%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ001+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:23:06 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ001+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Fri Jun 20 02:38:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(hates_type, type, (
% 0.20/0.38 hates: ( $i * $i ) > $o)).
% 0.20/0.38 tff(agatha_type, type, (
% 0.20/0.38 agatha: $i)).
% 0.20/0.38 tff(charles_type, type, (
% 0.20/0.38 charles: $i)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(butler_type, type, (
% 0.20/0.38 butler: $i)).
% 0.20/0.38 tff(killed_type, type, (
% 0.20/0.38 killed: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.38 tptp_fun_Y_1: $i > $i)).
% 0.20/0.38 tff(richer_type, type, (
% 0.20/0.38 richer: ( $i * $i ) > $o)).
% 0.20/0.38 tff(lives_type, type, (
% 0.20/0.38 lives: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (~hates(X, Y)) <=> ![X: $i] : ?[Y: $i] : (~hates(X, Y))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,axiom,(![X: $i] : ?[Y: $i] : (~hates(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_10')).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X: $i] : ?[Y: $i] : (~hates(X, Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.38 tff(4,plain,(
% 0.20/0.38 ![X: $i] : (~hates(X, tptp_fun_Y_1(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~![X: $i] : (~hates(X, tptp_fun_Y_1(X)))) | (~hates(butler, tptp_fun_Y_1(butler)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~hates(butler, tptp_fun_Y_1(butler))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (^[X: $i] : refl(((~hates(agatha, X)) | hates(butler, X)) <=> ((~hates(agatha, X)) | hates(butler, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X: $i] : ((~hates(agatha, X)) | hates(butler, X)) <=> ![X: $i] : ((~hates(agatha, X)) | hates(butler, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![X: $i] : ((~hates(agatha, X)) | hates(butler, X)) <=> ![X: $i] : ((~hates(agatha, X)) | hates(butler, X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (^[X: $i] : rewrite((hates(agatha, X) => hates(butler, X)) <=> ((~hates(agatha, X)) | hates(butler, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![X: $i] : (hates(agatha, X) => hates(butler, X)) <=> ![X: $i] : ((~hates(agatha, X)) | hates(butler, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.38 tff(12,axiom,(![X: $i] : (hates(agatha, X) => hates(butler, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_9')).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X: $i] : ((~hates(agatha, X)) | hates(butler, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X: $i] : ((~hates(agatha, X)) | hates(butler, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.38 tff(15,plain,(
% 0.20/0.38 ![X: $i] : ((~hates(agatha, X)) | hates(butler, X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[14])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X: $i] : ((~hates(agatha, X)) | hates(butler, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (((~![X: $i] : ((~hates(agatha, X)) | hates(butler, X))) | ((~hates(agatha, tptp_fun_Y_1(butler))) | hates(butler, tptp_fun_Y_1(butler)))) <=> ((~![X: $i] : ((~hates(agatha, X)) | hates(butler, X))) | (~hates(agatha, tptp_fun_Y_1(butler))) | hates(butler, tptp_fun_Y_1(butler)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~![X: $i] : ((~hates(agatha, X)) | hates(butler, X))) | ((~hates(agatha, tptp_fun_Y_1(butler))) | hates(butler, tptp_fun_Y_1(butler)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~![X: $i] : ((~hates(agatha, X)) | hates(butler, X))) | (~hates(agatha, tptp_fun_Y_1(butler))) | hates(butler, tptp_fun_Y_1(butler))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (~hates(agatha, tptp_fun_Y_1(butler))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[19, 16, 6])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (^[X: $i] : refl(((X = butler) | hates(agatha, X)) <=> ((X = butler) | hates(agatha, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![X: $i] : ((X = butler) | hates(agatha, X)) <=> ![X: $i] : ((X = butler) | hates(agatha, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![X: $i] : ((X = butler) | hates(agatha, X)) <=> ![X: $i] : ((X = butler) | hates(agatha, X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (^[X: $i] : rewrite(((~(X = butler)) => hates(agatha, X)) <=> ((X = butler) | hates(agatha, X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![X: $i] : ((~(X = butler)) => hates(agatha, X)) <=> ![X: $i] : ((X = butler) | hates(agatha, X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.38 tff(26,axiom,(![X: $i] : ((~(X = butler)) => hates(agatha, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_7')).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![X: $i] : ((X = butler) | hates(agatha, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X: $i] : ((X = butler) | hates(agatha, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.38 tff(29,plain,(
