%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN202-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:29 AM UTC 2025
% Result : Unsatisfiable 0.43s 0.60s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN202-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.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 12:29:42 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.43/0.60 % SZS status Unsatisfiable
% 0.43/0.60 % SZS output start Proof
% 0.43/0.60 tff(m0_type, type, (
% 0.43/0.60 m0: ( $i * $i * $i ) > $o)).
% 0.43/0.60 tff(b_type, type, (
% 0.43/0.60 b: $i)).
% 0.43/0.60 tff(d_type, type, (
% 0.43/0.60 d: $i)).
% 0.43/0.60 tff(a_type, type, (
% 0.43/0.60 a: $i)).
% 0.43/0.60 tff(q2_type, type, (
% 0.43/0.60 q2: ( $i * $i * $i ) > $o)).
% 0.43/0.60 tff(e_type, type, (
% 0.43/0.60 e: $i)).
% 0.43/0.60 tff(s1_type, type, (
% 0.43/0.60 s1: $i > $o)).
% 0.43/0.60 tff(p0_type, type, (
% 0.43/0.60 p0: ( $i * $i ) > $o)).
% 0.43/0.60 tff(s2_type, type, (
% 0.43/0.60 s2: $i > $o)).
% 0.43/0.60 tff(p1_type, type, (
% 0.43/0.60 p1: ( $i * $i * $i ) > $o)).
% 0.43/0.60 tff(k0_type, type, (
% 0.43/0.60 k0: $i > $o)).
% 0.43/0.60 tff(r0_type, type, (
% 0.43/0.60 r0: $i > $o)).
% 0.43/0.60 tff(r1_type, type, (
% 0.43/0.60 r1: $i > $o)).
% 0.43/0.60 tff(q1_type, type, (
% 0.43/0.60 q1: ( $i * $i * $i ) > $o)).
% 0.43/0.60 tff(s0_type, type, (
% 0.43/0.60 s0: $i > $o)).
% 0.43/0.60 tff(q0_type, type, (
% 0.43/0.60 q0: ( $i * $i ) > $o)).
% 0.43/0.60 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.43/0.60 tff(2,plain,
% 0.43/0.60 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(3,plain,
% 0.43/0.60 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.43/0.60 inference(quant_intro,[status(thm)],[2])).
% 0.43/0.60 tff(4,plain,
% 0.43/0.60 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.43/0.60 tff(6,plain,
% 0.43/0.60 (![X: $i] : p0(b, X)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.43/0.60 tff(7,plain,(
% 0.43/0.60 ![X: $i] : p0(b, X)),
% 0.43/0.60 inference(skolemize,[status(sab)],[6])).
% 0.43/0.60 tff(8,plain,
% 0.43/0.60 (![X: $i] : p0(b, X)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.43/0.60 tff(9,plain,
% 0.43/0.60 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(10,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.43/0.60 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.43/0.60 tff(12,plain,
% 0.43/0.60 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(13,plain,
% 0.43/0.60 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[12])).
% 0.43/0.60 tff(14,plain,
% 0.43/0.60 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.43/0.60 tff(16,plain,
% 0.43/0.60 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.43/0.60 tff(17,plain,(
% 0.43/0.60 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[16])).
% 0.43/0.60 tff(18,plain,
% 0.43/0.60 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.43/0.60 tff(19,plain,
% 0.43/0.60 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(20,plain,
% 0.43/0.60 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(21,plain,
% 0.43/0.60 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.43/0.60 tff(22,plain,
% 0.43/0.60 (s1(b)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.43/0.60 tff(23,plain,
% 0.43/0.60 ((~s2(e)) <=> (~s2(e))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(24,axiom,(~s2(e)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.43/0.60 tff(25,plain,
% 0.43/0.60 (~s2(e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.43/0.60 tff(26,plain,
% 0.43/0.60 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(27,plain,
% 0.43/0.60 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[26])).
% 0.43/0.60 tff(28,plain,
% 0.43/0.60 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(29,plain,
% 0.43/0.60 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(30,plain,
% 0.43/0.60 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[29])).
% 0.43/0.60 tff(31,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.43/0.60 tff(32,plain,
% 0.43/0.60 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.43/0.60 tff(33,plain,
% 0.43/0.60 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.43/0.60 tff(34,plain,(
% 0.43/0.60 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[33])).
