%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN203-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.64s 0.81s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN203-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:29:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.64/0.81 % SZS status Unsatisfiable
% 0.64/0.81 % SZS output start Proof
% 0.64/0.81 tff(s3_type, type, (
% 0.64/0.81 s3: ( $i * $i ) > $o)).
% 0.64/0.81 tff(b_type, type, (
% 0.64/0.81 b: $i)).
% 0.64/0.81 tff(e_type, type, (
% 0.64/0.81 e: $i)).
% 0.64/0.81 tff(m0_type, type, (
% 0.64/0.81 m0: ( $i * $i * $i ) > $o)).
% 0.64/0.81 tff(d_type, type, (
% 0.64/0.81 d: $i)).
% 0.64/0.81 tff(q2_type, type, (
% 0.64/0.81 q2: ( $i * $i * $i ) > $o)).
% 0.64/0.81 tff(p1_type, type, (
% 0.64/0.81 p1: ( $i * $i * $i ) > $o)).
% 0.64/0.81 tff(k0_type, type, (
% 0.64/0.81 k0: $i > $o)).
% 0.64/0.81 tff(r0_type, type, (
% 0.64/0.81 r0: $i > $o)).
% 0.64/0.81 tff(r1_type, type, (
% 0.64/0.81 r1: $i > $o)).
% 0.64/0.81 tff(q1_type, type, (
% 0.64/0.81 q1: ( $i * $i * $i ) > $o)).
% 0.64/0.81 tff(s0_type, type, (
% 0.64/0.81 s0: $i > $o)).
% 0.64/0.81 tff(q0_type, type, (
% 0.64/0.81 q0: ( $i * $i ) > $o)).
% 0.64/0.81 tff(s2_type, type, (
% 0.64/0.81 s2: $i > $o)).
% 0.64/0.81 tff(s1_type, type, (
% 0.64/0.81 s1: $i > $o)).
% 0.64/0.81 tff(p0_type, type, (
% 0.64/0.81 p0: ( $i * $i ) > $o)).
% 0.64/0.81 tff(1,assumption,(~m0(b, d, b)), introduced(assumption)).
% 0.64/0.81 tff(2,plain,
% 0.64/0.81 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.64/0.81 inference(bind,[status(th)],[])).
% 0.64/0.81 tff(3,plain,
% 0.64/0.81 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.64/0.81 inference(quant_intro,[status(thm)],[2])).
% 0.64/0.81 tff(4,plain,
% 0.64/0.81 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(5,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.64/0.81 tff(6,plain,
% 0.64/0.81 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.64/0.81 tff(7,plain,(
% 0.64/0.81 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.64/0.81 inference(skolemize,[status(sab)],[6])).
% 0.64/0.81 tff(8,plain,
% 0.64/0.81 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.64/0.81 tff(9,plain,
% 0.64/0.81 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(b, d, b)),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(10,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.64/0.81 tff(11,plain,(m0(b, d, b)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(12,assumption,(~q2(b, e, b)), introduced(assumption)).
% 0.64/0.81 tff(13,plain,
% 0.64/0.81 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.64/0.81 inference(bind,[status(th)],[])).
% 0.64/0.81 tff(14,plain,
% 0.64/0.81 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.64/0.81 inference(quant_intro,[status(thm)],[13])).
% 0.64/0.81 tff(15,plain,
% 0.64/0.81 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(16,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.64/0.81 tff(17,plain,
% 0.64/0.81 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.64/0.81 tff(18,plain,(
% 0.64/0.81 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.64/0.81 inference(skolemize,[status(sab)],[17])).
% 0.64/0.81 tff(19,plain,
% 0.64/0.81 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.64/0.81 tff(20,plain,
% 0.64/0.81 (k0(e) <=> k0(e)),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(21,axiom,(k0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.64/0.81 tff(22,plain,
% 0.64/0.81 (k0(e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.64/0.81 tff(23,plain,
% 0.64/0.81 (r0(e) <=> r0(e)),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(24,axiom,(r0(e)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.64/0.81 tff(25,plain,
% 0.64/0.81 (r0(e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.64/0.81 tff(26,plain,
% 0.64/0.81 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(27,plain,
% 0.64/0.81 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(28,plain,
% 0.64/0.81 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(29,plain,
% 0.64/0.81 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[28])).
% 0.64/0.81 tff(30,plain,
% 0.64/0.81 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.64/0.81 inference(transitivity,[status(thm)],[29, 27])).
