%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN138-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:38:19 AM UTC 2025
% Result : Unsatisfiable 0.49s 0.65s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN138-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.11 % 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 12:27:53 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.49/0.65 % SZS status Unsatisfiable
% 0.49/0.65 % SZS output start Proof
% 0.49/0.65 tff(m1_type, type, (
% 0.49/0.65 m1: ( $i * $i * $i ) > $o)).
% 0.49/0.65 tff(c_type, type, (
% 0.49/0.65 c: $i)).
% 0.49/0.65 tff(e_type, type, (
% 0.49/0.65 e: $i)).
% 0.49/0.65 tff(k1_type, type, (
% 0.49/0.65 k1: $i > $o)).
% 0.49/0.65 tff(n0_type, type, (
% 0.49/0.65 n0: ( $i * $i ) > $o)).
% 0.49/0.65 tff(d_type, type, (
% 0.49/0.65 d: $i)).
% 0.49/0.65 tff(k2_type, type, (
% 0.49/0.65 k2: ( $i * $i ) > $o)).
% 0.49/0.65 tff(r2_type, type, (
% 0.49/0.65 r2: $i > $o)).
% 0.49/0.65 tff(r1_type, type, (
% 0.49/0.65 r1: $i > $o)).
% 0.49/0.65 tff(q1_type, type, (
% 0.49/0.65 q1: ( $i * $i * $i ) > $o)).
% 0.49/0.65 tff(s0_type, type, (
% 0.49/0.65 s0: $i > $o)).
% 0.49/0.65 tff(q0_type, type, (
% 0.49/0.65 q0: ( $i * $i ) > $o)).
% 0.49/0.65 tff(k0_type, type, (
% 0.49/0.65 k0: $i > $o)).
% 0.49/0.65 tff(l0_type, type, (
% 0.49/0.65 l0: $i > $o)).
% 0.49/0.65 tff(m3_type, type, (
% 0.49/0.65 m3: ( $i * $i * $i ) > $o)).
% 0.49/0.65 tff(l1_type, type, (
% 0.49/0.65 l1: ( $i * $i ) > $o)).
% 0.49/0.65 tff(1,plain,
% 0.49/0.65 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(2,plain,
% 0.49/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[1])).
% 0.49/0.65 tff(3,plain,
% 0.49/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(4,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.49/0.65 tff(5,plain,
% 0.49/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.49/0.65 tff(6,plain,(
% 0.49/0.65 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.49/0.65 inference(skolemize,[status(sab)],[5])).
% 0.49/0.65 tff(7,plain,
% 0.49/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.49/0.65 tff(8,plain,
% 0.49/0.65 (n0(d, e) <=> n0(d, e)),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(9,axiom,(n0(d, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_3')).
% 0.49/0.65 tff(10,plain,
% 0.49/0.65 (n0(d, e)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.49/0.65 tff(11,plain,
% 0.49/0.65 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(12,plain,
% 0.49/0.65 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(13,plain,
% 0.49/0.65 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.49/0.65 tff(14,plain,
% 0.49/0.65 (k1(e)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.49/0.65 tff(15,plain,
% 0.49/0.65 (^[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)))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(16,plain,
% 0.49/0.65 (![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))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[15])).
% 0.49/0.65 tff(17,plain,
% 0.49/0.65 (![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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(18,plain,
% 0.49/0.65 (^[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))))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(19,plain,
% 0.49/0.65 (![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))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[18])).
% 0.49/0.65 tff(20,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')).
% 0.49/0.65 tff(21,plain,
% 0.49/0.65 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.49/0.65 tff(22,plain,
% 0.49/0.65 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.49/0.65 tff(23,plain,(
% 0.49/0.65 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.49/0.65 inference(skolemize,[status(sab)],[22])).
% 0.49/0.65 tff(24,plain,
% 0.49/0.65 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.49/0.65 tff(25,plain,
% 0.49/0.65 (k0(e) <=> k0(e)),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(26,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.49/0.65 tff(27,plain,
% 0.49/0.65 (k0(e)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.49/0.65 tff(28,plain,
% 0.49/0.65 (s0(d) <=> s0(d)),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(29,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.49/0.65 tff(30,plain,
% 0.49/0.65 (s0(d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.49/0.65 tff(31,plain,
% 0.49/0.65 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(32,plain,
% 0.49/0.65 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(33,plain,
% 0.49/0.65 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(34,plain,
% 0.49/0.65 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[33])).