% 0.20/0.38 ![X: $i] : ((X = butler) | hates(agatha, X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![X: $i] : ((X = butler) | hates(agatha, X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (((~![X: $i] : ((X = butler) | hates(agatha, X))) | ((tptp_fun_Y_1(butler) = butler) | hates(agatha, tptp_fun_Y_1(butler)))) <=> ((~![X: $i] : ((X = butler) | hates(agatha, X))) | (tptp_fun_Y_1(butler) = butler) | hates(agatha, tptp_fun_Y_1(butler)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ((~![X: $i] : ((X = butler) | hates(agatha, X))) | ((tptp_fun_Y_1(butler) = butler) | hates(agatha, tptp_fun_Y_1(butler)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 ((~![X: $i] : ((X = butler) | hates(agatha, X))) | (tptp_fun_Y_1(butler) = butler) | hates(agatha, tptp_fun_Y_1(butler))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (tptp_fun_Y_1(butler) = butler),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (butler = tptp_fun_Y_1(butler)),
% 0.20/0.38 inference(symmetry,[status(thm)],[34])).
% 0.20/0.38 tff(36,assumption,(X!0 = butler), introduced(assumption)).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (X!0 = tptp_fun_Y_1(butler)),
% 0.20/0.38 inference(transitivity,[status(thm)],[36, 35])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (killed(X!0, agatha) <=> killed(tptp_fun_Y_1(butler), agatha)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (killed(tptp_fun_Y_1(butler), agatha) <=> killed(X!0, agatha)),
% 0.20/0.38 inference(symmetry,[status(thm)],[38])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~killed(tptp_fun_Y_1(butler), agatha)) <=> (~killed(X!0, agatha))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (^[X: $i] : refl((hates(butler, X) | richer(X, agatha)) <=> (hates(butler, X) | richer(X, agatha)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![X: $i] : (hates(butler, X) | richer(X, agatha)) <=> ![X: $i] : (hates(butler, X) | richer(X, agatha))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![X: $i] : (hates(butler, X) | richer(X, agatha)) <=> ![X: $i] : (hates(butler, X) | richer(X, agatha))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (^[X: $i] : rewrite(((~richer(X, agatha)) => hates(butler, X)) <=> (hates(butler, X) | richer(X, agatha)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (![X: $i] : ((~richer(X, agatha)) => hates(butler, X)) <=> ![X: $i] : (hates(butler, X) | richer(X, agatha))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.38 tff(46,axiom,(![X: $i] : ((~richer(X, agatha)) => hates(butler, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_8')).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![X: $i] : (hates(butler, X) | richer(X, agatha))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (![X: $i] : (hates(butler, X) | richer(X, agatha))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.38 tff(49,plain,(
% 0.20/0.38 ![X: $i] : (hates(butler, X) | richer(X, agatha))),
% 0.20/0.38 inference(skolemize,[status(sab)],[48])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![X: $i] : (hates(butler, X) | richer(X, agatha))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (((~![X: $i] : (hates(butler, X) | richer(X, agatha))) | (hates(butler, tptp_fun_Y_1(butler)) | richer(tptp_fun_Y_1(butler), agatha))) <=> ((~![X: $i] : (hates(butler, X) | richer(X, agatha))) | hates(butler, tptp_fun_Y_1(butler)) | richer(tptp_fun_Y_1(butler), agatha))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~![X: $i] : (hates(butler, X) | richer(X, agatha))) | (hates(butler, tptp_fun_Y_1(butler)) | richer(tptp_fun_Y_1(butler), agatha))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~![X: $i] : (hates(butler, X) | richer(X, agatha))) | hates(butler, tptp_fun_Y_1(butler)) | richer(tptp_fun_Y_1(butler), agatha)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (richer(tptp_fun_Y_1(butler), agatha)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 50, 6])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : refl(((~killed(X, Y)) | (~richer(X, Y))) <=> ((~killed(X, Y)) | (~richer(X, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y))) <=> ![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y))) <=> ![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : rewrite((killed(X, Y) => (~richer(X, Y))) <=> ((~killed(X, Y)) | (~richer(X, Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (killed(X, Y) => (~richer(X, Y))) <=> ![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.39 tff(60,axiom,(![X: $i, Y: $i] : (killed(X, Y) => (~richer(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_5')).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.39 tff(63,plain,(