% 0.64/0.81 tff(31,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.64/0.81 tff(32,plain,
% 0.64/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.64/0.81 tff(33,plain,
% 0.64/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.64/0.81 tff(34,plain,
% 0.64/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.64/0.81 tff(35,plain,
% 0.64/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.64/0.81 tff(36,plain,
% 0.64/0.81 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[35, 26])).
% 0.64/0.81 tff(37,plain,
% 0.64/0.81 (p1(e, e, e)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[36, 25, 22])).
% 0.64/0.81 tff(38,plain,
% 0.64/0.81 (((~![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))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(39,plain,
% 0.64/0.81 ((q2(e, e, e) | (~p1(e, e, e))) <=> ((~p1(e, e, e)) | q2(e, e, e))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(40,plain,
% 0.64/0.81 (((~![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)))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[39])).
% 0.64/0.81 tff(41,plain,
% 0.64/0.81 (((~![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))),
% 0.64/0.81 inference(transitivity,[status(thm)],[40, 38])).
% 0.64/0.81 tff(42,plain,
% 0.64/0.81 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(e, e, e) | (~p1(e, e, e)))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(43,plain,
% 0.64/0.81 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(e, e, e)) | q2(e, e, e)),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.64/0.81 tff(44,plain,
% 0.64/0.81 (q2(e, e, e)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[43, 37, 19])).
% 0.64/0.81 tff(45,plain,
% 0.64/0.81 (^[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)))),
% 0.64/0.81 inference(bind,[status(th)],[])).
% 0.64/0.81 tff(46,plain,
% 0.64/0.81 (![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))),
% 0.64/0.81 inference(quant_intro,[status(thm)],[45])).
% 0.64/0.81 tff(47,plain,
% 0.64/0.81 (![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))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(48,plain,
% 0.64/0.81 (^[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))))),
% 0.64/0.81 inference(bind,[status(th)],[])).
% 0.64/0.81 tff(49,plain,
% 0.64/0.81 (![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))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[48])).
% 0.64/0.82 tff(50,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/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_187')).
% 0.64/0.82 tff(51,plain,
% 0.64/0.82 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.64/0.82 tff(52,plain,
% 0.64/0.82 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.64/0.82 tff(53,plain,(
% 0.64/0.82 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.64/0.82 inference(skolemize,[status(sab)],[52])).
% 0.64/0.82 tff(54,plain,
% 0.64/0.82 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.64/0.82 tff(55,plain,
% 0.64/0.82 (^[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)))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(56,plain,
% 0.64/0.82 (![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))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[55])).
% 0.64/0.82 tff(57,plain,
% 0.64/0.82 (![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))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(58,plain,
% 0.64/0.82 (^[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))))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(59,plain,
% 0.64/0.82 (![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))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[58])).
% 0.64/0.82 tff(60,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')).
% 0.64/0.82 tff(61,plain,
% 0.64/0.82 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.64/0.82 tff(62,plain,
% 0.64/0.82 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.64/0.82 tff(63,plain,(
% 0.64/0.82 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.64/0.82 inference(skolemize,[status(sab)],[62])).
% 0.64/0.82 tff(64,plain,
% 0.64/0.82 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.64/0.82 tff(65,plain,
% 0.64/0.82 (s0(d) <=> s0(d)),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(66,axiom,(s0(d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.64/0.82 tff(67,plain,
% 0.64/0.82 (s0(d)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.64/0.82 tff(68,plain,
% 0.64/0.82 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(69,plain,
% 0.64/0.82 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(70,plain,
% 0.64/0.82 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(71,plain,
% 0.64/0.82 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[70])).
% 0.64/0.82 tff(72,plain,
% 0.64/0.82 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.64/0.82 inference(transitivity,[status(thm)],[71, 69])).
% 0.64/0.82 tff(73,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.64/0.82 tff(74,plain,
% 0.64/0.82 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.64/0.82 tff(75,plain,
% 0.64/0.82 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[74, 68])).
% 0.64/0.82 tff(76,plain,
% 0.64/0.82 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.64/0.82 tff(77,plain,
% 0.64/0.82 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[76, 68])).
% 0.64/0.82 tff(78,plain,
% 0.64/0.82 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[77, 68])).
% 0.64/0.82 tff(79,plain,
% 0.64/0.82 (q1(d, d, d)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[78, 67, 22])).
