%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN179-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.47s 0.64s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN179-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:28:25 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.47/0.64 % SZS status Unsatisfiable
% 0.47/0.64 % SZS output start Proof
% 0.47/0.64 tff(q3_type, type, (
% 0.47/0.64 q3: ( $i * $i ) > $o)).
% 0.47/0.64 tff(b_type, type, (
% 0.47/0.64 b: $i)).
% 0.47/0.64 tff(d_type, type, (
% 0.47/0.64 d: $i)).
% 0.47/0.64 tff(q2_type, type, (
% 0.47/0.64 q2: ( $i * $i * $i ) > $o)).
% 0.47/0.64 tff(q1_type, type, (
% 0.47/0.64 q1: ( $i * $i * $i ) > $o)).
% 0.47/0.64 tff(c_type, type, (
% 0.47/0.64 c: $i)).
% 0.47/0.64 tff(n0_type, type, (
% 0.47/0.64 n0: ( $i * $i ) > $o)).
% 0.47/0.64 tff(p0_type, type, (
% 0.47/0.64 p0: ( $i * $i ) > $o)).
% 0.47/0.64 tff(r1_type, type, (
% 0.47/0.64 r1: $i > $o)).
% 0.47/0.64 tff(s0_type, type, (
% 0.47/0.64 s0: $i > $o)).
% 0.47/0.64 tff(q0_type, type, (
% 0.47/0.64 q0: ( $i * $i ) > $o)).
% 0.47/0.64 tff(m0_type, type, (
% 0.47/0.64 m0: ( $i * $i * $i ) > $o)).
% 0.47/0.64 tff(k0_type, type, (
% 0.47/0.64 k0: $i > $o)).
% 0.47/0.64 tff(s2_type, type, (
% 0.47/0.64 s2: $i > $o)).
% 0.47/0.64 tff(s1_type, type, (
% 0.47/0.64 s1: $i > $o)).
% 0.47/0.64 tff(e_type, type, (
% 0.47/0.64 e: $i)).
% 0.47/0.64 tff(n1_type, type, (
% 0.47/0.64 n1: ( $i * $i * $i ) > $o)).
% 0.47/0.64 tff(m1_type, type, (
% 0.47/0.64 m1: ( $i * $i * $i ) > $o)).
% 0.47/0.64 tff(k1_type, type, (
% 0.47/0.64 k1: $i > $o)).
% 0.47/0.64 tff(a_type, type, (
% 0.47/0.64 a: $i)).
% 0.47/0.64 tff(1,assumption,(~q2(d, b, d)), introduced(assumption)).
% 0.47/0.64 tff(2,plain,
% 0.47/0.64 (^[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)))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(3,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[2])).
% 0.47/0.64 tff(4,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(5,plain,
% 0.47/0.64 (^[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))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(6,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[5])).
% 0.47/0.64 tff(7,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')).
% 0.47/0.64 tff(8,plain,
% 0.47/0.64 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.47/0.64 tff(9,plain,
% 0.47/0.64 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.47/0.64 tff(10,plain,(
% 0.47/0.64 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.47/0.64 inference(skolemize,[status(sab)],[9])).
% 0.47/0.64 tff(11,plain,
% 0.47/0.64 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.47/0.64 tff(12,plain,
% 0.47/0.64 (n0(d, c) <=> n0(d, c)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(13,axiom,(n0(d, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_26')).
% 0.47/0.64 tff(14,plain,
% 0.47/0.64 (n0(d, c)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.47/0.64 tff(15,plain,
% 0.47/0.64 (p0(c, b) <=> p0(c, b)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(16,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.47/0.64 tff(17,plain,
% 0.47/0.64 (p0(c, b)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.47/0.64 tff(18,plain,
% 0.47/0.64 (((~![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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(19,plain,
% 0.47/0.64 ((~![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))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(20,plain,
% 0.47/0.64 ((~![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)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.47/0.64 tff(21,plain,
% 0.47/0.64 (q1(b, c, b)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[20, 17, 14, 11])).
% 0.47/0.64 tff(22,plain,
% 0.47/0.64 (^[B: $i, C: $i] : refl(((~q1(C, c, B)) | q2(B, B, B)) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(23,plain,
% 0.47/0.64 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[22])).
