%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN298-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:38:41 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.80s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN298-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:30:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.61/0.80 % SZS status Unsatisfiable
% 0.61/0.80 % SZS output start Proof
% 0.61/0.80 tff(s3_type, type, (
% 0.61/0.80 s3: ( $i * $i ) > $o)).
% 0.61/0.80 tff(c_type, type, (
% 0.61/0.80 c: $i)).
% 0.61/0.80 tff(b_type, type, (
% 0.61/0.80 b: $i)).
% 0.61/0.80 tff(s2_type, type, (
% 0.61/0.80 s2: $i > $o)).
% 0.61/0.80 tff(s1_type, type, (
% 0.61/0.80 s1: $i > $o)).
% 0.61/0.80 tff(p0_type, type, (
% 0.61/0.80 p0: ( $i * $i ) > $o)).
% 0.61/0.80 tff(q2_type, type, (
% 0.61/0.80 q2: ( $i * $i * $i ) > $o)).
% 0.61/0.80 tff(q1_type, type, (
% 0.61/0.80 q1: ( $i * $i * $i ) > $o)).
% 0.61/0.80 tff(n0_type, type, (
% 0.61/0.80 n0: ( $i * $i ) > $o)).
% 0.61/0.80 tff(d_type, type, (
% 0.61/0.80 d: $i)).
% 0.61/0.80 tff(e_type, type, (
% 0.61/0.80 e: $i)).
% 0.61/0.80 tff(p1_type, type, (
% 0.61/0.80 p1: ( $i * $i * $i ) > $o)).
% 0.61/0.80 tff(k0_type, type, (
% 0.61/0.80 k0: $i > $o)).
% 0.61/0.80 tff(n1_type, type, (
% 0.61/0.80 n1: ( $i * $i * $i ) > $o)).
% 0.61/0.80 tff(k1_type, type, (
% 0.61/0.80 k1: $i > $o)).
% 0.61/0.80 tff(m0_type, type, (
% 0.61/0.80 m0: ( $i * $i * $i ) > $o)).
% 0.61/0.80 tff(r0_type, type, (
% 0.61/0.80 r0: $i > $o)).
% 0.61/0.80 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.61/0.80 tff(2,plain,
% 0.61/0.80 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(3,plain,
% 0.61/0.80 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.61/0.80 inference(quant_intro,[status(thm)],[2])).
% 0.61/0.80 tff(4,plain,
% 0.61/0.80 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.61/0.80 tff(6,plain,
% 0.61/0.80 (![X: $i] : p0(b, X)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.61/0.80 tff(7,plain,(
% 0.61/0.80 ![X: $i] : p0(b, X)),
% 0.61/0.80 inference(skolemize,[status(sab)],[6])).
% 0.61/0.80 tff(8,plain,
% 0.61/0.80 (![X: $i] : p0(b, X)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.61/0.80 tff(9,plain,
% 0.61/0.80 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(10,plain,
% 0.61/0.80 ($false),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.61/0.80 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.61/0.80 tff(12,plain,
% 0.61/0.80 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(13,plain,
% 0.61/0.80 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[12])).
% 0.61/0.80 tff(14,plain,
% 0.61/0.80 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.61/0.80 tff(16,plain,
% 0.61/0.80 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.61/0.80 tff(17,plain,(
% 0.61/0.80 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[16])).
% 0.61/0.80 tff(18,plain,
% 0.61/0.80 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.61/0.80 tff(19,plain,
% 0.61/0.80 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(20,plain,
% 0.61/0.80 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(21,plain,
% 0.61/0.80 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.61/0.80 tff(22,plain,
% 0.61/0.80 (s1(b)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.61/0.80 tff(23,plain,
% 0.61/0.80 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(24,plain,
% 0.61/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[23])).
% 0.61/0.80 tff(25,plain,
% 0.61/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(26,plain,
% 0.61/0.80 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(rewrite((q1(J, A, J) | (~n0(B, A))) <=> ((~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> (((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))))), rewrite((((~n0(B, A)) | q1(J, A, J)) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))), (((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(27,plain,
% 0.61/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[26])).
% 0.61/0.80 tff(28,axiom,(![B: $i, A: $i, J: $i, C: $i] : ((q1(J, A, J) | (~n0(B, A))) | (~p0(C, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_092')).