% 0.64/0.82 tff(80,plain,
% 0.64/0.82 (q0(e, d) <=> q0(e, d)),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(81,axiom,(q0(e, d)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.64/0.82 tff(82,plain,
% 0.64/0.82 (q0(e, d)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.64/0.82 tff(83,plain,
% 0.64/0.82 (((~![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)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(84,plain,
% 0.64/0.82 (((~q0(e, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(e)) <=> ((~s0(d)) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(85,plain,
% 0.64/0.82 (((~![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))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[84])).
% 0.64/0.82 tff(86,plain,
% 0.64/0.82 (((~![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)))),
% 0.64/0.82 inference(transitivity,[status(thm)],[85, 83])).
% 0.64/0.82 tff(87,plain,
% 0.64/0.82 ((~![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))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(88,plain,
% 0.64/0.82 ((~![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))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.64/0.82 tff(89,plain,
% 0.64/0.82 (r1(e)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[88, 67, 82, 79, 64])).
% 0.64/0.82 tff(90,plain,
% 0.64/0.82 (((~![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(e, e, e)) | q2(b, e, b) | (~m0(b, 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(e, e, e)) | q2(b, e, b) | (~m0(b, d, b)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(91,plain,
% 0.64/0.82 (((~m0(b, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b)) <=> ((~k0(e)) | (~r1(e)) | (~q2(e, e, e)) | q2(b, e, b) | (~m0(b, d, b)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(92,plain,
% 0.64/0.82 (((~![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(b, 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(e, e, e)) | q2(b, e, b) | (~m0(b, d, b))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[91])).
% 0.64/0.82 tff(93,plain,
% 0.64/0.82 (((~![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(b, 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(e, e, e)) | q2(b, e, b) | (~m0(b, d, b)))),
% 0.64/0.82 inference(transitivity,[status(thm)],[92, 90])).
% 0.64/0.82 tff(94,plain,
% 0.64/0.82 ((~![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(b, d, b)) | (~q2(e, e, e)) | (~k0(e)) | (~r1(e)) | q2(b, e, b))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(95,plain,
% 0.64/0.82 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(e)) | (~r1(e)) | (~q2(e, e, e)) | q2(b, e, b) | (~m0(b, d, b))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.64/0.82 tff(96,plain,
% 0.64/0.82 ($false),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[95, 22, 89, 54, 44, 12, 11])).
% 0.64/0.82 tff(97,plain,(q2(b, e, b)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(98,plain,
% 0.64/0.82 (^[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)))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(99,plain,
% 0.64/0.82 (![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))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[98])).
% 0.64/0.82 tff(100,plain,
% 0.64/0.82 (![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))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(101,plain,
% 0.64/0.82 (^[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))))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(102,plain,
% 0.64/0.82 (![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))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[101])).
% 0.64/0.82 tff(103,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/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_273')).
% 0.64/0.82 tff(104,plain,
% 0.64/0.82 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.64/0.82 tff(105,plain,
% 0.64/0.82 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.64/0.82 tff(106,plain,(
% 0.64/0.82 ![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.64/0.82 inference(skolemize,[status(sab)],[105])).
% 0.64/0.82 tff(107,plain,
% 0.64/0.82 (![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.64/0.82 tff(108,assumption,(~p0(b, b)), introduced(assumption)).
% 0.64/0.82 tff(109,plain,
% 0.64/0.82 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(110,plain,
% 0.64/0.82 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.64/0.82 inference(quant_intro,[status(thm)],[109])).
% 0.64/0.82 tff(111,plain,
% 0.64/0.82 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(112,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.64/0.82 tff(113,plain,
% 0.64/0.82 (![X: $i] : p0(b, X)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.64/0.82 tff(114,plain,(
% 0.64/0.82 ![X: $i] : p0(b, X)),
% 0.64/0.82 inference(skolemize,[status(sab)],[113])).
% 0.64/0.82 tff(115,plain,
% 0.64/0.82 (![X: $i] : p0(b, X)),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.64/0.82 tff(116,plain,
% 0.64/0.82 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(117,plain,
% 0.64/0.82 ($false),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[116, 115, 108])).
% 0.64/0.82 tff(118,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(119,plain,
% 0.64/0.82 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(120,plain,
% 0.64/0.82 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[119])).
% 0.64/0.82 tff(121,plain,
% 0.64/0.82 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(122,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.64/0.82 tff(123,plain,
% 0.64/0.82 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.64/0.82 tff(124,plain,(
% 0.64/0.82 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.64/0.82 inference(skolemize,[status(sab)],[123])).
% 0.64/0.82 tff(125,plain,
% 0.64/0.82 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.64/0.82 tff(126,plain,
% 0.64/0.82 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(127,plain,
% 0.64/0.82 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(128,plain,
% 0.64/0.82 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.64/0.82 tff(129,plain,
% 0.64/0.82 (s1(b)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[128, 125, 118])).