% 0.43/0.60 tff(35,plain,
% 0.43/0.60 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.43/0.60 tff(36,plain,
% 0.43/0.60 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(e) | (~q2(b, e, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(e) | (~q2(b, e, b)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(37,plain,
% 0.43/0.60 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(e) | (~q2(b, e, b)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(38,plain,
% 0.43/0.60 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(e) | (~q2(b, e, b))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.43/0.60 tff(39,plain,
% 0.43/0.60 ((~s1(b)) | (~q2(b, e, b))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 0.43/0.60 tff(40,plain,
% 0.43/0.60 (~q2(b, e, b)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[39, 22])).
% 0.43/0.60 tff(41,plain,
% 0.43/0.60 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(42,plain,
% 0.43/0.60 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[41])).
% 0.43/0.60 tff(43,plain,
% 0.43/0.60 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(44,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.43/0.60 tff(45,plain,
% 0.43/0.60 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.43/0.60 tff(46,plain,(
% 0.43/0.60 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[45])).
% 0.43/0.60 tff(47,plain,
% 0.43/0.60 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.43/0.60 tff(48,plain,
% 0.43/0.60 (k0(e) <=> k0(e)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(49,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.43/0.60 tff(50,plain,
% 0.43/0.60 (k0(e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.43/0.60 tff(51,plain,
% 0.43/0.60 (r0(e) <=> r0(e)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(52,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.43/0.60 tff(53,plain,
% 0.43/0.60 (r0(e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.43/0.60 tff(54,plain,
% 0.43/0.60 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(55,plain,
% 0.43/0.60 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(56,plain,
% 0.43/0.60 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(57,plain,
% 0.43/0.60 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[56])).
% 0.43/0.60 tff(58,plain,
% 0.43/0.60 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.43/0.60 inference(transitivity,[status(thm)],[57, 55])).
% 0.43/0.60 tff(59,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.43/0.60 tff(60,plain,
% 0.43/0.60 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.43/0.60 tff(61,plain,
% 0.43/0.60 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[60, 54])).
% 0.43/0.60 tff(62,plain,
% 0.43/0.60 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.43/0.60 tff(63,plain,
% 0.43/0.60 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[62, 54])).
% 0.43/0.60 tff(64,plain,
% 0.43/0.60 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[63, 54])).
% 0.43/0.60 tff(65,plain,
% 0.43/0.60 (p1(e, e, e)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[64, 53, 50])).
% 0.43/0.60 tff(66,plain,
% 0.43/0.60 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(67,plain,
% 0.43/0.60 ((q2(e, e, e) | (~p1(e, e, e))) <=> ((~p1(e, e, e)) | q2(e, e, e))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(68,plain,
% 0.43/0.60 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(e, e, e)) | q2(e, e, e)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[67])).
% 0.43/0.60 tff(69,plain,
% 0.43/0.60 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e))),
% 0.43/0.60 inference(transitivity,[status(thm)],[68, 66])).
% 0.43/0.60 tff(70,plain,
% 0.43/0.60 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(71,plain,
% 0.43/0.60 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.43/0.60 tff(72,plain,
% 0.43/0.60 (q2(e, e, e)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[71, 65, 47])).
% 0.43/0.60 tff(73,plain,
% 0.43/0.60 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(74,plain,
% 0.43/0.60 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[73])).
% 0.43/0.60 tff(75,plain,
% 0.43/0.60 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(76,plain,
% 0.43/0.60 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((q2(C, D, C) | (~r1(D))) <=> ((~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> (((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))))), rewrite((((~r1(D)) | q2(C, D, C)) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C))), (((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) <=> ((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> (((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))))), rewrite((((~m0(E, F, C)) | (~r1(D)) | q2(C, D, C)) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) <=> ((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> (((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))))), rewrite((((~m0(E, F, C)) | (~k0(D)) | (~r1(D)) | q2(C, D, C)) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))), (((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(77,plain,
% 0.43/0.60 (![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[76])).
% 0.43/0.60 tff(78,axiom,(![D: $i, E: $i, F: $i, C: $i] : ((((q2(C, D, C) | (~r1(D))) | (~m0(E, F, C))) | (~k0(D))) | (~q2(D, D, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 0.43/0.60 tff(79,plain,
% 0.43/0.60 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.43/0.60 tff(80,plain,
% 0.43/0.60 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.43/0.60 tff(81,plain,(
% 0.43/0.60 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.43/0.60 inference(skolemize,[status(sab)],[80])).
% 0.43/0.60 tff(82,plain,
% 0.43/0.60 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.43/0.60 tff(83,plain,
% 0.43/0.60 (^[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)))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(84,plain,
% 0.43/0.60 (![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))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[83])).
