%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN072-1 : TPTP v9.0.0. Released v1.0.0.
% 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 05:38:09 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN072-1 : TPTP v9.0.0. Released v1.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:27:23 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_p_type, type, (
% 0.11/0.36 big_p: $i > $o)).
% 0.11/0.36 tff(b_type, type, (
% 0.11/0.36 b: $i)).
% 0.11/0.36 tff(e_type, type, (
% 0.11/0.36 e: $i)).
% 0.11/0.36 tff(c_type, type, (
% 0.11/0.36 c: $i)).
% 0.11/0.36 tff(d_type, type, (
% 0.11/0.36 d: $i)).
% 0.11/0.36 tff(a_type, type, (
% 0.11/0.36 a: $i)).
% 0.11/0.36 tff(1,assumption,(e = d), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (d = e),
% 0.11/0.36 inference(symmetry,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((c = b) <=> (b = c)),
% 0.11/0.36 inference(commutativity,[status(thm)],[])).
% 0.11/0.36 tff(4,assumption,(a = d), introduced(assumption)).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (a = e),
% 0.11/0.36 inference(transitivity,[status(thm)],[4, 2])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (big_p(a) <=> big_p(e)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[5])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (big_p(e) <=> big_p(a)),
% 0.11/0.36 inference(symmetry,[status(thm)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 ((~big_p(e)) <=> (~big_p(a))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~big_p(e)) <=> (~big_p(e))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(10,axiom,(~big_p(e)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (~big_p(e)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (~big_p(a)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (big_p(a) <=> big_p(a)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(14,axiom,(big_p(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (big_p(a)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.11/0.36 tff(17,plain,((~(a = d)) | (~(e = d))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (~(a = d)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[17, 1])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![X: $i] : ((X = c) | (X = d)) <=> ![X: $i] : ((X = c) | (X = d))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(20,axiom,(![X: $i] : ((X = c) | (X = d))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![X: $i] : ((X = c) | (X = d))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.11/0.36 tff(22,plain,(
% 0.11/0.36 ![X: $i] : ((X = c) | (X = d))),
% 0.11/0.36 inference(skolemize,[status(sab)],[21])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (((~![X: $i] : ((X = c) | (X = d))) | ((a = c) | (a = d))) <=> ((~![X: $i] : ((X = c) | (X = d))) | (a = c) | (a = d))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 ((~![X: $i] : ((X = c) | (X = d))) | ((a = c) | (a = d))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 ((~![X: $i] : ((X = c) | (X = d))) | (a = c) | (a = d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 ((a = c) | (a = d)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (a = c),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[26, 18])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 ((a = b) <=> (c = b)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[27])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 ((a = b) <=> (b = c)),
% 0.11/0.36 inference(transitivity,[status(thm)],[28, 3])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 ((~(a = b)) <=> (~(b = c))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[29])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 ((~(a = b)) <=> (~(a = b))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(32,axiom,(~(a = b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (~(a = b)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (~(b = c)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (((~![X: $i] : ((X = c) | (X = d))) | ((b = c) | (b = d))) <=> ((~![X: $i] : ((X = c) | (X = d))) | (b = c) | (b = d))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 ((~![X: $i] : ((X = c) | (X = d))) | ((b = c) | (b = d))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 ((~![X: $i] : ((X = c) | (X = d))) | (b = c) | (b = d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 ((b = c) | (b = d)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[37, 22])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (b = d),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[38, 34])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (b = e),
% 0.11/0.36 inference(transitivity,[status(thm)],[39, 2])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 (big_p(b) <=> big_p(e)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[40])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (big_p(e) <=> big_p(b)),
% 0.11/0.36 inference(symmetry,[status(thm)],[41])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 ((~big_p(e)) <=> (~big_p(b))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[42])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (~big_p(b)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[11, 43])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (big_p(b) <=> big_p(b)),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(46,axiom,(big_p(b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 (big_p(b)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.11/0.36 tff(49,plain,(~(e = d)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(50,plain,
% 0.11/0.36 (((~![X: $i] : ((X = c) | (X = d))) | ((e = c) | (e = d))) <=> ((~![X: $i] : ((X = c) | (X = d))) | (e = c) | (e = d))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(51,plain,
% 0.11/0.36 ((~![X: $i] : ((X = c) | (X = d))) | ((e = c) | (e = d))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(52,plain,
% 0.11/0.36 ((~![X: $i] : ((X = c) | (X = d))) | (e = c) | (e = d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.36 tff(53,plain,
% 0.11/0.36 ((e = c) | (e = d)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[52, 22])).
% 0.11/0.36 tff(54,plain,
% 0.11/0.36 (e = c),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[53, 49])).
% 0.11/0.36 tff(55,plain,
% 0.11/0.36 (c = e),
% 0.11/0.36 inference(symmetry,[status(thm)],[54])).
% 0.11/0.36 tff(56,plain,
% 0.11/0.36 ((d = b) <=> (b = d)),
% 0.11/0.36 inference(commutativity,[status(thm)],[])).
% 0.11/0.36 tff(57,assumption,(a = c), introduced(assumption)).
% 0.11/0.36 tff(58,plain,
% 0.11/0.36 (a = e),
% 0.11/0.36 inference(transitivity,[status(thm)],[57, 55])).
% 0.11/0.36 tff(59,plain,
% 0.11/0.36 (big_p(a) <=> big_p(e)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[58])).
% 0.11/0.36 tff(60,plain,
% 0.11/0.36 (big_p(e) <=> big_p(a)),
% 0.11/0.36 inference(symmetry,[status(thm)],[59])).
% 0.11/0.36 tff(61,plain,
% 0.11/0.36 ((~big_p(e)) <=> (~big_p(a))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[60])).
% 0.11/0.36 tff(62,plain,
% 0.11/0.36 (~big_p(a)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[11, 61])).
% 0.11/0.36 tff(63,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[15, 62])).
% 0.11/0.36 tff(64,plain,(~(a = c)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(65,plain,
% 0.11/0.36 (a = d),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[26, 64])).
% 0.11/0.36 tff(66,plain,
% 0.11/0.36 ((a = b) <=> (d = b)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[65])).
% 0.11/0.36 tff(67,plain,
% 0.11/0.36 ((a = b) <=> (b = d)),
% 0.11/0.36 inference(transitivity,[status(thm)],[66, 56])).
% 0.11/0.36 tff(68,plain,
% 0.11/0.36 ((~(a = b)) <=> (~(b = d))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[67])).
% 0.11/0.36 tff(69,plain,
% 0.11/0.36 (~(b = d)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[33, 68])).
% 0.11/0.36 tff(70,plain,
% 0.11/0.36 (b = c),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[38, 69])).
% 0.11/0.36 tff(71,plain,
% 0.11/0.36 (b = e),
% 0.11/0.36 inference(transitivity,[status(thm)],[70, 55])).
% 0.11/0.36 tff(72,plain,
% 0.11/0.36 (big_p(b) <=> big_p(e)),
% 0.11/0.36 inference(monotonicity,[status(thm)],[71])).
% 0.11/0.36 tff(73,plain,
% 0.11/0.36 (big_p(e) <=> big_p(b)),
% 0.11/0.36 inference(symmetry,[status(thm)],[72])).
% 0.11/0.36 tff(74,plain,
% 0.11/0.36 ((~big_p(e)) <=> (~big_p(b))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[73])).
% 0.11/0.36 tff(75,plain,
% 0.11/0.36 (~big_p(b)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[11, 74])).
% 0.11/0.36 tff(76,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[47, 75])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------