%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN189-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:38:27 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.52s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SYN189-1 : TPTP v9.0.0. Released v1.1.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 12:29:38 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.52 % SZS status Unsatisfiable
% 0.23/0.52 % SZS output start Proof
% 0.23/0.52 tff(r1_type, type, (
% 0.23/0.52 r1: $i > $o)).
% 0.23/0.52 tff(c_type, type, (
% 0.23/0.52 c: $i)).
% 0.23/0.52 tff(r2_type, type, (
% 0.23/0.52 r2: $i > $o)).
% 0.23/0.52 tff(l0_type, type, (
% 0.23/0.52 l0: $i > $o)).
% 0.23/0.52 tff(q1_type, type, (
% 0.23/0.52 q1: ( $i * $i * $i ) > $o)).
% 0.23/0.52 tff(d_type, type, (
% 0.23/0.52 d: $i)).
% 0.23/0.52 tff(s0_type, type, (
% 0.23/0.52 s0: $i > $o)).
% 0.23/0.52 tff(q0_type, type, (
% 0.23/0.52 q0: ( $i * $i ) > $o)).
% 0.23/0.52 tff(k0_type, type, (
% 0.23/0.52 k0: $i > $o)).
% 0.23/0.52 tff(e_type, type, (
% 0.23/0.52 e: $i)).
% 0.23/0.52 tff(1,plain,
% 0.23/0.52 ((~r2(c)) <=> (~r2(c))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(2,axiom,(~r2(c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.23/0.52 tff(3,plain,
% 0.23/0.52 (~r2(c)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.23/0.52 tff(4,plain,
% 0.23/0.52 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(5,plain,
% 0.23/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[4])).
% 0.23/0.52 tff(6,plain,
% 0.23/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(7,plain,
% 0.23/0.52 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(8,plain,
% 0.23/0.52 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[7])).
% 0.23/0.52 tff(9,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.23/0.52 tff(10,plain,
% 0.23/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.23/0.52 tff(11,plain,
% 0.23/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.23/0.52 tff(12,plain,(
% 0.23/0.52 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.23/0.52 inference(skolemize,[status(sab)],[11])).
% 0.23/0.52 tff(13,plain,
% 0.23/0.52 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.23/0.52 tff(14,plain,
% 0.23/0.52 (l0(c) <=> l0(c)),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(15,axiom,(l0(c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.23/0.52 tff(16,plain,
% 0.23/0.52 (l0(c)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.23/0.52 tff(17,plain,
% 0.23/0.52 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | r2(c) | (~r1(c)))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(c)) | r2(c) | (~r1(c)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(18,plain,
% 0.23/0.52 (((~l0(c)) | (~r1(c)) | r2(c)) <=> ((~l0(c)) | r2(c) | (~r1(c)))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(19,plain,
% 0.23/0.52 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | (~r1(c)) | r2(c))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | r2(c) | (~r1(c))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[18])).
% 0.23/0.52 tff(20,plain,
% 0.23/0.52 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | (~r1(c)) | r2(c))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(c)) | r2(c) | (~r1(c)))),
% 0.23/0.52 inference(transitivity,[status(thm)],[19, 17])).
% 0.23/0.52 tff(21,plain,
% 0.23/0.52 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | (~r1(c)) | r2(c))),
% 0.23/0.52 inference(quant_inst,[status(thm)],[])).
% 0.23/0.52 tff(22,plain,
% 0.23/0.52 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(c)) | r2(c) | (~r1(c))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.23/0.52 tff(23,plain,
% 0.23/0.52 (~r1(c)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[22, 16, 13, 3])).
% 0.23/0.52 tff(24,plain,
% 0.23/0.52 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(25,plain,
% 0.23/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[24])).
% 0.23/0.52 tff(26,plain,
% 0.23/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(27,plain,
% 0.23/0.52 (^[D: $i, E: $i] : trans(monotonicity(rewrite(((r1(D) | (~q0(D, E))) | (~s0(d))) <=> ((~q0(D, E)) | (~s0(d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> (((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))))), rewrite((((~q0(D, E)) | (~s0(d)) | r1(D)) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))), ((((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(28,plain,
% 0.23/0.52 (![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d))) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.23/0.52 inference(quant_intro,[status(thm)],[27])).
