%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL094-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:47 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COL094-1 : TPTP v9.0.0. Released v2.7.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:15:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(comb_app_type, type, (
% 0.19/0.41 comb_app: ( $i * $i ) > $i)).
% 0.19/0.41 tff(ap_parcontractE_sk2q_type, type, (
% 0.19/0.41 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(r_type, type, (
% 0.19/0.41 r: $i)).
% 0.19/0.41 tff(q_type, type, (
% 0.19/0.41 q: $i)).
% 0.19/0.41 tff(p_type, type, (
% 0.19/0.41 p: $i)).
% 0.19/0.41 tff(combS_type, type, (
% 0.19/0.41 combS: $i)).
% 0.19/0.41 tff(combK_type, type, (
% 0.19/0.41 combK: $i)).
% 0.19/0.41 tff(ap_parcontractE_c2_type, type, (
% 0.19/0.41 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(ap_parcontractE_c1_type, type, (
% 0.19/0.41 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(ap_parcontractE_sk2s_type, type, (
% 0.19/0.41 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(ap_parcontractE_c4_type, type, (
% 0.19/0.41 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(member_type, type, (
% 0.19/0.41 member: ( $i * $i ) > $o)).
% 0.19/0.41 tff(comb_type, type, (
% 0.19/0.41 comb: $i)).
% 0.19/0.41 tff(parcontract_type, type, (
% 0.19/0.41 parcontract: $i)).
% 0.19/0.41 tff(pair_type, type, (
% 0.19/0.41 pair: ( $i * $i ) > $i)).
% 0.19/0.41 tff(ap_parcontractE_c3_type, type, (
% 0.19/0.41 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(ap_parcontractE_sk1q_type, type, (
% 0.19/0.41 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(ap_parcontractE_sk1p_type, type, (
% 0.19/0.41 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.19/0.41 tff(1,assumption,(comb_app(combS, p) = comb_app(combK, r)), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (comb_app(combK, r) = comb_app(combS, p)),
% 0.19/0.41 inference(symmetry,[status(thm)],[1])).
% 0.19/0.41 tff(3,assumption,(comb_app(combK, r) = comb_app(combS, p)), introduced(assumption)).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(7,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','app_app1')).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.41 tff(9,plain,(
% 0.19/0.41 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.19/0.41 inference(skolemize,[status(sab)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(12,axiom,(~(combK = combS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_s')).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (~(combK = combS)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, p))) | (combK = combS)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[16, 13, 10, 3])).
% 0.19/0.41 tff(18,plain,(~(comb_app(combK, r) = comb_app(combS, p))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[18, 2])).
% 0.19/0.41 tff(20,plain,(~(comb_app(combS, p) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(21,assumption,(ap_parcontractE_c2(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(25,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,(
% 0.19/0.41 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (((~![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 ((~![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)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[31, 28, 21, 20])).
% 0.19/0.41 tff(33,plain,(~ap_parcontractE_c2(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(34,assumption,(ap_parcontractE_c1(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(38,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE2')).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.41 tff(40,plain,(
% 0.19/0.41 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.19/0.41 inference(skolemize,[status(sab)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![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))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~![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)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (member(comb_app(comb_app(combS, p), q), comb)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 41, 34])).
% 0.19/0.41 tff(46,assumption,(~member(p, comb)), introduced(assumption)).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(Q, comb)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(50,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E2')).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.41 tff(52,plain,(
% 0.19/0.41 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.19/0.41 inference(skolemize,[status(sab)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 ((~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (~member(comb_app(combS, p), comb)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[57, 46])).
% 0.19/0.41 tff(59,assumption,(ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.41 tff(60,assumption,(~member(comb_app(combS, p), comb)), introduced(assumption)).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ((~![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))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[63, 41, 60, 59])).
% 0.19/0.41 tff(65,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,[]))).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 58])).
% 0.19/0.41 tff(67,assumption,(ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(71,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE9')).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.41 tff(73,plain,(
% 0.19/0.41 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.19/0.41 inference(skolemize,[status(sab)],[72])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ((~![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))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[77, 74, 46, 67])).
