%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN101-1.002.002 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:38:15 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN101-1.002.002 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.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 12:28:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.36 % SZS status Unsatisfiable
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(p_2_2_type, type, (
% 0.19/0.36 p_2_2: ( $i * $i ) > $o)).
% 0.19/0.36 tff(a_type, type, (
% 0.19/0.36 a: $i)).
% 0.19/0.36 tff(p_1_1_type, type, (
% 0.19/0.36 p_1_1: ( $i * $i ) > $o)).
% 0.19/0.36 tff(nq_2_type, type, (
% 0.19/0.36 nq_2: $i > $o)).
% 0.19/0.36 tff(nq_1_type, type, (
% 0.19/0.36 nq_1: $i > $o)).
% 0.19/0.36 tff(p_1_2_type, type, (
% 0.19/0.36 p_1_2: ( $i * $i ) > $o)).
% 0.19/0.36 tff(1,assumption,(~p_1_1(a, a)), introduced(assumption)).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (nq_2(a) <=> nq_2(a)),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(3,axiom,(nq_2(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','n_3')).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (nq_2(a)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (nq_1(a) <=> nq_1(a)),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(6,axiom,(nq_1(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','n_1')).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (nq_1(a)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (^[X_2: $i, X_1: $i] : refl((p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))) <=> (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))) <=> ![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))) <=> ![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (^[X_2: $i, X_1: $i] : trans(monotonicity(rewrite((p_1_1(X_1, X_2) | (~nq_1(X_1))) <=> (p_1_1(X_1, X_2) | (~nq_1(X_1)))), (((p_1_1(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> ((p_1_1(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))))), rewrite(((p_1_1(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))), (((p_1_1(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((p_1_1(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> ![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.36 tff(13,axiom,(![X_2: $i, X_1: $i] : ((p_1_1(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','n_t2_1')).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.36 tff(16,plain,(
% 0.19/0.36 ![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[15])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 (((~![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | (p_1_1(a, a) | (~nq_2(a)) | (~nq_1(a)))) <=> ((~![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | p_1_1(a, a) | (~nq_2(a)) | (~nq_1(a)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 ((~![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | (p_1_1(a, a) | (~nq_2(a)) | (~nq_1(a)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 ((~![X_2: $i, X_1: $i] : (p_1_1(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | p_1_1(a, a) | (~nq_2(a)) | (~nq_1(a))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[20, 17, 7, 4, 1])).
% 0.19/0.36 tff(22,plain,(p_1_1(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 (^[X_2: $i, X_1: $i] : refl(((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2)) <=> ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2)))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(24,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2)) <=> ![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.36 tff(25,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2)) <=> ![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(26,plain,
% 0.19/0.36 (^[X_2: $i, X_1: $i] : trans(monotonicity(rewrite((p_1_2(X_1, X_2) | (~p_2_2(X_1, X_2))) <=> ((~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))), (((p_1_2(X_1, X_2) | (~p_2_2(X_1, X_2))) | (~p_1_1(X_1, X_2))) <=> (((~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2)) | (~p_1_1(X_1, X_2))))), rewrite((((~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2)) | (~p_1_1(X_1, X_2))) <=> ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))), (((p_1_2(X_1, X_2) | (~p_2_2(X_1, X_2))) | (~p_1_1(X_1, X_2))) <=> ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(27,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((p_1_2(X_1, X_2) | (~p_2_2(X_1, X_2))) | (~p_1_1(X_1, X_2))) <=> ![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.36 tff(28,axiom,(![X_2: $i, X_1: $i] : ((p_1_2(X_1, X_2) | (~p_2_2(X_1, X_2))) | (~p_1_1(X_1, X_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','n_s2_type11_1')).
% 0.19/0.36 tff(29,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.36 tff(30,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.19/0.36 tff(31,plain,(
% 0.19/0.36 ![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))),
% 0.19/0.36 inference(skolemize,[status(sab)],[30])).
% 0.19/0.36 tff(32,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.19/0.36 tff(33,plain,
% 0.19/0.36 ((~p_1_2(a, a)) <=> (~p_1_2(a, a))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(34,axiom,(~p_1_2(a, a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','n_s2_goal_1')).
% 0.19/0.36 tff(35,plain,
% 0.19/0.36 (~p_1_2(a, a)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.36 tff(36,plain,
% 0.19/0.36 (((~![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))) | ((~p_1_1(a, a)) | (~p_2_2(a, a)) | p_1_2(a, a))) <=> ((~![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))) | (~p_1_1(a, a)) | (~p_2_2(a, a)) | p_1_2(a, a))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(37,plain,
% 0.19/0.36 ((~![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))) | ((~p_1_1(a, a)) | (~p_2_2(a, a)) | p_1_2(a, a))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(38,plain,
% 0.19/0.36 ((~![X_2: $i, X_1: $i] : ((~p_1_1(X_1, X_2)) | (~p_2_2(X_1, X_2)) | p_1_2(X_1, X_2))) | (~p_1_1(a, a)) | (~p_2_2(a, a)) | p_1_2(a, a)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.36 tff(39,plain,
% 0.19/0.36 ((~p_1_1(a, a)) | (~p_2_2(a, a))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[38, 35, 32])).
% 0.19/0.36 tff(40,plain,
% 0.19/0.36 (~p_2_2(a, a)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[39, 22])).
% 0.19/0.36 tff(41,plain,
% 0.19/0.36 (^[X_2: $i, X_1: $i] : refl((p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))) <=> (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(42,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))) <=> ![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[41])).
% 0.19/0.36 tff(43,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1))) <=> ![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(44,plain,
% 0.19/0.36 (^[X_2: $i, X_1: $i] : trans(monotonicity(rewrite((p_2_2(X_1, X_2) | (~nq_1(X_1))) <=> (p_2_2(X_1, X_2) | (~nq_1(X_1)))), (((p_2_2(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> ((p_2_2(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))))), rewrite(((p_2_2(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))), (((p_2_2(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(45,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : ((p_2_2(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2))) <=> ![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.36 tff(46,axiom,(![X_2: $i, X_1: $i] : ((p_2_2(X_1, X_2) | (~nq_1(X_1))) | (~nq_2(X_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','n_t2_3')).
% 0.19/0.36 tff(47,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.36 tff(48,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.36 tff(49,plain,(
% 0.19/0.36 ![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[48])).
% 0.19/0.36 tff(50,plain,
% 0.19/0.36 (![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.19/0.36 tff(51,plain,
% 0.19/0.36 (((~![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | (p_2_2(a, a) | (~nq_2(a)) | (~nq_1(a)))) <=> ((~![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | p_2_2(a, a) | (~nq_2(a)) | (~nq_1(a)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(52,plain,
% 0.19/0.36 ((~![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | (p_2_2(a, a) | (~nq_2(a)) | (~nq_1(a)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(53,plain,
% 0.19/0.36 ((~![X_2: $i, X_1: $i] : (p_2_2(X_1, X_2) | (~nq_2(X_2)) | (~nq_1(X_1)))) | p_2_2(a, a) | (~nq_2(a)) | (~nq_1(a))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.36 tff(54,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[53, 50, 7, 4, 40])).
% 0.19/0.36 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------