%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN176-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:25 AM UTC 2025
% Result : Unsatisfiable 0.25s 0.53s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.15 % Problem : SYN176-1 : TPTP v9.0.0. Released v1.1.0.
% 0.05/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 12:29:08 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.25/0.53 % SZS status Unsatisfiable
% 0.25/0.53 % SZS output start Proof
% 0.25/0.53 tff(q2_type, type, (
% 0.25/0.53 q2: ( $i * $i * $i ) > $o)).
% 0.25/0.53 tff(e_type, type, (
% 0.25/0.53 e: $i)).
% 0.25/0.53 tff(c_type, type, (
% 0.25/0.53 c: $i)).
% 0.25/0.53 tff(l2_type, type, (
% 0.25/0.53 l2: ( $i * $i ) > $o)).
% 0.25/0.53 tff(s1_type, type, (
% 0.25/0.53 s1: $i > $o)).
% 0.25/0.53 tff(b_type, type, (
% 0.25/0.53 b: $i)).
% 0.25/0.53 tff(p0_type, type, (
% 0.25/0.53 p0: ( $i * $i ) > $o)).
% 0.25/0.53 tff(m0_type, type, (
% 0.25/0.53 m0: ( $i * $i * $i ) > $o)).
% 0.25/0.53 tff(k1_type, type, (
% 0.25/0.53 k1: $i > $o)).
% 0.25/0.53 tff(n0_type, type, (
% 0.25/0.53 n0: ( $i * $i ) > $o)).
% 0.25/0.53 tff(d_type, type, (
% 0.25/0.53 d: $i)).
% 0.25/0.53 tff(l0_type, type, (
% 0.25/0.53 l0: $i > $o)).
% 0.25/0.53 tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.25/0.53 tff(2,plain,
% 0.25/0.53 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(3,plain,
% 0.25/0.53 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.25/0.53 inference(quant_intro,[status(thm)],[2])).
% 0.25/0.53 tff(4,plain,
% 0.25/0.53 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.25/0.53 tff(6,plain,
% 0.25/0.53 (![X: $i] : p0(b, X)),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.25/0.53 tff(7,plain,(
% 0.25/0.53 ![X: $i] : p0(b, X)),
% 0.25/0.53 inference(skolemize,[status(sab)],[6])).
% 0.25/0.53 tff(8,plain,
% 0.25/0.53 (![X: $i] : p0(b, X)),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.25/0.53 tff(9,plain,
% 0.25/0.53 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.25/0.53 inference(quant_inst,[status(thm)],[])).
% 0.25/0.53 tff(10,plain,
% 0.25/0.53 ($false),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.25/0.53 tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.25/0.53 tff(12,plain,
% 0.25/0.53 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(13,plain,
% 0.25/0.53 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[12])).
% 0.25/0.53 tff(14,plain,
% 0.25/0.53 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.25/0.53 tff(16,plain,
% 0.25/0.53 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.25/0.53 tff(17,plain,(
% 0.25/0.53 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.25/0.53 inference(skolemize,[status(sab)],[16])).
% 0.25/0.53 tff(18,plain,
% 0.25/0.53 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.25/0.53 tff(19,plain,
% 0.25/0.53 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(20,plain,
% 0.25/0.53 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.25/0.53 inference(quant_inst,[status(thm)],[])).
% 0.25/0.53 tff(21,plain,
% 0.25/0.53 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.25/0.53 tff(22,plain,
% 0.25/0.53 (s1(b)),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.25/0.53 tff(23,plain,
% 0.25/0.53 (^[B: $i, A: $i, J: $i, C: $i] : refl(((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(24,plain,
% 0.25/0.53 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[23])).
% 0.25/0.53 tff(25,plain,
% 0.25/0.53 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J)) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(26,plain,
% 0.25/0.53 (^[B: $i, A: $i, J: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l2(J, J) | (~p0(A, A))) <=> ((~p0(A, A)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> (((~p0(A, A)) | l2(J, J)) | (~s1(B))))), rewrite((((~p0(A, A)) | l2(J, J)) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J))), (((l2(J, J) | (~p0(A, A))) | (~s1(B))) <=> ((~p0(A, A)) | (~s1(B)) | l2(J, J)))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> (((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))))), rewrite((((~p0(A, A)) | (~s1(B)) | l2(J, J)) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))), ((((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(27,plain,
% 0.25/0.53 (![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J))) <=> ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[26])).