% 0.19/0.41 tff(79,plain,((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[79, 46])).
% 0.19/0.41 tff(81,assumption,(ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(85,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE5')).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,(
% 0.19/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.19/0.42 inference(skolemize,[status(sab)],[86])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~![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))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[91, 88, 46, 81])).
% 0.19/0.42 tff(93,plain,((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 46])).
% 0.19/0.42 tff(95,assumption,(ap_parcontractE_c4(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(99,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/sandbox/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.42 tff(101,plain,(
% 0.19/0.42 ![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))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[100])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 102, 95])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (ap_parcontractE_sk2s(comb_app(combS, p), q, r) = 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)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = 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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (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)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (^[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)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(113,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/sandbox/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.42 tff(115,plain,(
% 0.19/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.19/0.42 inference(skolemize,[status(sab)],[114])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (((~![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, r)) | member(pair(q, 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, r)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 ((~![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, r)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~![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, r)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[119, 116, 95])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (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)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[120, 109])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (^[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)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(125,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/sandbox/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.42 tff(127,plain,(
% 0.19/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.19/0.42 inference(skolemize,[status(sab)],[126])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (((~![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))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 ((~![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))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 ((~![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)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[131, 128, 95])).
% 0.19/0.43 tff(133,assumption,(~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.43 tff(134,assumption,(~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.43 tff(135,assumption,(~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 (^[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)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[139])).
% 0.19/0.43 tff(141,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/sandbox/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.19/0.43 tff(144,plain,(
% 0.19/0.43 ![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)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[143])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (![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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 (((~![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)))) | 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)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 ((~![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)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 ((~![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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[148, 145, 135, 134, 133, 132])).
% 0.19/0.43 tff(150,assumption,(r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = r),
% 0.19/0.43 inference(symmetry,[status(thm)],[150])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (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)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[151])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 (ap_parcontractE_sk2s(comb_app(combS, p), q, r) = 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)))),
% 0.19/0.43 inference(symmetry,[status(thm)],[152])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = 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))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (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)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (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)),
% 0.19/0.43 inference(symmetry,[status(thm)],[155])).
% 0.19/0.43 tff(157,assumption,(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)), introduced(assumption)).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.19/0.43 tff(159,assumption,(ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((~![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)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 ((~![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)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(162,plain,
% 0.19/0.44 ((~![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.44 tff(163,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[162, 102, 159])).
% 0.19/0.44 tff(164,plain,
% 0.19/0.44 (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)),
% 0.19/0.44 inference(symmetry,[status(thm)],[163])).
% 0.19/0.44 tff(165,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(167,plain,
% 0.19/0.44 ((~![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)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 (member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[167, 128, 159])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 (^[R: $i] : refl(((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ((~member(pair(combS, R), parcontract)) | (R = combS)))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[169])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(172,axiom,(![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_parcontractE2')).
% 0.19/0.44 tff(173,plain,
% 0.19/0.44 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.44 tff(174,plain,(
% 0.19/0.44 ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.44 inference(skolemize,[status(sab)],[173])).
% 0.19/0.44 tff(175,plain,
% 0.19/0.44 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.19/0.44 tff(176,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(177,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(178,plain,
% 0.19/0.44 ((~![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)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.19/0.44 tff(179,plain,
% 0.19/0.44 (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[178, 175, 168])).
% 0.19/0.44 tff(180,plain,
% 0.19/0.44 (combS = ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.44 inference(symmetry,[status(thm)],[179])).
% 0.19/0.44 tff(181,plain,
% 0.19/0.44 (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)))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[180])).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 (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)),
% 0.19/0.44 inference(transitivity,[status(thm)],[181, 164])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 (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))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[182])).
% 0.19/0.44 tff(184,plain,
% 0.19/0.44 (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))),
% 0.19/0.44 inference(symmetry,[status(thm)],[183])).