% 0.64/0.82 tff(130,plain,
% 0.64/0.82 (^[H: $i] : refl(((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(131,plain,
% 0.64/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[130])).
% 0.64/0.82 tff(132,plain,
% 0.64/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(133,plain,
% 0.64/0.82 (^[H: $i] : rewrite(((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ((~s1(b)) | s2(H) | (~q2(b, H, b))))),
% 0.64/0.82 inference(bind,[status(th)],[])).
% 0.64/0.82 tff(134,plain,
% 0.64/0.82 (![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b))) <=> ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.64/0.82 inference(quant_intro,[status(thm)],[133])).
% 0.64/0.82 tff(135,axiom,(![H: $i] : ((s2(H) | (~q2(b, H, b))) | (~s1(b)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_189')).
% 0.64/0.82 tff(136,plain,
% 0.64/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.64/0.82 tff(137,plain,
% 0.64/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.64/0.82 tff(138,plain,(
% 0.64/0.82 ![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.64/0.82 inference(skolemize,[status(sab)],[137])).
% 0.64/0.82 tff(139,plain,
% 0.64/0.82 (![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.64/0.82 tff(140,plain,
% 0.64/0.82 (((~![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)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(141,plain,
% 0.64/0.82 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | ((~s1(b)) | s2(e) | (~q2(b, e, b)))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(142,plain,
% 0.64/0.82 ((~![H: $i] : ((~s1(b)) | s2(H) | (~q2(b, H, b)))) | (~s1(b)) | s2(e) | (~q2(b, e, b))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.64/0.82 tff(143,plain,
% 0.64/0.82 (s2(e)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[142, 139, 129, 97])).
% 0.64/0.82 tff(144,plain,
% 0.64/0.82 (((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(e)) | (~m0(b, d, b)) | (~q2(b, e, b)) | s3(e, b))) <=> ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(e)) | (~m0(b, d, b)) | (~q2(b, e, b)) | s3(e, b))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(145,plain,
% 0.67/0.83 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | ((~s2(e)) | (~m0(b, d, b)) | (~q2(b, e, b)) | s3(e, b))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(146,plain,
% 0.67/0.83 ((~![I: $i, B: $i, A: $i, J: $i] : ((~s2(I)) | (~m0(A, B, J)) | (~q2(A, I, A)) | s3(I, J))) | (~s2(e)) | (~m0(b, d, b)) | (~q2(b, e, b)) | s3(e, b)),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.67/0.83 tff(147,plain,
% 0.67/0.83 (s3(e, b)),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[146, 143, 107, 97, 11])).
% 0.67/0.83 tff(148,plain,
% 0.67/0.83 (^[X: $i] : refl((~s3(X, b)) <=> (~s3(X, b)))),
% 0.67/0.83 inference(bind,[status(th)],[])).
% 0.67/0.83 tff(149,plain,
% 0.67/0.83 (![X: $i] : (~s3(X, b)) <=> ![X: $i] : (~s3(X, b))),
% 0.67/0.83 inference(quant_intro,[status(thm)],[148])).
% 0.67/0.83 tff(150,plain,
% 0.67/0.83 (![X: $i] : (~s3(X, b)) <=> ![X: $i] : (~s3(X, b))),
% 0.67/0.83 inference(rewrite,[status(thm)],[])).
% 0.67/0.83 tff(151,axiom,(![X: $i] : (~s3(X, b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.67/0.83 tff(152,plain,
% 0.67/0.83 (![X: $i] : (~s3(X, b))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.67/0.83 tff(153,plain,(
% 0.67/0.83 ![X: $i] : (~s3(X, b))),
% 0.67/0.83 inference(skolemize,[status(sab)],[152])).
% 0.67/0.83 tff(154,plain,
% 0.67/0.83 (![X: $i] : (~s3(X, b))),
% 0.67/0.83 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.67/0.83 tff(155,plain,
% 0.67/0.83 ((~![X: $i] : (~s3(X, b))) | (~s3(e, b))),
% 0.67/0.83 inference(quant_inst,[status(thm)],[])).
% 0.67/0.83 tff(156,plain,
% 0.67/0.83 ($false),
% 0.67/0.83 inference(unit_resolution,[status(thm)],[155, 154, 147])).
% 0.67/0.83 % SZS output end Proof
% 0.67/0.84 % E exiting
%------------------------------------------------------------------------------