% 0.25/0.53 tff(28,axiom,(![B: $i, A: $i, J: $i, C: $i] : (((l2(J, J) | (~p0(A, A))) | (~s1(B))) | (~m0(C, B, J)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_133')).
% 0.25/0.53 tff(29,plain,
% 0.25/0.53 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.25/0.53 tff(30,plain,
% 0.25/0.53 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.25/0.53 tff(31,plain,(
% 0.25/0.53 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.25/0.53 inference(skolemize,[status(sab)],[30])).
% 0.25/0.53 tff(32,plain,
% 0.25/0.53 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.25/0.53 tff(33,plain,
% 0.25/0.53 (m0(b, b, e) <=> m0(b, b, e)),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(34,axiom,(m0(b, b, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_31')).
% 0.25/0.53 tff(35,plain,
% 0.25/0.53 (m0(b, b, e)),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.25/0.53 tff(36,plain,
% 0.25/0.53 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(37,plain,
% 0.25/0.53 (((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e)) <=> ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(38,plain,
% 0.25/0.53 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))))),
% 0.25/0.53 inference(monotonicity,[status(thm)],[37])).
% 0.25/0.53 tff(39,plain,
% 0.25/0.53 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b)))),
% 0.25/0.53 inference(transitivity,[status(thm)],[38, 36])).
% 0.25/0.53 tff(40,plain,
% 0.25/0.53 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | ((~p0(b, b)) | (~m0(b, b, e)) | (~s1(b)) | l2(e, e))),
% 0.25/0.53 inference(quant_inst,[status(thm)],[])).
% 0.25/0.53 tff(41,plain,
% 0.25/0.53 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(A, A)) | (~m0(C, B, J)) | (~s1(B)) | l2(J, J))) | (~s1(b)) | l2(e, e) | (~m0(b, b, e)) | (~p0(b, b))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.25/0.53 tff(42,plain,
% 0.25/0.53 ((~s1(b)) | l2(e, e)),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[41, 35, 32, 11])).
% 0.25/0.53 tff(43,plain,
% 0.25/0.53 (l2(e, e)),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[42, 22])).
% 0.25/0.53 tff(44,plain,
% 0.25/0.53 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(45,plain,
% 0.25/0.53 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[44])).
% 0.25/0.53 tff(46,plain,
% 0.25/0.53 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(47,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.25/0.53 tff(48,plain,
% 0.25/0.53 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.25/0.53 tff(49,plain,(
% 0.25/0.53 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.25/0.53 inference(skolemize,[status(sab)],[48])).
% 0.25/0.53 tff(50,plain,
% 0.25/0.53 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.25/0.53 tff(51,plain,
% 0.25/0.53 (n0(d, e) <=> n0(d, e)),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(52,axiom,(n0(d, e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_3')).
% 0.25/0.53 tff(53,plain,
% 0.25/0.53 (n0(d, e)),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.25/0.53 tff(54,plain,
% 0.25/0.53 (((~![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)))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(55,plain,
% 0.25/0.53 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))),
% 0.25/0.53 inference(quant_inst,[status(thm)],[])).
% 0.25/0.53 tff(56,plain,
% 0.25/0.53 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.25/0.53 tff(57,plain,
% 0.25/0.53 (k1(e)),
% 0.25/0.53 inference(unit_resolution,[status(thm)],[56, 53, 50])).
% 0.25/0.53 tff(58,plain,
% 0.25/0.53 (^[D: $i, E: $i] : refl(((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(59,plain,
% 0.25/0.53 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[58])).
% 0.25/0.53 tff(60,plain,
% 0.25/0.53 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E)) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(61,plain,
% 0.25/0.53 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((q2(D, c, E) | (~k1(E))) <=> ((~k1(E)) | q2(D, c, E))), (((q2(D, c, E) | (~k1(E))) | (~l0(c))) <=> (((~k1(E)) | q2(D, c, E)) | (~l0(c))))), rewrite((((~k1(E)) | q2(D, c, E)) | (~l0(c))) <=> ((~k1(E)) | (~l0(c)) | q2(D, c, E))), (((q2(D, c, E) | (~k1(E))) | (~l0(c))) <=> ((~k1(E)) | (~l0(c)) | q2(D, c, E)))), ((((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> (((~k1(E)) | (~l0(c)) | q2(D, c, E)) | (~l2(E, D))))), rewrite((((~k1(E)) | (~l0(c)) | q2(D, c, E)) | (~l2(E, D))) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))), ((((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))))),
% 0.25/0.53 inference(bind,[status(th)],[])).