% 0.19/0.44 tff(185,plain,
% 0.19/0.44 (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))),
% 0.19/0.44 inference(transitivity,[status(thm)],[150, 184])).
% 0.19/0.44 tff(186,plain,
% 0.19/0.44 (((~![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))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(187,plain,
% 0.19/0.44 ((~![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))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 ((~![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)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 (member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[188, 116, 159])).
% 0.19/0.44 tff(190,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(191,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[190])).
% 0.19/0.44 tff(192,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(193,plain,
% 0.19/0.44 (^[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))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(194,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.45 tff(195,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/sandbox/benchmark/theBenchmark.p','s2_parcontractD_c1')).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.19/0.45 tff(198,plain,(
% 0.19/0.45 ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[197])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (((~![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)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 ((~![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)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.45 tff(203,plain,
% 0.19/0.45 ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[202, 199, 189])).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[203, 185, 158])).
% 0.19/0.45 tff(205,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, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(206,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[205, 149, 121, 106])).
% 0.19/0.45 tff(207,plain,((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | ap_parcontractE_c2(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_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(208,plain,
% 0.19/0.45 (~ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[207, 94, 80, 66])).
% 0.19/0.45 tff(209,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)).
% 0.19/0.45 tff(210,assumption,(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.19/0.45 tff(211,plain,
% 0.19/0.45 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(212,plain,
% 0.19/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.45 tff(213,plain,
% 0.19/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(214,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_app')).
% 0.19/0.45 tff(215,plain,
% 0.19/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.19/0.45 tff(216,plain,(
% 0.19/0.45 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[215])).
% 0.19/0.45 tff(217,plain,
% 0.19/0.45 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.19/0.45 tff(218,plain,
% 0.19/0.45 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(219,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[218, 217, 210])).
% 0.19/0.45 tff(220,plain,(~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(221,plain,
% 0.19/0.45 (((~![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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(222,plain,
% 0.19/0.45 ((~![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))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(223,plain,
% 0.19/0.45 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.19/0.45 tff(224,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[223, 10, 220, 209])).
% 0.19/0.45 tff(225,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,[]))).
% 0.19/0.45 tff(226,plain,
% 0.19/0.45 (^[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)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(227,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.45 tff(228,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(229,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/sandbox/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.19/0.45 tff(230,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.19/0.45 tff(231,plain,(
% 0.19/0.45 ![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))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[230])).
% 0.19/0.45 tff(232,plain,
% 0.19/0.45 (![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))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.19/0.45 tff(233,plain,
% 0.19/0.45 (((~![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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(234,plain,
% 0.19/0.45 ((~![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))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(235,plain,
% 0.19/0.45 ((~![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)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.45 tff(236,plain,
% 0.19/0.46 ((~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)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[235, 232])).
% 0.19/0.46 tff(237,plain,
% 0.19/0.46 (~ap_parcontractE_c3(comb_app(combS, p), q, r)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[236, 225])).
% 0.19/0.46 tff(238,plain,
% 0.19/0.46 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract) <=> member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(239,axiom,(member(pair(comb_app(comb_app(combS, p), q), r), parcontract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s2_parcontractD_h1')).
% 0.19/0.46 tff(240,plain,
% 0.19/0.46 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.46 tff(241,plain,
% 0.19/0.46 (((~![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)))) | 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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 ((~![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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(243,plain,
% 0.19/0.46 ((~![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))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.46 tff(244,plain,
% 0.19/0.46 (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)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[243, 145, 240])).
% 0.19/0.46 tff(245,plain,
% 0.19/0.46 (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[244, 237])).
% 0.19/0.46 tff(246,plain,
% 0.19/0.46 (ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[245, 208, 33])).
% 0.19/0.46 tff(247,plain,
% 0.19/0.46 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(P, comb)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(248,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[247])).
% 0.19/0.46 tff(249,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(250,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E1')).
% 0.19/0.46 tff(251,plain,
% 0.19/0.46 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.19/0.46 tff(252,plain,(
% 0.19/0.46 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.19/0.46 inference(skolemize,[status(sab)],[251])).
