%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL093-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL093-1 : TPTP v9.0.0. Released v2.7.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 12:15:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(comb_app_type, type, (
% 0.19/0.39 comb_app: ( $i * $i ) > $i)).
% 0.19/0.39 tff(ap_parcontractE_sk1q_type, type, (
% 0.19/0.39 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(r_type, type, (
% 0.19/0.39 r: $i)).
% 0.19/0.39 tff(p_type, type, (
% 0.19/0.39 p: $i)).
% 0.19/0.39 tff(combS_type, type, (
% 0.19/0.39 combS: $i)).
% 0.19/0.39 tff(ap_parcontractE_sk1p_type, type, (
% 0.19/0.39 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(ap_parcontractE_c3_type, type, (
% 0.19/0.39 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(ap_parcontractE_c2_type, type, (
% 0.19/0.39 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(combK_type, type, (
% 0.19/0.39 combK: $i)).
% 0.19/0.39 tff(ap_parcontractE_c1_type, type, (
% 0.19/0.39 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(member_type, type, (
% 0.19/0.39 member: ( $i * $i ) > $o)).
% 0.19/0.39 tff(parcontract_type, type, (
% 0.19/0.39 parcontract: $i)).
% 0.19/0.39 tff(pair_type, type, (
% 0.19/0.39 pair: ( $i * $i ) > $i)).
% 0.19/0.39 tff(comb_type, type, (
% 0.19/0.39 comb: $i)).
% 0.19/0.39 tff(ap_parcontractE_c4_type, type, (
% 0.19/0.39 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(ap_parcontractE_sk2s_type, type, (
% 0.19/0.39 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(ap_parcontractE_sk2q_type, type, (
% 0.19/0.39 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(1,assumption,(combS = comb_app(combK, r)), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_app')).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,(
% 0.19/0.39 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, r)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.39 tff(11,plain,(~(combS = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(12,assumption,(ap_parcontractE_c2(combS, p, r)), introduced(assumption)).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,(
% 0.19/0.39 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[22, 19, 12, 11])).
% 0.19/0.39 tff(24,plain,(~ap_parcontractE_c2(combS, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(25,assumption,(~member(p, comb)), introduced(assumption)).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (^[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)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(29,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE5')).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.39 tff(31,plain,(
% 0.19/0.39 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.19/0.39 inference(skolemize,[status(sab)],[30])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, r)) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, r)) | member(p, comb))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, r)) | member(p, comb))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, r)) | member(p, comb)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 32, 25, 12])).
% 0.19/0.39 tff(37,plain,((~ap_parcontractE_c2(combS, p, r)) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~ap_parcontractE_c2(combS, p, r)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 25])).
% 0.19/0.39 tff(39,assumption,(ap_parcontractE_c3(combS, p, r)), introduced(assumption)).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (^[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)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE9')).
% 0.19/0.39 tff(44,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.40 tff(45,plain,(
% 0.19/0.40 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.19/0.40 inference(skolemize,[status(sab)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, r)) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, r)) | member(p, comb))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, r)) | member(p, comb))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, r)) | member(p, comb)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[49, 46, 25, 39])).
% 0.19/0.40 tff(51,plain,((~ap_parcontractE_c3(combS, p, r)) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (~ap_parcontractE_c3(combS, p, r)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[51, 25])).
% 0.19/0.40 tff(53,assumption,(ap_parcontractE_c4(combS, p, r)), introduced(assumption)).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(57,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,(
% 0.19/0.40 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.19/0.40 inference(skolemize,[status(sab)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (((~![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, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, 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(combS, p, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~![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, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 ((~![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, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[63, 60, 53])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (^[R: $i] : refl(((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ((~member(pair(combS, R), parcontract)) | (R = combS)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(68,axiom,(![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_parcontractE2')).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.40 tff(70,plain,(
% 0.19/0.40 ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.40 inference(skolemize,[status(sab)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS))) <=> ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (ap_parcontractE_sk2q(combS, p, r) = combS),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[74, 71, 64])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (combS = ap_parcontractE_sk2q(combS, p, r)),
% 0.19/0.40 inference(symmetry,[status(thm)],[75])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (comb_app(combS, ap_parcontractE_sk2s(combS, p, r)) = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r)) = comb_app(combS, ap_parcontractE_sk2s(combS, p, r))),
% 0.19/0.40 inference(symmetry,[status(thm)],[77])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(82,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.40 tff(84,plain,(
% 0.19/0.40 ![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))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[83])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~![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, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, 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(combS, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~![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, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((~![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, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[88, 85, 53])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r))),
% 0.19/0.40 inference(transitivity,[status(thm)],[89, 78])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(94,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.40 tff(96,plain,(
% 0.19/0.40 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.19/0.40 inference(skolemize,[status(sab)],[95])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (((~![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, r)) | member(pair(p, ap_parcontractE_sk2s(combS, 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(combS, p, r)) | member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 ((~![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, r)) | member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 ((~![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, r)) | member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 97, 53])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (^[PP: $i] : refl(((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))) <=> ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(105,axiom,(![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_parcontractD_c1')).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.19/0.40 tff(107,plain,(
% 0.19/0.40 ![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[106])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 108, 101])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[112, 90])).