% 0.20/0.39 ![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[62])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))) | ((~killed(tptp_fun_Y_1(butler), agatha)) | (~richer(tptp_fun_Y_1(butler), agatha)))) <=> ((~![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))) | (~killed(tptp_fun_Y_1(butler), agatha)) | (~richer(tptp_fun_Y_1(butler), agatha)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))) | ((~killed(tptp_fun_Y_1(butler), agatha)) | (~richer(tptp_fun_Y_1(butler), agatha)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : ((~killed(X, Y)) | (~richer(X, Y)))) | (~killed(tptp_fun_Y_1(butler), agatha)) | (~richer(tptp_fun_Y_1(butler), agatha))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (~killed(tptp_fun_Y_1(butler), agatha)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 64, 54])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 (~killed(X!0, agatha)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[68, 40])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (?[X: $i] : (lives(X) & killed(X, agatha)) <=> ?[X: $i] : (lives(X) & killed(X, agatha))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(71,axiom,(?[X: $i] : (lives(X) & killed(X, agatha))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_1')).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (?[X: $i] : (lives(X) & killed(X, agatha))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.39 tff(73,plain,(
% 0.20/0.39 lives(X!0) & killed(X!0, agatha)),
% 0.20/0.39 inference(skolemize,[status(sab)],[72])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (killed(X!0, agatha)),
% 0.20/0.39 inference(and_elim,[status(thm)],[73])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[74, 69])).
% 0.20/0.39 tff(76,plain,(~(X!0 = butler)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(77,assumption,(X!0 = agatha), introduced(assumption)).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (killed(X!0, agatha) <=> killed(agatha, agatha)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (killed(agatha, agatha) <=> killed(X!0, agatha)),
% 0.20/0.39 inference(symmetry,[status(thm)],[78])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 ((~killed(agatha, agatha)) <=> (~killed(X!0, agatha))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 ((~killed(agatha, agatha)) <=> (~killed(agatha, agatha))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(82,axiom,(~killed(agatha, agatha)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55')).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (~killed(agatha, agatha)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (~killed(X!0, agatha)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[74, 84])).
% 0.20/0.39 tff(86,plain,(~(X!0 = agatha)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (^[X: $i] : refl(((X = charles) | (X = butler) | (X = agatha) | (~lives(X))) <=> ((X = charles) | (X = butler) | (X = agatha) | (~lives(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X))) <=> ![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X))) <=> ![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (^[X: $i] : trans(monotonicity(rewrite((((X = agatha) | (X = butler)) | (X = charles)) <=> ((X = charles) | (X = butler) | (X = agatha))), ((lives(X) => (((X = agatha) | (X = butler)) | (X = charles))) <=> (lives(X) => ((X = charles) | (X = butler) | (X = agatha))))), rewrite((lives(X) => ((X = charles) | (X = butler) | (X = agatha))) <=> ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))), ((lives(X) => (((X = agatha) | (X = butler)) | (X = charles))) <=> ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (![X: $i] : (lives(X) => (((X = agatha) | (X = butler)) | (X = charles))) <=> ![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.39 tff(92,axiom,(![X: $i] : (lives(X) => (((X = agatha) | (X = butler)) | (X = charles)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_3')).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.39 tff(95,plain,(
% 0.20/0.39 ![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[94])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (lives(X!0)),
% 0.20/0.39 inference(and_elim,[status(thm)],[73])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (((~![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))) | ((X!0 = charles) | (X!0 = butler) | (X!0 = agatha) | (~lives(X!0)))) <=> ((~![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))) | (X!0 = charles) | (X!0 = butler) | (X!0 = agatha) | (~lives(X!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 ((~![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))) | ((X!0 = charles) | (X!0 = butler) | (X!0 = agatha) | (~lives(X!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 ((~![X: $i] : ((X = charles) | (X = butler) | (X = agatha) | (~lives(X)))) | (X!0 = charles) | (X!0 = butler) | (X!0 = agatha) | (~lives(X!