% 0.19/0.46 tff(253,plain,
% 0.19/0.46 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.19/0.46 tff(254,plain,
% 0.19/0.46 (((~![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(255,plain,
% 0.19/0.46 ((~![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))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(256,plain,
% 0.19/0.46 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.19/0.46 tff(257,plain,
% 0.19/0.46 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[256, 253])).
% 0.19/0.46 tff(258,plain,
% 0.19/0.46 (~member(comb_app(comb_app(combS, p), q), comb)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[257, 58])).
% 0.19/0.46 tff(259,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[44, 41, 258, 246])).
% 0.19/0.46 tff(260,plain,(member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(261,plain,
% 0.19/0.46 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(262,plain,
% 0.19/0.46 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[261])).
% 0.19/0.46 tff(263,plain,
% 0.19/0.46 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(264,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.19/0.46 tff(265,plain,
% 0.19/0.46 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.19/0.46 tff(266,plain,(
% 0.19/0.46 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.46 inference(skolemize,[status(sab)],[265])).
% 0.19/0.46 tff(267,plain,
% 0.19/0.46 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.19/0.46 tff(268,plain,
% 0.19/0.46 (((~![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(269,plain,
% 0.19/0.46 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(270,plain,
% 0.19/0.46 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.19/0.46 tff(271,plain,
% 0.19/0.46 (member(pair(p, p), parcontract)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[270, 267, 260])).
% 0.19/0.46 tff(272,assumption,(~(r = comb_app(comb_app(combS, p), q))), introduced(assumption)).
% 0.19/0.46 tff(273,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(274,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[273])).
% 0.19/0.46 tff(275,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(276,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.19/0.46 tff(277,plain,
% 0.19/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.19/0.46 tff(278,plain,(
% 0.19/0.46 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[277])).
% 0.19/0.46 tff(279,plain,
% 0.19/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[278, 274])).
% 0.19/0.46 tff(280,plain,
% 0.19/0.46 (((~![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(281,plain,
% 0.19/0.46 ((~![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)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(282,plain,
% 0.19/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.46 tff(283,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[282, 279, 272, 34])).
% 0.19/0.46 tff(284,plain,((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(285,plain,
% 0.19/0.46 (r = comb_app(comb_app(combS, p), q)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[284, 34])).
% 0.19/0.46 tff(286,plain,
% 0.19/0.46 (((~![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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(287,plain,
% 0.19/0.46 (((~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))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(288,plain,
% 0.19/0.46 (((~![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)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[287])).
% 0.19/0.46 tff(289,plain,
% 0.19/0.46 (((~![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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[288, 286])).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 ((~![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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.19/0.47 tff(292,plain,
% 0.19/0.47 ((~member(pair(p, p), parcontract)) | (~member(pair(q, q), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[291, 199])).
% 0.19/0.47 tff(293,plain,
% 0.19/0.47 (~member(pair(q, q), parcontract)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[292, 285, 271])).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 (((~![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(295,plain,
% 0.19/0.47 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(q, comb)) | member(pair(q, q), parcontract))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(296,plain,
% 0.19/0.47 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(q, comb)) | member(pair(q, q), parcontract)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.19/0.47 tff(297,plain,
% 0.19/0.47 (~member(q, comb)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[296, 267, 293])).
% 0.19/0.47 tff(298,plain,
% 0.19/0.47 (((~![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 ((~![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))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(300,plain,
% 0.19/0.47 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.19/0.47 tff(301,plain,
% 0.19/0.47 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[300, 53])).
% 0.19/0.47 tff(302,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[301, 297, 45])).
% 0.19/0.47 tff(303,plain,(~ap_parcontractE_c1(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(304,plain,
% 0.19/0.47 (ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[245, 303, 33])).
% 0.19/0.47 tff(305,plain,
% 0.19/0.47 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[105, 102, 304])).
% 0.19/0.47 tff(306,plain,
% 0.19/0.47 (ap_parcontractE_sk2s(comb_app(combS, p), q, r) = 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)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[305])).