% 0.61/0.80 tff(29,plain,
% 0.61/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.61/0.80 tff(30,plain,
% 0.61/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.61/0.80 tff(31,plain,(
% 0.61/0.80 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.61/0.80 inference(skolemize,[status(sab)],[30])).
% 0.61/0.80 tff(32,plain,
% 0.61/0.80 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.61/0.80 tff(33,plain,
% 0.61/0.80 (n0(d, c) <=> n0(d, c)),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(34,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.61/0.80 tff(35,plain,
% 0.61/0.80 (n0(d, c)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.61/0.80 tff(36,plain,
% 0.61/0.80 (p0(c, b) <=> p0(c, b)),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(37,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.61/0.80 tff(38,plain,
% 0.61/0.80 (p0(c, b)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.61/0.80 tff(39,plain,
% 0.61/0.80 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(40,plain,
% 0.61/0.80 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(c, b)) | (~n0(d, c)) | q1(b, c, b))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(41,plain,
% 0.61/0.80 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(c, b)) | (~n0(d, c)) | q1(b, c, b)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.61/0.80 tff(42,plain,
% 0.61/0.80 (q1(b, c, b)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[41, 38, 35, 32])).
% 0.61/0.80 tff(43,plain,
% 0.61/0.80 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(44,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[43])).
% 0.61/0.80 tff(45,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(46,plain,
% 0.61/0.80 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(47,plain,
% 0.61/0.80 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[46])).
% 0.61/0.80 tff(48,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 0.61/0.80 tff(49,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.61/0.80 tff(50,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.61/0.80 tff(51,plain,(
% 0.61/0.80 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.61/0.80 inference(skolemize,[status(sab)],[50])).
% 0.61/0.80 tff(52,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.61/0.80 tff(53,plain,
% 0.61/0.80 (((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))) <=> ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(54,plain,
% 0.61/0.80 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(55,plain,
% 0.61/0.80 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.61/0.80 tff(56,plain,
% 0.61/0.80 (q2(b, b, b)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[55, 52, 42])).
% 0.61/0.80 tff(57,plain,
% 0.61/0.80 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(58,plain,
% 0.61/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[57])).
% 0.61/0.80 tff(59,plain,
% 0.61/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(60,plain,
% 0.61/0.80 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(61,plain,
% 0.61/0.80 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[60])).
% 0.61/0.80 tff(62,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.61/0.80 tff(63,plain,
% 0.61/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.61/0.80 tff(64,plain,
% 0.61/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.61/0.80 tff(65,plain,(
% 0.61/0.80 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.61/0.80 inference(skolemize,[status(sab)],[64])).
% 0.61/0.80 tff(66,plain,
% 0.61/0.80 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.61/0.80 tff(67,plain,
% 0.61/0.80 (((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(b) | (~q2(b, b, b)))) <=> ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(b) | (~q2(b, b, b)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(68,plain,
% 0.61/0.80 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(b) | (~q2(b, b, b)))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(69,plain,
% 0.61/0.80 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(b) | (~q2(b, b, b))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.61/0.80 tff(70,plain,
% 0.61/0.80 ((~s1(b)) | s2(b)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[69, 66, 56])).
% 0.61/0.80 tff(71,plain,
% 0.61/0.80 (s2(b)),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[70, 22])).
% 0.61/0.80 tff(72,assumption,(~q2(b, e, e)), introduced(assumption)).
% 0.61/0.80 tff(73,plain,
% 0.61/0.80 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(74,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[73])).
% 0.61/0.80 tff(75,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(76,plain,
% 0.61/0.80 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.61/0.80 inference(bind,[status(th)],[])).
% 0.61/0.80 tff(77,plain,
% 0.61/0.80 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.61/0.80 inference(quant_intro,[status(thm)],[76])).
% 0.61/0.80 tff(78,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.61/0.80 tff(79,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.61/0.80 tff(80,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.61/0.80 tff(81,plain,(
% 0.61/0.80 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.61/0.80 inference(skolemize,[status(sab)],[80])).
% 0.61/0.80 tff(82,plain,
% 0.61/0.80 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.61/0.80 tff(83,plain,
% 0.61/0.80 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(84,plain,
% 0.65/0.80 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(85,plain,
% 0.65/0.80 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.65/0.80 tff(86,plain,
% 0.65/0.80 (p1(b, b, b)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[85, 38, 82])).