% 0.47/0.64 tff(24,plain,
% 0.47/0.64 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B)) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(25,plain,
% 0.47/0.64 (^[B: $i, C: $i] : rewrite((q2(B, B, B) | (~q1(C, c, B))) <=> ((~q1(C, c, B)) | q2(B, B, B)))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(26,plain,
% 0.47/0.64 (![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B))) <=> ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[25])).
% 0.47/0.64 tff(27,axiom,(![B: $i, C: $i] : (q2(B, B, B) | (~q1(C, c, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_184')).
% 0.47/0.64 tff(28,plain,
% 0.47/0.64 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.47/0.64 tff(29,plain,
% 0.47/0.64 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.47/0.64 tff(30,plain,(
% 0.47/0.64 ![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.47/0.64 inference(skolemize,[status(sab)],[29])).
% 0.47/0.64 tff(31,plain,
% 0.47/0.64 (![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.47/0.64 tff(32,plain,
% 0.47/0.64 (((~![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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(33,plain,
% 0.47/0.64 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | ((~q1(b, c, b)) | q2(b, b, b))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(34,plain,
% 0.47/0.64 ((~![B: $i, C: $i] : ((~q1(C, c, B)) | q2(B, B, B))) | (~q1(b, c, b)) | q2(b, b, b)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.47/0.64 tff(35,plain,
% 0.47/0.64 (q2(b, b, b)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.47/0.64 tff(36,plain,
% 0.47/0.64 (p0(b, d) <=> p0(b, d)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(37,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.47/0.64 tff(38,plain,
% 0.47/0.64 (p0(b, d)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.47/0.64 tff(39,plain,
% 0.47/0.64 (n0(d, b) <=> n0(d, b)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(40,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.47/0.64 tff(41,plain,
% 0.47/0.64 (n0(d, b)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.47/0.64 tff(42,plain,
% 0.47/0.64 (((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))) <=> ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(43,plain,
% 0.47/0.64 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | ((~p0(b, d)) | (~n0(d, b)) | q1(d, b, d))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(44,plain,
% 0.47/0.64 ((~![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))) | (~p0(b, d)) | (~n0(d, b)) | q1(d, b, d)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.47/0.64 tff(45,plain,
% 0.47/0.64 (q1(d, b, d)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[44, 41, 38, 11])).
% 0.47/0.64 tff(46,plain,
% 0.47/0.64 (^[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)))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(47,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[46])).
% 0.47/0.64 tff(48,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(49,plain,
% 0.47/0.64 (^[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))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(50,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[49])).
% 0.47/0.64 tff(51,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')).
% 0.47/0.64 tff(52,plain,
% 0.47/0.64 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.47/0.64 tff(53,plain,
% 0.47/0.64 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.47/0.64 tff(54,plain,(
% 0.47/0.64 ![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.47/0.64 inference(skolemize,[status(sab)],[53])).
% 0.47/0.64 tff(55,plain,
% 0.47/0.64 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.47/0.64 tff(56,plain,
% 0.47/0.64 (q0(b, b) <=> q0(b, b)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(57,axiom,(q0(b, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_6')).
% 0.47/0.64 tff(58,plain,
% 0.47/0.64 (q0(b, b)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.47/0.64 tff(59,plain,
% 0.47/0.64 (s0(d) <=> s0(d)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(60,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.47/0.64 tff(61,plain,
% 0.47/0.64 (s0(d)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.47/0.64 tff(62,plain,
% 0.47/0.64 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(63,plain,
% 0.47/0.64 (((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b)) <=> ((~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(64,plain,
% 0.47/0.64 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[63])).
% 0.47/0.64 tff(65,plain,
% 0.47/0.64 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[64, 62])).
% 0.47/0.64 tff(66,plain,
% 0.47/0.64 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(b, b)) | (~s0(d)) | (~q1(d, b, d)) | r1(b))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(67,plain,
% 0.47/0.64 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(b, b)) | r1(b) | (~q1(d, b, d))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.47/0.64 tff(68,plain,
% 0.47/0.64 (r1(b)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[67, 61, 58, 55, 45])).