% 0.19/0.47 tff(307,plain,
% 0.19/0.47 (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)),
% 0.19/0.47 inference(symmetry,[status(thm)],[306])).
% 0.19/0.47 tff(308,assumption,(ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)), introduced(assumption)).
% 0.19/0.47 tff(309,plain,
% 0.19/0.47 (comb_app(combS, p) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.19/0.47 inference(symmetry,[status(thm)],[308])).
% 0.19/0.47 tff(310,plain,
% 0.19/0.47 (comb_app(comb_app(combS, p), 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)))) = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[309, 307])).
% 0.19/0.47 tff(311,plain,
% 0.19/0.47 (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, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.19/0.47 inference(symmetry,[status(thm)],[310])).
% 0.19/0.47 tff(312,plain,
% 0.19/0.47 (r = comb_app(comb_app(combS, p), 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))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[305, 311])).
% 0.19/0.47 tff(313,plain,
% 0.19/0.47 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = 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))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[306])).
% 0.19/0.47 tff(314,plain,
% 0.19/0.47 (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)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[313])).
% 0.19/0.47 tff(315,plain,
% 0.19/0.47 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[119, 116, 304])).
% 0.19/0.47 tff(316,plain,
% 0.19/0.47 (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)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.19/0.47 tff(317,plain,
% 0.19/0.47 (((~![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, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), 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, comb_app(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(p, p), 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)) | (~(r = comb_app(comb_app(combS, p), 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)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(318,plain,
% 0.19/0.47 (((~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(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), 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))))))) <=> ((~member(pair(p, p), 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)) | (~(r = comb_app(comb_app(combS, p), 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)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(319,plain,
% 0.19/0.47 (((~![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, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), 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, comb_app(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(p, p), 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)) | (~(r = comb_app(comb_app(combS, p), 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))))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[318])).
% 0.19/0.47 tff(320,plain,
% 0.19/0.47 (((~![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, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), 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, comb_app(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(p, p), 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)) | (~(r = comb_app(comb_app(combS, p), 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)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[319, 317])).
% 0.19/0.47 tff(321,plain,
% 0.19/0.47 ((~![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, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), 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, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(322,plain,
% 0.19/0.47 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.19/0.48 tff(323,plain,
% 0.19/0.48 (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[322, 199, 271, 316])).
% 0.19/0.48 tff(324,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[323, 312])).
% 0.19/0.48 tff(325,plain,(~(ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(326,plain,
% 0.19/0.48 (((~![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)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(327,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(328,plain,
% 0.19/0.48 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.19/0.48 tff(329,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[328, 279, 59, 325])).
% 0.19/0.48 tff(330,plain,(~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(331,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)).
% 0.19/0.48 tff(332,plain,
% 0.19/0.48 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(333,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[332, 217, 331])).
% 0.19/0.48 tff(334,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,[]))).
% 0.19/0.48 tff(335,plain,
% 0.19/0.48 (((~![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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(336,plain,
% 0.19/0.48 ((~![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)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(337,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.19/0.48 tff(338,plain,
% 0.19/0.48 (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[337, 232, 334])).
% 0.19/0.48 tff(339,plain,
% 0.19/0.48 (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[205, 316, 305])).
% 0.19/0.48 tff(340,plain,
% 0.19/0.48 (member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[131, 128, 304])).
% 0.19/0.48 tff(341,plain,
% 0.19/0.48 (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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[148, 145, 340])).
% 0.19/0.48 tff(342,plain,
% 0.19/0.48 (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))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[341, 339])).
% 0.19/0.48 tff(343,plain,
% 0.19/0.48 (ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[342, 338, 330])).
% 0.19/0.48 tff(344,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(345,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(346,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.19/0.48 tff(347,plain,
% 0.19/0.48 (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[346, 28, 343])).
% 0.19/0.48 tff(348,plain,
% 0.19/0.48 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(349,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[348, 217, 347])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------