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 ((X!0 = charles) | (X!0 = butler) | (X!0 = agatha)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[100, 97, 96])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (X!0 = charles),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[101, 86, 76])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 (hates(X!0, agatha) <=> hates(charles, agatha)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : refl(((~killed(X, Y)) | hates(X, Y)) <=> ((~killed(X, Y)) | hates(X, Y)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y)) <=> ![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.39 tff(106,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y)) <=> ![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (^[X: $i, Y: $i] : rewrite((killed(X, Y) => hates(X, Y)) <=> ((~killed(X, Y)) | hates(X, Y)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (![X: $i, Y: $i] : (killed(X, Y) => hates(X, Y)) <=> ![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.39 tff(109,axiom,(![X: $i, Y: $i] : (killed(X, Y) => hates(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_4')).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.39 tff(112,plain,(
% 0.20/0.39 ![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))),
% 0.20/0.39 inference(skolemize,[status(sab)],[111])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))) | ((~killed(X!0, agatha)) | hates(X!0, agatha))) <=> ((~![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))) | (~killed(X!0, agatha)) | hates(X!0, agatha))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))) | ((~killed(X!0, agatha)) | hates(X!0, agatha))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : ((~killed(X, Y)) | hates(X, Y))) | (~killed(X!0, agatha)) | hates(X!0, agatha)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.39 tff(117,plain,
% 0.20/0.39 (hates(X!0, agatha)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[116, 74, 113])).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (hates(charles, agatha)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[117, 103])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 (^[X: $i] : refl(((~hates(agatha, X)) | (~hates(charles, X))) <=> ((~hates(agatha, X)) | (~hates(charles, X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(120,plain,
% 0.20/0.39 (![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X))) <=> ![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 (![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X))) <=> ![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (^[X: $i] : rewrite((hates(agatha, X) => (~hates(charles, X))) <=> ((~hates(agatha, X)) | (~hates(charles, X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(123,plain,
% 0.20/0.39 (![X: $i] : (hates(agatha, X) => (~hates(charles, X))) <=> ![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.39 tff(124,axiom,(![X: $i] : (hates(agatha, X) => (~hates(charles, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_6')).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.39 tff(126,plain,
% 0.20/0.39 (![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.20/0.39 tff(127,plain,(
% 0.20/0.39 ![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[126])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 (![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.20/0.39 tff(129,plain,
% 0.20/0.39 (((~![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))) | ((~hates(agatha, agatha)) | (~hates(charles, agatha)))) <=> ((~![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))) | (~hates(agatha, agatha)) | (~hates(charles, agatha)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(130,plain,
% 0.20/0.40 ((~![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))) | ((~hates(agatha, agatha)) | (~hates(charles, agatha)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 ((~![X: $i] : ((~hates(agatha, X)) | (~hates(charles, X)))) | (~hates(agatha, agatha)) | (~hates(charles, agatha))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 ((~hates(agatha, agatha)) | (~hates(charles, agatha))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[131, 128])).
% 0.20/0.40 tff(133,plain,
% 0.20/0.40 (~hates(agatha, agatha)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[132, 118])).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 ((~(agatha = butler)) <=> (~(agatha = butler))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(135,axiom,(~(agatha = butler)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel55_11')).
% 0.20/0.40 tff(136,plain,
% 0.20/0.40 (~(agatha = butler)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 (((~![X: $i] : ((X = butler) | hates(agatha, X))) | ((agatha = butler) | hates(agatha, agatha))) <=> ((~![X: $i] : ((X = butler) | hates(agatha, X))) | (agatha = butler) | hates(agatha, agatha))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(138,plain,
% 0.20/0.40 ((~![X: $i] : ((X = butler) | hates(agatha, X))) | ((agatha = butler) | hates(agatha, agatha))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 ((~![X: $i] : ((X = butler) | hates(agatha, X))) | (agatha = butler) | hates(agatha, agatha)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[139, 30, 136, 133])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------