% 0.65/0.80 tff(87,plain,
% 0.65/0.80 (^[E: $i, F: $i] : refl(((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(88,plain,
% 0.65/0.80 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[87])).
% 0.65/0.80 tff(89,plain,
% 0.65/0.80 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F)) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(90,plain,
% 0.65/0.80 (^[E: $i, F: $i] : trans(monotonicity(rewrite((q2(E, F, F) | (~k0(F))) <=> ((~k0(F)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> (((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))))), rewrite((((~k0(F)) | q2(E, F, F)) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))), (((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(91,plain,
% 0.65/0.80 (![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E))) <=> ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[90])).
% 0.65/0.80 tff(92,axiom,(![E: $i, F: $i] : ((q2(E, F, F) | (~k0(F))) | (~p1(E, E, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_177')).
% 0.65/0.80 tff(93,plain,
% 0.65/0.80 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.65/0.80 tff(94,plain,
% 0.65/0.80 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.65/0.80 tff(95,plain,(
% 0.65/0.80 ![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.65/0.80 inference(skolemize,[status(sab)],[94])).
% 0.65/0.80 tff(96,plain,
% 0.65/0.80 (![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.65/0.80 tff(97,plain,
% 0.65/0.80 (k0(e) <=> k0(e)),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(98,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.65/0.80 tff(99,plain,
% 0.65/0.80 (k0(e)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.65/0.80 tff(100,plain,
% 0.65/0.80 (((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(b, b, b)) | q2(b, e, e))) <=> ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(b, b, b)) | q2(b, e, e))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(101,plain,
% 0.65/0.80 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | ((~k0(e)) | (~p1(b, b, b)) | q2(b, e, e))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(102,plain,
% 0.65/0.80 ((~![E: $i, F: $i] : ((~k0(F)) | (~p1(E, E, E)) | q2(E, F, F))) | (~k0(e)) | (~p1(b, b, b)) | q2(b, e, e)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.65/0.80 tff(103,plain,
% 0.65/0.80 ($false),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[102, 99, 96, 86, 72])).
% 0.65/0.80 tff(104,plain,(q2(b, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.80 tff(105,plain,
% 0.65/0.80 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(106,plain,
% 0.65/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[105])).
% 0.65/0.80 tff(107,plain,
% 0.65/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(108,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.65/0.80 tff(109,plain,
% 0.65/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.65/0.80 tff(110,plain,(
% 0.65/0.80 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.65/0.80 inference(skolemize,[status(sab)],[109])).
% 0.65/0.80 tff(111,plain,
% 0.65/0.80 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.65/0.80 tff(112,plain,
% 0.65/0.80 (n0(d, b) <=> n0(d, b)),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(113,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.65/0.80 tff(114,plain,
% 0.65/0.80 (n0(d, b)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.65/0.80 tff(115,plain,
% 0.65/0.80 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b)))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(116,plain,
% 0.65/0.80 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(117,plain,
% 0.65/0.80 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.65/0.80 tff(118,plain,
% 0.65/0.80 (k1(b)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[117, 114, 111])).
% 0.65/0.80 tff(119,plain,
% 0.65/0.80 (^[D: $i, C: $i] : refl(((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(120,plain,
% 0.65/0.80 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[119])).
% 0.65/0.80 tff(121,plain,
% 0.65/0.80 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e)) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(122,plain,
% 0.65/0.80 (^[D: $i, C: $i] : trans(monotonicity(rewrite((n1(C, e, e) | (~m0(C, D, e))) <=> ((~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> (((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))))), rewrite((((~m0(C, D, e)) | n1(C, e, e)) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))), (((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(123,plain,
% 0.65/0.80 (![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C))) <=> ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[122])).
% 0.65/0.80 tff(124,axiom,(![D: $i, C: $i] : ((n1(C, e, e) | (~m0(C, D, e))) | (~k1(C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_040')).
% 0.65/0.80 tff(125,plain,
% 0.65/0.80 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.65/0.80 tff(126,plain,
% 0.65/0.80 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.65/0.80 tff(127,plain,(
% 0.65/0.80 ![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.65/0.80 inference(skolemize,[status(sab)],[126])).