% 0.49/0.65 tff(35,plain,
% 0.49/0.65 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.49/0.65 inference(transitivity,[status(thm)],[34, 32])).
% 0.49/0.65 tff(36,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.49/0.65 tff(37,plain,
% 0.49/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.49/0.65 tff(38,plain,
% 0.49/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.49/0.65 tff(39,plain,
% 0.49/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.49/0.65 tff(40,plain,
% 0.49/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[39, 31])).
% 0.49/0.65 tff(41,plain,
% 0.49/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[40, 31])).
% 0.49/0.65 tff(42,plain,
% 0.49/0.65 (q1(d, d, d)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[41, 30, 27])).
% 0.49/0.65 tff(43,assumption,(~q0(c, d)), introduced(assumption)).
% 0.49/0.65 tff(44,plain,
% 0.49/0.65 (^[X: $i] : refl(q0(X, d) <=> q0(X, d))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(45,plain,
% 0.49/0.65 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.49/0.65 inference(quant_intro,[status(thm)],[44])).
% 0.49/0.65 tff(46,plain,
% 0.49/0.65 (![X: $i] : q0(X, d) <=> ![X: $i] : q0(X, d)),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(47,axiom,(![X: $i] : q0(X, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_17')).
% 0.49/0.65 tff(48,plain,
% 0.49/0.65 (![X: $i] : q0(X, d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.49/0.65 tff(49,plain,(
% 0.49/0.65 ![X: $i] : q0(X, d)),
% 0.49/0.65 inference(skolemize,[status(sab)],[48])).
% 0.49/0.65 tff(50,plain,
% 0.49/0.65 (![X: $i] : q0(X, d)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.49/0.65 tff(51,plain,
% 0.49/0.65 ((~![X: $i] : q0(X, d)) | q0(c, d)),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(52,plain,
% 0.49/0.65 ($false),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[51, 50, 43])).
% 0.49/0.65 tff(53,plain,(q0(c, d)), inference(lemma,lemma(discharge,[]))).
% 0.49/0.65 tff(54,plain,
% 0.49/0.65 (((~![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))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(55,plain,
% 0.49/0.65 (((~q0(c, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(c)) <=> ((~s0(d)) | (~q0(c, d)) | (~q1(d, d, d)) | r1(c))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(56,plain,
% 0.49/0.65 (((~![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)))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[55])).
% 0.49/0.65 tff(57,plain,
% 0.49/0.65 (((~![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))),
% 0.49/0.65 inference(transitivity,[status(thm)],[56, 54])).
% 0.49/0.65 tff(58,plain,
% 0.49/0.65 ((~![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))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(59,plain,
% 0.49/0.65 ((~![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)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.49/0.65 tff(60,plain,
% 0.49/0.65 (r1(c)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[59, 30, 53, 42, 24])).
% 0.49/0.65 tff(61,plain,
% 0.49/0.65 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(62,plain,
% 0.49/0.65 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[61])).
% 0.49/0.65 tff(63,plain,
% 0.49/0.65 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(64,plain,
% 0.49/0.65 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.49/0.65 inference(bind,[status(th)],[])).
% 0.49/0.65 tff(65,plain,
% 0.49/0.65 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.49/0.65 inference(quant_intro,[status(thm)],[64])).
% 0.49/0.65 tff(66,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.49/0.65 tff(67,plain,
% 0.49/0.65 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.49/0.65 tff(68,plain,
% 0.49/0.65 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.49/0.65 tff(69,plain,(
% 0.49/0.65 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.49/0.65 inference(skolemize,[status(sab)],[68])).
% 0.49/0.65 tff(70,plain,
% 0.49/0.65 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.49/0.65 tff(71,plain,
% 0.49/0.65 (l0(c) <=> l0(c)),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(72,axiom,(l0(c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.49/0.65 tff(73,plain,
% 0.49/0.65 (l0(c)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.49/0.65 tff(74,plain,
% 0.49/0.65 (((~![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)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(75,plain,
% 0.49/0.65 (((~l0(c)) | (~r1(c)) | r2(c)) <=> ((~l0(c)) | r2(c) | (~r1(c)))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(76,plain,
% 0.49/0.65 (((~![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))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[75])).
