%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN072+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:09 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN072+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n013.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Jun 20 12:27:53 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(big_p_type, type, (
% 0.21/0.39 big_p: $i > $o)).
% 0.21/0.39 tff(b_type, type, (
% 0.21/0.39 b: $i)).
% 0.21/0.39 tff(tptp_fun_X_2_type, type, (
% 0.21/0.39 tptp_fun_X_2: $i)).
% 0.21/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.39 tptp_fun_Y_0: $i)).
% 0.21/0.39 tff(tptp_fun_X_1_type, type, (
% 0.21/0.39 tptp_fun_X_1: $i)).
% 0.21/0.39 tff(a_type, type, (
% 0.21/0.39 a: $i)).
% 0.21/0.39 tff(1,assumption,(X!2 = X!1), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (X!1 = X!2),
% 0.21/0.39 inference(symmetry,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 ((Y!0 = b) <=> (b = Y!0)),
% 0.21/0.39 inference(commutativity,[status(thm)],[])).
% 0.21/0.39 tff(4,assumption,(a = X!1), introduced(assumption)).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (a = X!2),
% 0.21/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (big_p(a) <=> big_p(X!2)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (big_p(X!2) <=> big_p(a)),
% 0.21/0.39 inference(symmetry,[status(thm)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 ((~big_p(X!2)) <=> (~big_p(a))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[7])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((~![X: $i] : big_p(X)) <=> (~![X: $i] : big_p(X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(10,axiom,(~![X: $i] : big_p(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel49')).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 9])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.39 tff(15,plain,(
% 0.21/0.39 ~big_p(X!2)),
% 0.21/0.39 inference(skolemize,[status(sab)],[14])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (~big_p(a)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (big_p(a) <=> big_p(a)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(18,axiom,(big_p(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel49_2')).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (big_p(a)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.21/0.39 tff(21,plain,((~(a = X!1)) | (~(X!2 = X!1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (~(a = X!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (?[X: $i, Y: $i] : ![Z: $i] : ((Z = Y) | (Z = X)) <=> ?[X: $i, Y: $i] : ![Z: $i] : ((Z = Y) | (Z = X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : quant_intro(proof_bind(^[Z: $i] : rewrite(((Z = X) | (Z = Y)) <=> ((Z = Y) | (Z = X)))), (![Z: $i] : ((Z = X) | (Z = Y)) <=> ![Z: $i] : ((Z = Y) | (Z = X))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (?[X: $i, Y: $i] : ![Z: $i] : ((Z = X) | (Z = Y)) <=> ?[X: $i, Y: $i] : ![Z: $i] : ((Z = Y) | (Z = X))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.39 tff(26,axiom,(?[X: $i, Y: $i] : ![Z: $i] : ((Z = X) | (Z = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel49_1')).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (?[X: $i, Y: $i] : ![Z: $i] : ((Z = Y) | (Z = X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (?[X: $i, Y: $i] : ![Z: $i] : ((Z = Y) | (Z = X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.39 tff(29,plain,(
% 0.21/0.39 $oeq(![Z: $i] : ((Z = Y!0) | (Z = X!1)), ![Z: $i] : ((Z = Y!0) | (Z = X!1)))),
% 0.21/0.39 inference(transitivity,[status(sab)],[28])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((a = Y!0) | (a = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (a = Y!0) | (a = X!1))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((a = Y!0) | (a = X!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (a = Y!0) | (a = X!1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ((a = Y!0) | (a = X!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[32, 29])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (a = Y!0),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((a = b) <=> (Y!0 = b)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 ((a = b) <=> (b = Y!0)),
% 0.21/0.39 inference(transitivity,[status(thm)],[35, 3])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 ((~(a = b)) <=> (~(b = Y!0))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 ((~(a = b)) <=> (~(a = b))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(39,axiom,(~(a = b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel49_4')).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (~(a = b)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (~(b = Y!0)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((b = Y!0) | (b = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (b = Y!0) | (b = X!1))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((b = Y!0) | (b = X!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (b = Y!0) | (b = X!1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 ((b = Y!0) | (b = X!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[44, 29])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (b = X!1),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (b = X!2),
% 0.21/0.39 inference(transitivity,[status(thm)],[46, 2])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (big_p(b) <=> big_p(X!2)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[47])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (big_p(X!2) <=> big_p(b)),
% 0.21/0.39 inference(symmetry,[status(thm)],[48])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 ((~big_p(X!2)) <=> (~big_p(b))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (~big_p(b)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 50])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (big_p(b) <=> big_p(b)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(53,axiom,(big_p(b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel49_3')).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 (big_p(b)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.21/0.39 tff(56,plain,(~(X!2 = X!1)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((X!2 = Y!0) | (X!2 = X!1))) <=> ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (X!2 = Y!0) | (X!2 = X!1))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | ((X!2 = Y!0) | (X!2 = X!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(59,plain,
% 0.21/0.39 ((~![Z: $i] : ((Z = Y!0) | (Z = X!1))) | (X!2 = Y!0) | (X!2 = X!1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.39 tff(60,plain,
% 0.21/0.39 ((X!2 = Y!0) | (X!2 = X!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[59, 29])).
% 0.21/0.39 tff(61,plain,
% 0.21/0.39 (X!2 = Y!0),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[60, 56])).
% 0.21/0.39 tff(62,plain,
% 0.21/0.39 (Y!0 = X!2),
% 0.21/0.39 inference(symmetry,[status(thm)],[61])).
% 0.21/0.39 tff(63,plain,
% 0.21/0.39 ((X!1 = b) <=> (b = X!1)),
% 0.21/0.39 inference(commutativity,[status(thm)],[])).
% 0.21/0.39 tff(64,assumption,(a = Y!0), introduced(assumption)).
% 0.21/0.39 tff(65,plain,
% 0.21/0.39 (a = X!2),
% 0.21/0.39 inference(transitivity,[status(thm)],[64, 62])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 (big_p(a) <=> big_p(X!2)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 (big_p(X!2) <=> big_p(a)),
% 0.21/0.39 inference(symmetry,[status(thm)],[66])).
% 0.21/0.39 tff(68,plain,
% 0.21/0.39 ((~big_p(X!2)) <=> (~big_p(a))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 (~big_p(a)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 68])).
% 0.21/0.39 tff(70,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[19, 69])).
% 0.21/0.39 tff(71,plain,(~(a = Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (a = X!1),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[33, 71])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 ((a = b) <=> (X!1 = b)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 ((a = b) <=> (b = X!1)),
% 0.21/0.39 inference(transitivity,[status(thm)],[73, 63])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 ((~(a = b)) <=> (~(b = X!1))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (~(b = X!1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 75])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 (b = Y!0),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[45, 76])).
% 0.21/0.39 tff(78,plain,
% 0.21/0.39 (b = X!2),
% 0.21/0.39 inference(transitivity,[status(thm)],[77, 62])).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (big_p(b) <=> big_p(X!2)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.39 tff(80,plain,
% 0.21/0.39 (big_p(X!2) <=> big_p(b)),
% 0.21/0.39 inference(symmetry,[status(thm)],[79])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 ((~big_p(X!2)) <=> (~big_p(b))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[80])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 (~big_p(b)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 81])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[54, 82])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------