% 0.43/0.60 tff(85,plain,
% 0.43/0.60 (![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))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(86,plain,
% 0.43/0.60 (^[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))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(87,plain,
% 0.43/0.60 (![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))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[86])).
% 0.43/0.60 tff(88,axiom,(![D: $i, E: $i] : (((r1(D) | (~q0(D, E))) | (~s0(d))) | (~q1(d, E, d)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_124')).
% 0.43/0.60 tff(89,plain,
% 0.43/0.60 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.43/0.60 tff(90,plain,
% 0.43/0.60 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.43/0.60 tff(91,plain,(
% 0.43/0.60 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.43/0.60 inference(skolemize,[status(sab)],[90])).
% 0.43/0.60 tff(92,plain,
% 0.43/0.60 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.43/0.60 tff(93,plain,
% 0.43/0.60 (s0(d) <=> s0(d)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(94,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.43/0.60 tff(95,plain,
% 0.43/0.60 (s0(d)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.43/0.60 tff(96,plain,
% 0.43/0.60 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(97,plain,
% 0.43/0.60 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(98,plain,
% 0.43/0.60 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(99,plain,
% 0.43/0.60 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[98])).
% 0.43/0.60 tff(100,plain,
% 0.43/0.60 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.43/0.60 inference(transitivity,[status(thm)],[99, 97])).
% 0.43/0.60 tff(101,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.43/0.60 tff(102,plain,
% 0.43/0.60 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.43/0.60 tff(103,plain,
% 0.43/0.60 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[102, 96])).
% 0.43/0.60 tff(104,plain,
% 0.43/0.60 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.43/0.60 tff(105,plain,
% 0.43/0.60 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[104, 96])).
% 0.43/0.60 tff(106,plain,
% 0.43/0.60 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[105, 96])).
% 0.43/0.60 tff(107,plain,
% 0.43/0.60 (q1(d, d, d)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[106, 95, 50])).
% 0.43/0.60 tff(108,plain,
% 0.43/0.60 (q0(e, d) <=> q0(e, d)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(109,axiom,(q0(e, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.43/0.60 tff(110,plain,
% 0.43/0.60 (q0(e, d)),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.43/0.60 tff(111,plain,
% 0.43/0.60 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(112,plain,
% 0.43/0.60 (((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e)) <=> ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(113,plain,
% 0.43/0.60 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[112])).
% 0.43/0.60 tff(114,plain,
% 0.43/0.60 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[113, 111])).
% 0.43/0.60 tff(115,plain,
% 0.43/0.60 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(116,plain,
% 0.43/0.60 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.43/0.60 tff(117,plain,
% 0.43/0.60 (r1(e)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[116, 95, 110, 107, 92])).
% 0.43/0.60 tff(118,plain,
% 0.43/0.60 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(a, d, b)))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(a, d, b)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(119,plain,
% 0.43/0.60 (((~m0(a, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b)) <=> ((~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(a, d, b)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(120,plain,
% 0.43/0.60 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(a, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(a, d, b))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[119])).
% 0.43/0.60 tff(121,plain,
% 0.43/0.60 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(a, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(a, d, b)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[120, 118])).
% 0.43/0.60 tff(122,plain,
% 0.43/0.60 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | ((~m0(a, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(123,plain,
% 0.43/0.60 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | q2(b, e, b) | (~q2(e, e, e)) | (~m0(a, d, b))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.43/0.61 tff(124,plain,
% 0.43/0.61 (~m0(a, d, b)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[123, 50, 117, 82, 72, 40])).
% 0.43/0.61 tff(125,plain,
% 0.43/0.61 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(126,plain,
% 0.43/0.61 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.43/0.61 inference(quant_intro,[status(thm)],[125])).
% 0.43/0.61 tff(127,plain,
% 0.43/0.61 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(128,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.43/0.61 tff(129,plain,
% 0.43/0.61 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.43/0.61 tff(130,plain,(
% 0.43/0.61 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.43/0.61 inference(skolemize,[status(sab)],[129])).
% 0.43/0.61 tff(131,plain,
% 0.43/0.61 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.43/0.61 tff(132,plain,
% 0.43/0.61 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(a, d, b)),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(133,plain,
% 0.43/0.61 ($false),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[132, 131, 124])).
% 0.43/0.61 % SZS output end Proof
% 0.43/0.61 % E exiting
%------------------------------------------------------------------------------