% 0.49/0.65 tff(77,plain,
% 0.49/0.65 (((~![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)))),
% 0.49/0.65 inference(transitivity,[status(thm)],[76, 74])).
% 0.49/0.65 tff(78,plain,
% 0.49/0.65 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(c)) | (~r1(c)) | r2(c))),
% 0.49/0.65 inference(quant_inst,[status(thm)],[])).
% 0.49/0.65 tff(79,plain,
% 0.49/0.65 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(c)) | r2(c) | (~r1(c))),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.49/0.65 tff(80,plain,
% 0.49/0.65 (r2(c) | (~r1(c))),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[79, 73, 70])).
% 0.49/0.65 tff(81,plain,
% 0.49/0.65 (r2(c)),
% 0.49/0.65 inference(unit_resolution,[status(thm)],[80, 60])).
% 0.49/0.65 tff(82,plain,
% 0.49/0.65 ((~m3(c, e, c)) <=> (~m3(c, e, c))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(83,axiom,(~m3(c, e, c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.49/0.65 tff(84,plain,
% 0.49/0.65 (~m3(c, e, c)),
% 0.49/0.65 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.49/0.65 tff(85,plain,
% 0.49/0.65 (^[I: $i, H: $i] : refl(((~r2(H)) | (~k2(c, I)) | m3(H, I, H)) <=> ((~r2(H)) | (~k2(c, I)) | m3(H, I, H)))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(86,plain,
% 0.49/0.66 (![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H)) <=> ![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[85])).
% 0.49/0.66 tff(87,plain,
% 0.49/0.66 (![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H)) <=> ![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(88,plain,
% 0.49/0.66 (^[I: $i, H: $i] : trans(monotonicity(rewrite((m3(H, I, H) | (~r2(H))) <=> ((~r2(H)) | m3(H, I, H))), (((m3(H, I, H) | (~r2(H))) | (~k2(c, I))) <=> (((~r2(H)) | m3(H, I, H)) | (~k2(c, I))))), rewrite((((~r2(H)) | m3(H, I, H)) | (~k2(c, I))) <=> ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))), (((m3(H, I, H) | (~r2(H))) | (~k2(c, I))) <=> ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(89,plain,
% 0.49/0.66 (![I: $i, H: $i] : ((m3(H, I, H) | (~r2(H))) | (~k2(c, I))) <=> ![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[88])).
% 0.49/0.66 tff(90,axiom,(![I: $i, H: $i] : ((m3(H, I, H) | (~r2(H))) | (~k2(c, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_231')).
% 0.49/0.66 tff(91,plain,
% 0.49/0.66 (![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.49/0.66 tff(92,plain,
% 0.49/0.66 (![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.49/0.66 tff(93,plain,(
% 0.49/0.66 ![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))),
% 0.49/0.66 inference(skolemize,[status(sab)],[92])).
% 0.49/0.66 tff(94,plain,
% 0.49/0.66 (![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.49/0.66 tff(95,plain,
% 0.49/0.66 (((~![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))) | ((~r2(c)) | (~k2(c, e)) | m3(c, e, c))) <=> ((~![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))) | (~r2(c)) | (~k2(c, e)) | m3(c, e, c))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(96,plain,
% 0.49/0.66 ((~![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))) | ((~r2(c)) | (~k2(c, e)) | m3(c, e, c))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(97,plain,
% 0.49/0.66 ((~![I: $i, H: $i] : ((~r2(H)) | (~k2(c, I)) | m3(H, I, H))) | (~r2(c)) | (~k2(c, e)) | m3(c, e, c)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.49/0.66 tff(98,plain,
% 0.49/0.66 ((~r2(c)) | (~k2(c, e))),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[97, 94, 84])).
% 0.49/0.66 tff(99,plain,
% 0.49/0.66 (~k2(c, e)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[98, 81])).
% 0.49/0.66 tff(100,plain,
% 0.49/0.66 (^[H: $i, G: $i] : refl(((~n0(H, G)) | l1(G, G)) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(101,plain,
% 0.49/0.66 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[100])).