% 0.19/0.40 tff(114,plain,(~ap_parcontractE_c4(combS, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (member(pair(comb_app(combS, p), r), parcontract) <=> member(pair(comb_app(combS, p), r), parcontract)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(116,axiom,(member(pair(comb_app(combS, p), r), parcontract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_parcontractD_h1')).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (member(pair(comb_app(combS, p), r), parcontract)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.41 tff(123,axiom,(![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.19/0.41 tff(126,plain,(
% 0.19/0.41 ![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)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[125])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (((~![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, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, 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)))) | ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, p), r), parcontract)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ((~![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, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, p), r), parcontract)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 ((~![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, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, p), r), parcontract))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[130, 127, 117])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[131, 114])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (ap_parcontractE_c1(combS, p, r)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[132, 52, 38])).
% 0.19/0.41 tff(134,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(135,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)],[134])).
% 0.19/0.41 tff(136,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(137,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_E2')).
% 0.19/0.41 tff(138,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)],[137, 136])).
% 0.19/0.41 tff(139,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)],[138])).
% 0.19/0.41 tff(140,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)],[139, 135])).
% 0.19/0.41 tff(141,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(142,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(143,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)],[142, 141])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 ((~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (~member(comb_app(combS, p), comb)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[144, 25])).
% 0.19/0.41 tff(146,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(147,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)],[146])).
% 0.19/0.41 tff(148,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(149,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE2')).
% 0.19/0.41 tff(150,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)],[149, 148])).
% 0.19/0.41 tff(151,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)],[150])).
% 0.19/0.41 tff(152,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)],[151, 147])).
% 0.19/0.41 tff(153,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, 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, r)) | member(comb_app(combS, p), comb))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, r)) | member(comb_app(combS, p), comb))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, r)) | member(comb_app(combS, p), comb)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 152, 145, 133])).
% 0.19/0.42 tff(157,plain,(member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(161,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.42 tff(163,plain,(
% 0.19/0.42 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.42 inference(skolemize,[status(sab)],[162])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (((~![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))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (member(pair(p, p), parcontract)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[167, 164, 157])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 ((~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[171, 108])).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 (~(r = comb_app(combS, p))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[172, 168])).
% 0.19/0.42 tff(174,assumption,(ap_parcontractE_c1(combS, p, r)), introduced(assumption)).
% 0.19/0.42 tff(175,assumption,(~(r = comb_app(combS, p))), introduced(assumption)).
% 0.19/0.42 tff(176,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(177,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.42 tff(178,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(179,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.42 tff(181,plain,(
% 0.19/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[180])).
% 0.19/0.42 tff(182,plain,
% 0.19/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.19/0.42 tff(183,plain,
% 0.19/0.42 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, r)) | (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, r)) | (r = comb_app(combS, p)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(184,plain,
% 0.19/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, r)) | (r = comb_app(combS, p)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(185,plain,
% 0.19/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, r)) | (r = comb_app(combS, p))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[185, 182, 175, 174])).
% 0.19/0.42 tff(187,plain,((~ap_parcontractE_c1(combS, p, r)) | (r = comb_app(combS, p))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(188,plain,
% 0.19/0.42 (~ap_parcontractE_c1(combS, p, r)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[187, 173])).
% 0.19/0.42 tff(189,plain,
% 0.19/0.42 (ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[132, 188])).
% 0.19/0.42 tff(190,plain,
% 0.19/0.42 (ap_parcontractE_c3(combS, p, r)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[189, 24])).
% 0.19/0.42 tff(191,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(192,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[191])).
% 0.19/0.42 tff(193,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(194,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.19/0.42 tff(195,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.42 tff(196,plain,(
% 0.20/0.42 ![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))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[195])).
% 0.20/0.42 tff(197,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.20/0.42 tff(198,plain,
% 0.20/0.42 (((~![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, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, 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(combS, p, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(199,plain,
% 0.20/0.42 ((~![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, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(200,plain,
% 0.20/0.42 ((~![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, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.42 tff(201,plain,
% 0.20/0.42 (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[200, 197, 190])).
% 0.20/0.42 tff(202,plain,
% 0.20/0.42 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(203,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[202, 8, 201])).
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------