% 0.65/0.80 tff(128,plain,
% 0.65/0.80 (![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.65/0.80 tff(129,plain,
% 0.65/0.80 (m0(b, b, e) <=> m0(b, b, e)),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(130,axiom,(m0(b, b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.65/0.80 tff(131,plain,
% 0.65/0.80 (m0(b, b, e)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.65/0.80 tff(132,plain,
% 0.65/0.80 (((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))) <=> ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(133,plain,
% 0.65/0.80 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | ((~k1(b)) | (~m0(b, b, e)) | n1(b, e, e))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(134,plain,
% 0.65/0.80 ((~![D: $i, C: $i] : ((~k1(C)) | (~m0(C, D, e)) | n1(C, e, e))) | (~k1(b)) | (~m0(b, b, e)) | n1(b, e, e)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.65/0.80 tff(135,plain,
% 0.65/0.80 ((~k1(b)) | n1(b, e, e)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[134, 131, 128])).
% 0.65/0.80 tff(136,plain,
% 0.65/0.80 (n1(b, e, e)),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[135, 118])).
% 0.65/0.80 tff(137,plain,
% 0.65/0.80 (^[H: $i, F: $i, G: $i] : refl(((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(138,plain,
% 0.65/0.80 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[137])).
% 0.65/0.80 tff(139,plain,
% 0.65/0.80 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(140,plain,
% 0.65/0.80 (^[H: $i, F: $i, G: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(F, G, F) | (~p1(F, F, H))) <=> ((~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> (((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))))), rewrite((((~p1(F, F, H)) | q2(F, G, F)) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) <=> ((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> (((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))))), rewrite((((~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F)) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))), ((((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))))),
% 0.65/0.80 inference(bind,[status(th)],[])).
% 0.65/0.80 tff(141,plain,
% 0.65/0.80 (![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F))) <=> ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.65/0.80 inference(quant_intro,[status(thm)],[140])).
% 0.65/0.80 tff(142,axiom,(![H: $i, F: $i, G: $i] : (((q2(F, G, F) | (~p1(F, F, H))) | (~n1(G, F, H))) | (~q2(G, H, F)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_182')).
% 0.65/0.80 tff(143,plain,
% 0.65/0.80 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.65/0.80 tff(144,plain,
% 0.65/0.80 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.65/0.80 tff(145,plain,(
% 0.65/0.80 ![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.65/0.80 inference(skolemize,[status(sab)],[144])).
% 0.65/0.80 tff(146,plain,
% 0.65/0.80 (![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.65/0.80 tff(147,plain,
% 0.65/0.80 (r0(e) <=> r0(e)),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(148,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.65/0.80 tff(149,plain,
% 0.65/0.80 (r0(e)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.65/0.80 tff(150,plain,
% 0.65/0.80 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(151,plain,
% 0.65/0.80 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(152,plain,
% 0.65/0.80 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(153,plain,
% 0.65/0.80 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[152])).
% 0.65/0.80 tff(154,plain,
% 0.65/0.80 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.65/0.80 inference(transitivity,[status(thm)],[153, 151])).
% 0.65/0.80 tff(155,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.65/0.80 tff(156,plain,
% 0.65/0.80 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.65/0.80 tff(157,plain,
% 0.65/0.80 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[156, 150])).
% 0.65/0.81 tff(158,plain,
% 0.65/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.65/0.81 tff(159,plain,
% 0.65/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[158, 150])).
% 0.65/0.81 tff(160,plain,
% 0.65/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[159, 150])).
% 0.65/0.81 tff(161,plain,
% 0.65/0.81 (p1(e, e, e)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[160, 149, 99])).
% 0.65/0.81 tff(162,plain,
% 0.65/0.81 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(163,plain,
% 0.65/0.81 (((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, e)) <=> ((~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(164,plain,
% 0.65/0.81 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[163])).
% 0.65/0.81 tff(165,plain,
% 0.65/0.81 (((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, e))) <=> ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e))),
% 0.65/0.81 inference(transitivity,[status(thm)],[164, 162])).