% 0.23/0.52 tff(29,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.23/0.52 tff(30,plain,
% 0.23/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.23/0.52 tff(31,plain,
% 0.23/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.23/0.52 tff(32,plain,(
% 0.23/0.52 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.23/0.52 inference(skolemize,[status(sab)],[31])).
% 0.23/0.52 tff(33,plain,
% 0.23/0.52 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.23/0.52 tff(34,plain,
% 0.23/0.52 (k0(e) <=> k0(e)),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(35,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.23/0.52 tff(36,plain,
% 0.23/0.52 (k0(e)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.23/0.52 tff(37,plain,
% 0.23/0.52 (s0(d) <=> s0(d)),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(38,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.23/0.52 tff(39,plain,
% 0.23/0.52 (s0(d)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.23/0.52 tff(40,plain,
% 0.23/0.52 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(41,plain,
% 0.23/0.52 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(42,plain,
% 0.23/0.52 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(43,plain,
% 0.23/0.52 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[42])).
% 0.23/0.52 tff(44,plain,
% 0.23/0.52 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.23/0.52 inference(transitivity,[status(thm)],[43, 41])).
% 0.23/0.52 tff(45,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.23/0.52 tff(46,plain,
% 0.23/0.52 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.23/0.52 tff(47,plain,
% 0.23/0.52 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.23/0.52 tff(48,plain,
% 0.23/0.52 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.23/0.52 tff(49,plain,
% 0.23/0.52 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.23/0.52 tff(50,plain,
% 0.23/0.52 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[49, 40])).
% 0.23/0.52 tff(51,plain,
% 0.23/0.52 (q1(d, d, d)),
% 0.23/0.52 inference(unit_resolution,[status(thm)],[50, 39, 36])).
% 0.23/0.52 tff(52,assumption,(~q0(c, d)), introduced(assumption)).
% 0.23/0.52 tff(53,plain,
% 0.23/0.52 (^[X: $i] : refl(q0(X, d) <=> q0(X, d))),
% 0.23/0.52 inference(bind,[status(th)],[])).
% 0.23/0.52 tff(54,plain,
% 0.23/0.52 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.23/0.52 inference(quant_intro,[status(thm)],[53])).
% 0.23/0.52 tff(55,plain,
% 0.23/0.52 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.23/0.52 inference(rewrite,[status(thm)],[])).
% 0.23/0.52 tff(56,axiom,(![X: $i] : q0(X, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_17')).
% 0.23/0.52 tff(57,plain,
% 0.23/0.52 (![X: $i] : q0(X, d)),
% 0.23/0.52 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.23/0.52 tff(58,plain,(
% 0.23/0.52 ![X: $i] : q0(X, d)),
% 0.23/0.52 inference(skolemize,[status(sab)],[57])).
% 0.23/0.52 tff(59,plain,
% 0.23/0.52 (![X: $i] : q0(X, d)),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.23/0.53 tff(60,plain,
% 0.23/0.53 ((~![X: $i] : q0(X, d)) | q0(c, d)),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(61,plain,
% 0.23/0.53 ($false),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[60, 59, 52])).
% 0.23/0.53 tff(62,plain,(q0(c, d)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.53 tff(63,plain,
% 0.23/0.53 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(64,plain,
% 0.23/0.53 (((~q0(c, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(c)) <=> ((~s0(d)) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(65,plain,
% 0.23/0.53 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(c, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(c))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c)))),
% 0.23/0.53 inference(monotonicity,[status(thm)],[64])).
% 0.23/0.53 tff(66,plain,
% 0.23/0.53 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(c, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(c))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c))),
% 0.23/0.53 inference(transitivity,[status(thm)],[65, 63])).
% 0.23/0.53 tff(67,plain,
% 0.23/0.53 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(c, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(c))),
% 0.23/0.53 inference(quant_inst,[status(thm)],[])).
% 0.23/0.53 tff(68,plain,
% 0.23/0.53 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c)),
% 0.23/0.53 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.23/0.53 tff(69,plain,
% 0.23/0.53 ($false),
% 0.23/0.53 inference(unit_resolution,[status(thm)],[68, 39, 62, 51, 33, 23])).
% 0.23/0.53 % SZS output end Proof
% 0.23/0.53 % E exiting
%------------------------------------------------------------------------------