.21/0.55 tff(333,plain,
% 0.21/0.55 (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[332, 254, 279, 300])).
% 0.21/0.55 tff(334,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[333, 326])).
% 0.21/0.55 tff(335,plain,(~ap_parcontractE_c4(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(336,plain,
% 0.21/0.55 (ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[124, 335])).
% 0.21/0.55 tff(337,plain,
% 0.21/0.55 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(338,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(339,plain,
% 0.21/0.55 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.21/0.55 tff(340,plain,
% 0.21/0.55 (r = comb_app(comb_app(combS, p), q)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[339, 318, 336])).
% 0.21/0.56 tff(341,plain,
% 0.21/0.56 (member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[39, 336])).
% 0.21/0.56 tff(342,plain,
% 0.21/0.56 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(343,plain,
% 0.21/0.56 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(344,plain,
% 0.21/0.56 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.21/0.56 tff(345,plain,
% 0.21/0.56 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[344, 8])).
% 0.21/0.56 tff(346,plain,
% 0.21/0.56 (member(q, comb)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[345, 341])).
% 0.21/0.56 tff(347,plain,
% 0.21/0.56 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(q, comb)) | member(pair(q, q), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(q, comb)) | member(pair(q, q), parcontract))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(348,plain,
% 0.21/0.56 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(q, comb)) | member(pair(q, q), parcontract))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(349,plain,
% 0.21/0.56 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(q, comb)) | member(pair(q, q), parcontract)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.21/0.56 tff(350,plain,
% 0.21/0.56 (member(pair(q, q), parcontract)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[349, 275, 346])).
% 0.21/0.56 tff(351,plain,
% 0.21/0.56 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(352,plain,
% 0.21/0.56 (((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))) <=> ((~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(353,plain,
% 0.21/0.56 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[352])).
% 0.21/0.56 tff(354,plain,
% 0.21/0.56 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[353, 351])).
% 0.21/0.56 tff(355,plain,
% 0.21/0.56 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(356,plain,
% 0.21/0.56 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.21/0.56 tff(357,plain,
% 0.21/0.56 ((~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[356, 254])).
% 0.21/0.56 tff(358,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[357, 350, 340, 279])).
% 0.21/0.56 % SZS output end Proof
% 0.21/0.56 % E exiting
%------------------------------------------------------------------------------