% 0.65/0.81 tff(166,plain,
% 0.65/0.81 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | ((~q2(b, e, e)) | (~n1(b, e, e)) | (~p1(e, e, e)) | q2(e, b, e))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(167,plain,
% 0.65/0.81 ((~![H: $i, F: $i, G: $i] : ((~q2(G, H, F)) | (~n1(G, F, H)) | (~p1(F, F, H)) | q2(F, G, F))) | (~p1(e, e, e)) | (~n1(b, e, e)) | (~q2(b, e, e)) | q2(e, b, e)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.65/0.81 tff(168,plain,
% 0.65/0.81 ((~q2(b, e, e)) | q2(e, b, e)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[167, 161, 146, 136])).
% 0.65/0.81 tff(169,plain,
% 0.65/0.81 (q2(e, b, e)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[168, 104])).
% 0.65/0.81 tff(170,plain,
% 0.65/0.81 (^[I: $i, B: $i, A: $i, J: $i] : refl(((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(171,plain,
% 0.65/0.81 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[170])).
% 0.65/0.81 tff(172,plain,
% 0.65/0.81 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J)) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(173,plain,
% 0.65/0.81 (^[I: $i, B: $i, A: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((s3(I, J) | (~q2(A, I, A))) <=> ((~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> (((~q2(A, I, A)) | s3(I, J)) | (~s2(I))))), rewrite((((~q2(A, I, A)) | s3(I, J)) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J))), (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) <=> ((~s2(I)) | (~q2(A, I, A)) | s3(I, J)))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> (((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))))), rewrite((((~s2(I)) | (~q2(A, I, A)) | s3(I, J)) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))), ((((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(174,plain,
% 0.65/0.81 (![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J))) <=> ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[173])).
% 0.65/0.81 tff(175,axiom,(![I: $i, B: $i, A: $i, J: $i] : (((s3(I, J) | (~q2(A, I, A))) | (~s2(I))) | (~m0(A, B, J)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 0.65/0.81 tff(176,plain,
% 0.65/0.81 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.65/0.81 tff(177,plain,
% 0.65/0.81 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.65/0.81 tff(178,plain,(
% 0.65/0.81 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.65/0.81 inference(skolemize,[status(sab)],[177])).
% 0.65/0.81 tff(179,plain,
% 0.65/0.81 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.65/0.82 tff(180,plain,
% 0.65/0.82 (m0(e, b, c) <=> m0(e, b, c)),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(181,axiom,(m0(e, b, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.65/0.82 tff(182,plain,
% 0.65/0.82 (m0(e, b, c)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.65/0.82 tff(183,plain,
% 0.65/0.82 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(e, b, c)) | (~q2(e, b, e)) | s3(b, c))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(e, b, c)) | (~q2(e, b, e)) | s3(b, c))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(184,plain,
% 0.65/0.82 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(b)) | (~m0(e, b, c)) | (~q2(e, b, e)) | s3(b, c))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(185,plain,
% 0.65/0.82 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(b)) | (~m0(e, b, c)) | (~q2(e, b, e)) | s3(b, c)),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.65/0.82 tff(186,plain,
% 0.65/0.82 (s3(b, c)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[185, 182, 179, 169, 71])).
% 0.65/0.82 tff(187,plain,
% 0.65/0.82 (^[X: $i] : refl((~s3(b, X)) <=> (~s3(b, X)))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(188,plain,
% 0.65/0.82 (![X: $i] : (~s3(b, X)) <=> ![X: $i] : (~s3(b, X))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[187])).
% 0.65/0.82 tff(189,plain,
% 0.65/0.82 (![X: $i] : (~s3(b, X)) <=> ![X: $i] : (~s3(b, X))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(190,axiom,(![X: $i] : (~s3(b, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.65/0.82 tff(191,plain,
% 0.65/0.82 (![X: $i] : (~s3(b, X))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.65/0.82 tff(192,plain,(
% 0.65/0.82 ![X: $i] : (~s3(b, X))),
% 0.65/0.82 inference(skolemize,[status(sab)],[191])).
% 0.65/0.82 tff(193,plain,
% 0.65/0.82 (![X: $i] : (~s3(b, X))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.65/0.82 tff(194,plain,
% 0.65/0.82 ((~![X: $i] : (~s3(b, X))) | (~s3(b, c))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(195,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[194, 193, 186])).
% 0.65/0.82 % SZS output end Proof
% 0.65/0.82 % E exiting
%------------------------------------------------------------------------------