% 0.49/0.66 tff(102,plain,
% 0.49/0.66 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G)) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(103,plain,
% 0.49/0.66 (^[H: $i, G: $i] : rewrite((l1(G, G) | (~n0(H, G))) <=> ((~n0(H, G)) | l1(G, G)))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(104,plain,
% 0.49/0.66 (![H: $i, G: $i] : (l1(G, G) | (~n0(H, G))) <=> ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[103])).
% 0.49/0.66 tff(105,axiom,(![H: $i, G: $i] : (l1(G, G) | (~n0(H, G)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_002')).
% 0.49/0.66 tff(106,plain,
% 0.49/0.66 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.49/0.66 tff(107,plain,
% 0.49/0.66 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.49/0.66 tff(108,plain,(
% 0.49/0.66 ![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.49/0.66 inference(skolemize,[status(sab)],[107])).
% 0.49/0.66 tff(109,plain,
% 0.49/0.66 (![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.49/0.66 tff(110,plain,
% 0.49/0.66 (((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(d, e)) | l1(e, e))) <=> ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(d, e)) | l1(e, e))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(111,plain,
% 0.49/0.66 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | ((~n0(d, e)) | l1(e, e))),
% 0.49/0.66 inference(quant_inst,[status(thm)],[])).
% 0.49/0.66 tff(112,plain,
% 0.49/0.66 ((~![H: $i, G: $i] : ((~n0(H, G)) | l1(G, G))) | (~n0(d, e)) | l1(e, e)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.49/0.66 tff(113,plain,
% 0.49/0.66 (l1(e, e)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[112, 10, 109])).
% 0.49/0.66 tff(114,plain,
% 0.49/0.66 (((~l1(e, e)) | k2(e, e)) <=> ((~l1(e, e)) | k2(e, e))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(115,plain,
% 0.49/0.66 ((k2(e, e) | (~l1(e, e))) <=> ((~l1(e, e)) | k2(e, e))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(116,axiom,(k2(e, e) | (~l1(e, e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_130')).
% 0.49/0.66 tff(117,plain,
% 0.49/0.66 ((~l1(e, e)) | k2(e, e)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.49/0.66 tff(118,plain,
% 0.49/0.66 ((~l1(e, e)) | k2(e, e)),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.49/0.66 tff(119,plain,
% 0.49/0.66 (k2(e, e)),
% 0.49/0.66 inference(unit_resolution,[status(thm)],[118, 113])).
% 0.49/0.66 tff(120,plain,
% 0.49/0.66 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(121,plain,
% 0.49/0.66 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[120])).
% 0.49/0.66 tff(122,plain,
% 0.49/0.66 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(123,plain,
% 0.49/0.66 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k2(C, D) | (~m1(E, D, C))) <=> ((~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> (((~m1(E, D, C)) | k2(C, D)) | (~k1(F))))), rewrite((((~m1(E, D, C)) | k2(C, D)) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D))), (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) <=> ((~k1(F)) | (~m1(E, D, C)) | k2(C, D)))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> (((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))))), rewrite((((~k1(F)) | (~m1(E, D, C)) | k2(C, D)) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))), ((((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))))),
% 0.49/0.66 inference(bind,[status(th)],[])).
% 0.49/0.66 tff(124,plain,
% 0.49/0.66 (![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.49/0.66 inference(quant_intro,[status(thm)],[123])).
% 0.49/0.66 tff(125,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((k2(C, D) | (~m1(E, D, C))) | (~k1(F))) | (~k2(F, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_127')).
% 0.49/0.66 tff(126,plain,
% 0.49/0.66 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.49/0.66 tff(127,plain,
% 0.49/0.66 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.49/0.66 tff(128,plain,(
% 0.49/0.66 ![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.49/0.66 inference(skolemize,[status(sab)],[127])).
% 0.49/0.66 tff(129,plain,
% 0.49/0.66 (![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))),
% 0.49/0.66 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.49/0.66 tff(130,plain,
% 0.49/0.66 (((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(e)) | (~k2(e, e)) | (~m1(c, e, c)) | k2(c, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(e)) | (~k2(e, e)) | (~m1(c, e, c)) | k2(c, e))),
% 0.49/0.66 inference(rewrite,[status(thm)],[])).
