%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL092-2 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL092-2 : TPTP v9.0.0. Released v2.7.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 12:15:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(comb_app_type, type, (
% 0.20/0.43 comb_app: ( $i * $i ) > $i)).
% 0.20/0.43 tff(ap_parcontractE_sk1q_type, type, (
% 0.20/0.43 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(r_type, type, (
% 0.20/0.43 r: $i)).
% 0.20/0.43 tff(p_type, type, (
% 0.20/0.43 p: $i)).
% 0.20/0.43 tff(combK_type, type, (
% 0.20/0.43 combK: $i)).
% 0.20/0.43 tff(ap_parcontractE_sk1p_type, type, (
% 0.20/0.43 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(combS_type, type, (
% 0.20/0.43 combS: $i)).
% 0.20/0.43 tff(ap_parcontractE_c3_type, type, (
% 0.20/0.43 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(ap_parcontractE_c2_type, type, (
% 0.20/0.43 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(ap_parcontractE_c4_type, type, (
% 0.20/0.43 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(ap_parcontractE_sk2s_type, type, (
% 0.20/0.43 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(ap_parcontractE_sk2q_type, type, (
% 0.20/0.43 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(member_type, type, (
% 0.20/0.43 member: ( $i * $i ) > $o)).
% 0.20/0.43 tff(parcontract_type, type, (
% 0.20/0.43 parcontract: $i)).
% 0.20/0.43 tff(pair_type, type, (
% 0.20/0.43 pair: ( $i * $i ) > $i)).
% 0.20/0.43 tff(ap_parcontractE_c1_type, type, (
% 0.20/0.43 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(comb_type, type, (
% 0.20/0.43 comb: $i)).
% 0.20/0.43 tff(1,assumption,(combK = comb_app(combK, r)), introduced(assumption)).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (comb_app(combK, r) = combK),
% 0.20/0.43 inference(symmetry,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (comb_app(comb_app(combK, r), r) = comb_app(combK, r)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (comb_app(combK, r) = comb_app(comb_app(combK, r), r)),
% 0.20/0.43 inference(symmetry,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (combK = comb_app(comb_app(combK, r), r)),
% 0.20/0.43 inference(transitivity,[status(thm)],[1, 4])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (^[Q: $i, P: $i] : refl((~(combK = comb_app(P, Q))) <=> (~(combK = comb_app(P, Q))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(9,axiom,(![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_app')).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.43 tff(11,plain,(
% 0.20/0.43 ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[10])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combK, r), r)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (~(combK = comb_app(comb_app(combK, r), r))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[14, 5])).
% 0.20/0.43 tff(16,plain,(~(combK = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(17,assumption,(ap_parcontractE_c2(combK, p, r)), introduced(assumption)).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,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')).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.43 tff(23,plain,(
% 0.20/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[22])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[27, 24, 17, 16])).
% 0.20/0.43 tff(29,plain,(~ap_parcontractE_c2(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(30,assumption,(ap_parcontractE_c4(combK, p, r)), introduced(assumption)).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(34,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')).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.43 tff(36,plain,(
% 0.20/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.20/0.43 inference(skolemize,[status(sab)],[35])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (((~![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(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, 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(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ((~![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(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 ((~![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(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[40, 37, 30])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (^[R: $i] : refl(((~member(pair(combK, R), parcontract)) | (R = combK)) <=> ((~member(pair(combK, R), parcontract)) | (R = combK)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK)) <=> ![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK)) <=> ![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(45,axiom,(![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_parcontractE2')).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.43 tff(47,plain,(
% 0.20/0.43 ![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.20/0.43 inference(skolemize,[status(sab)],[46])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | ((~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK))) <=> ((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | (~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 ((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | ((~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | (~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (ap_parcontractE_sk2q(combK, p, r) = combK),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[51, 48, 41])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (combK = ap_parcontractE_sk2q(combK, p, r)),
% 0.20/0.43 inference(symmetry,[status(thm)],[52])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (comb_app(combK, ap_parcontractE_sk2s(combK, p, r)) = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r)) = comb_app(combK, ap_parcontractE_sk2s(combK, p, r))),
% 0.20/0.43 inference(symmetry,[status(thm)],[54])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![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)))) <=> ![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))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (![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)))) <=> ![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(59,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')).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.43 tff(61,plain,(
% 0.20/0.43 ![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))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[60])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (((~![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(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, 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(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![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(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~![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(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 62, 30])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r))),
% 0.20/0.43 inference(transitivity,[status(thm)],[66, 55])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(71,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')).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.43 tff(73,plain,(
% 0.20/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.20/0.43 inference(skolemize,[status(sab)],[72])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (((~![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(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, 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(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 ((~![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(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 ((~![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(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[77, 74, 30])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (^[PP: $i] : refl(((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))) <=> ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(82,axiom,(![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k1_parcontractD_c1')).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.44 tff(84,plain,(
% 0.20/0.44 ![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[83])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[88, 85, 78])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[89, 67])).
% 0.20/0.44 tff(91,plain,(~ap_parcontractE_c4(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(92,assumption,(ap_parcontractE_c1(combK, p, r)), introduced(assumption)).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(96,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')).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.44 tff(98,plain,(
% 0.20/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.20/0.44 inference(skolemize,[status(sab)],[97])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (member(comb_app(combK, p), comb)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[102, 99, 92])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(Q, comb)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(107,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E2')).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.44 tff(109,plain,(
% 0.20/0.44 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.20/0.44 inference(skolemize,[status(sab)],[108])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combK, p), comb)) | member(p, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combK, p), comb)) | member(p, comb))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combK, p), comb)) | member(p, comb))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combK, p), comb)) | member(p, comb)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((~member(comb_app(combK, p), comb)) | member(p, comb)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (member(p, comb)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 103])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(119,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')).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.44 tff(121,plain,(
% 0.20/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[120])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (r = comb_app(combK, p)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[125, 122, 92])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 ((~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[129, 85])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (~member(pair(p, p), parcontract)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[130, 126])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(135,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.45 tff(137,plain,(
% 0.20/0.45 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.20/0.45 inference(skolemize,[status(sab)],[136])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[141, 138, 131, 115])).
% 0.20/0.45 tff(143,plain,(~ap_parcontractE_c1(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (member(pair(comb_app(combK, p), r), parcontract) <=> member(pair(comb_app(combK, p), r), parcontract)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(145,axiom,(member(pair(comb_app(combK, p), r), parcontract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k1_parcontractD_h1')).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (member(pair(comb_app(combK, p), r), parcontract)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[150])).
% 0.20/0.45 tff(152,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')).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.20/0.45 tff(155,plain,(
% 0.20/0.45 ![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)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[154])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(combK, p), r), parcontract)) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combK, p), r), parcontract)) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 ((ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract))) <=> ((~member(pair(comb_app(combK, p), r), parcontract)) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 (((~![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(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(combK, p), r), parcontract)) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[158])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (((~![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(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combK, p), r), parcontract)) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r))),
% 0.20/0.45 inference(transitivity,[status(thm)],[159, 157])).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 ((~![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(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combK, p), r), parcontract)) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[162, 156, 146])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[163, 143])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[164, 91])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (ap_parcontractE_c3(combK, p, r)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[165, 29])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(170,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')).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.46 tff(172,plain,(
% 0.20/0.46 ![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))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[171])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, 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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 ((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 ((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[176, 173, 166])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[178, 12, 177])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------