% 0.25/0.53 tff(62,plain,
% 0.25/0.53 (![D: $i, E: $i] : (((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D))) <=> ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.25/0.53 inference(quant_intro,[status(thm)],[61])).
% 0.25/0.53 tff(63,axiom,(![D: $i, E: $i] : (((q2(D, c, E) | (~k1(E))) | (~l0(c))) | (~l2(E, D)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_183')).
% 0.25/0.53 tff(64,plain,
% 0.25/0.53 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.25/0.53 tff(65,plain,
% 0.25/0.53 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.25/0.53 tff(66,plain,(
% 0.25/0.53 ![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.25/0.53 inference(skolemize,[status(sab)],[65])).
% 0.25/0.53 tff(67,plain,
% 0.25/0.53 (![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.25/0.53 tff(68,plain,
% 0.25/0.53 (l0(c) <=> l0(c)),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(69,axiom,(l0(c)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_24')).
% 0.25/0.53 tff(70,plain,
% 0.25/0.53 (l0(c)),
% 0.25/0.53 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.25/0.53 tff(71,plain,
% 0.25/0.53 (((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(e)) | (~l0(c)) | (~l2(e, e)) | q2(e, c, e))) <=> ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(e)) | (~l0(c)) | (~l2(e, e)) | q2(e, c, e))),
% 0.25/0.53 inference(rewrite,[status(thm)],[])).
% 0.25/0.53 tff(72,plain,
% 0.25/0.53 ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | ((~k1(e)) | (~l0(c)) | (~l2(e, e)) | q2(e, c, e))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(73,plain,
% 0.39/0.54 ((~![D: $i, E: $i] : ((~k1(E)) | (~l0(c)) | (~l2(E, D)) | q2(D, c, E))) | (~k1(e)) | (~l0(c)) | (~l2(e, e)) | q2(e, c, e)),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.39/0.54 tff(74,plain,
% 0.39/0.54 (q2(e, c, e)),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[73, 70, 67, 57, 43])).
% 0.39/0.54 tff(75,plain,
% 0.39/0.54 (^[X: $i] : refl((~q2(e, c, X)) <=> (~q2(e, c, X)))),
% 0.39/0.54 inference(bind,[status(th)],[])).
% 0.39/0.54 tff(76,plain,
% 0.39/0.54 (![X: $i] : (~q2(e, c, X)) <=> ![X: $i] : (~q2(e, c, X))),
% 0.39/0.54 inference(quant_intro,[status(thm)],[75])).
% 0.39/0.54 tff(77,plain,
% 0.39/0.54 (![X: $i] : (~q2(e, c, X)) <=> ![X: $i] : (~q2(e, c, X))),
% 0.39/0.54 inference(rewrite,[status(thm)],[])).
% 0.39/0.54 tff(78,axiom,(![X: $i] : (~q2(e, c, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.39/0.54 tff(79,plain,
% 0.39/0.54 (![X: $i] : (~q2(e, c, X))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.39/0.54 tff(80,plain,(
% 0.39/0.54 ![X: $i] : (~q2(e, c, X))),
% 0.39/0.54 inference(skolemize,[status(sab)],[79])).
% 0.39/0.54 tff(81,plain,
% 0.39/0.54 (![X: $i] : (~q2(e, c, X))),
% 0.39/0.54 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.39/0.54 tff(82,plain,
% 0.39/0.54 ((~![X: $i] : (~q2(e, c, X))) | (~q2(e, c, e))),
% 0.39/0.54 inference(quant_inst,[status(thm)],[])).
% 0.39/0.54 tff(83,plain,
% 0.39/0.54 ($false),
% 0.39/0.54 inference(unit_resolution,[status(thm)],[82, 81, 74])).
% 0.39/0.54 % SZS output end Proof
% 0.39/0.54 % E exiting
%------------------------------------------------------------------------------