% 0.49/0.66 tff(131,plain,
% 0.49/0.66 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | ((~k1(e)) | (~k2(e, e)) | (~m1(c, e, c)) | k2(c, e))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(132,plain,
% 0.49/0.67 ((~![D: $i, E: $i, F: $i, C: $i] : ((~k1(F)) | (~k2(F, D)) | (~m1(E, D, C)) | k2(C, D))) | (~k1(e)) | (~k2(e, e)) | (~m1(c, e, c)) | k2(c, e)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.49/0.67 tff(133,plain,
% 0.49/0.67 (~m1(c, e, c)),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[132, 129, 119, 99, 14])).
% 0.49/0.67 tff(134,plain,
% 0.49/0.67 (^[I: $i, J: $i] : refl((m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> (m1(I, J, I) | (~l0(I)) | (~k0(J))))),
% 0.49/0.67 inference(bind,[status(th)],[])).
% 0.49/0.67 tff(135,plain,
% 0.49/0.67 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.49/0.67 inference(quant_intro,[status(thm)],[134])).
% 0.49/0.67 tff(136,plain,
% 0.49/0.67 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(137,plain,
% 0.49/0.67 (^[I: $i, J: $i] : trans(monotonicity(rewrite((m1(I, J, I) | (~l0(I))) <=> (m1(I, J, I) | (~l0(I)))), (((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> ((m1(I, J, I) | (~l0(I))) | (~k0(J))))), rewrite(((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> (m1(I, J, I) | (~l0(I)) | (~k0(J)))), (((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> (m1(I, J, I) | (~l0(I)) | (~k0(J)))))),
% 0.49/0.67 inference(bind,[status(th)],[])).
% 0.49/0.67 tff(138,plain,
% 0.49/0.67 (![I: $i, J: $i] : ((m1(I, J, I) | (~l0(I))) | (~k0(J))) <=> ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.49/0.67 inference(quant_intro,[status(thm)],[137])).
% 0.49/0.67 tff(139,axiom,(![I: $i, J: $i] : ((m1(I, J, I) | (~l0(I))) | (~k0(J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_021')).
% 0.49/0.67 tff(140,plain,
% 0.49/0.67 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.49/0.67 tff(141,plain,
% 0.49/0.67 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.49/0.67 tff(142,plain,(
% 0.49/0.67 ![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.49/0.67 inference(skolemize,[status(sab)],[141])).
% 0.49/0.67 tff(143,plain,
% 0.49/0.67 (![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.49/0.67 tff(144,plain,
% 0.49/0.67 (((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | ((~l0(c)) | (~k0(e)) | m1(c, e, c))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (~l0(c)) | (~k0(e)) | m1(c, e, c))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(145,plain,
% 0.49/0.67 ((m1(c, e, c) | (~l0(c)) | (~k0(e))) <=> ((~l0(c)) | (~k0(e)) | m1(c, e, c))),
% 0.49/0.67 inference(rewrite,[status(thm)],[])).
% 0.49/0.67 tff(146,plain,
% 0.49/0.67 (((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (m1(c, e, c) | (~l0(c)) | (~k0(e)))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | ((~l0(c)) | (~k0(e)) | m1(c, e, c)))),
% 0.49/0.67 inference(monotonicity,[status(thm)],[145])).
% 0.49/0.67 tff(147,plain,
% 0.49/0.67 (((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (m1(c, e, c) | (~l0(c)) | (~k0(e)))) <=> ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (~l0(c)) | (~k0(e)) | m1(c, e, c))),
% 0.49/0.67 inference(transitivity,[status(thm)],[146, 144])).
% 0.49/0.67 tff(148,plain,
% 0.49/0.67 ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (m1(c, e, c) | (~l0(c)) | (~k0(e)))),
% 0.49/0.67 inference(quant_inst,[status(thm)],[])).
% 0.49/0.67 tff(149,plain,
% 0.49/0.67 ((~![I: $i, J: $i] : (m1(I, J, I) | (~l0(I)) | (~k0(J)))) | (~l0(c)) | (~k0(e)) | m1(c, e, c)),
% 0.49/0.67 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.49/0.67 tff(150,plain,
% 0.49/0.67 ($false),
% 0.49/0.67 inference(unit_resolution,[status(thm)],[149, 73, 27, 143, 133])).
% 0.49/0.67 % SZS output end Proof
% 0.49/0.67 % E exiting
%------------------------------------------------------------------------------