% 0.47/0.64 tff(69,assumption,(~m0(d, d, d)), introduced(assumption)).
% 0.47/0.64 tff(70,plain,
% 0.47/0.64 (^[Y: $i, X: $i] : refl(m0(X, d, Y) <=> m0(X, d, Y))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(71,plain,
% 0.47/0.64 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.47/0.64 inference(quant_intro,[status(thm)],[70])).
% 0.47/0.64 tff(72,plain,
% 0.47/0.64 (![Y: $i, X: $i] : m0(X, d, Y) <=> ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(73,axiom,(![Y: $i, X: $i] : m0(X, d, Y)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_19')).
% 0.47/0.64 tff(74,plain,
% 0.47/0.64 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.47/0.64 tff(75,plain,(
% 0.47/0.64 ![Y: $i, X: $i] : m0(X, d, Y)),
% 0.47/0.64 inference(skolemize,[status(sab)],[74])).
% 0.47/0.64 tff(76,plain,
% 0.47/0.64 (![Y: $i, X: $i] : m0(X, d, Y)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.47/0.64 tff(77,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : m0(X, d, Y)) | m0(d, d, d)),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(78,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[77, 76, 69])).
% 0.47/0.64 tff(79,plain,(m0(d, d, d)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(80,plain,
% 0.47/0.64 (^[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)))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(81,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[80])).
% 0.47/0.64 tff(82,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(83,plain,
% 0.47/0.64 (^[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))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(84,plain,
% 0.47/0.64 (![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))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[83])).
% 0.47/0.64 tff(85,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')).
% 0.47/0.64 tff(86,plain,
% 0.47/0.64 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.47/0.64 tff(87,plain,
% 0.47/0.64 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.47/0.64 tff(88,plain,(
% 0.47/0.64 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.47/0.64 inference(skolemize,[status(sab)],[87])).
% 0.47/0.64 tff(89,plain,
% 0.47/0.64 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.47/0.64 tff(90,plain,
% 0.47/0.64 (k0(b) <=> k0(b)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(91,axiom,(k0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_32')).
% 0.47/0.65 tff(92,plain,
% 0.47/0.65 (k0(b)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.47/0.65 tff(93,plain,
% 0.47/0.65 (((~![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(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, 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))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(94,plain,
% 0.47/0.65 (((~m0(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d)) <=> ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(95,plain,
% 0.47/0.65 (((~![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(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, 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))) | ((~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[94])).
% 0.47/0.65 tff(96,plain,
% 0.47/0.65 (((~![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(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, 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))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d))),
% 0.47/0.65 inference(transitivity,[status(thm)],[95, 93])).
% 0.47/0.65 tff(97,plain,
% 0.47/0.65 ((~![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(d, d, d)) | (~q2(b, b, b)) | (~k0(b)) | (~r1(b)) | q2(d, b, d))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(98,plain,
% 0.47/0.65 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(E, F, C)) | (~q2(D, D, D)) | (~k0(D)) | (~r1(D)) | q2(C, D, C))) | (~k0(b)) | (~r1(b)) | (~m0(d, d, d)) | (~q2(b, b, b)) | q2(d, b, d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.47/0.65 tff(99,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[98, 92, 89, 79, 68, 35, 1])).
% 0.47/0.65 tff(100,plain,(q2(d, b, d)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(101,plain,
% 0.47/0.65 (^[I: $i, H: $i, G: $i] : refl(((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(102,plain,
% 0.47/0.65 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[101])).
% 0.47/0.65 tff(103,plain,
% 0.47/0.65 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H)) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(104,plain,
% 0.47/0.65 (^[I: $i, H: $i, G: $i] : trans(monotonicity(rewrite((q3(G, H) | (~q2(I, G, H))) <=> ((~q2(I, G, H)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> (((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))))), rewrite((((~q2(I, G, H)) | q3(G, H)) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))), (((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(105,plain,
% 0.47/0.65 (![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G))) <=> ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[104])).
% 0.47/0.65 tff(106,axiom,(![I: $i, H: $i, G: $i] : ((q3(G, H) | (~q2(I, G, H))) | (~n0(I, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_255')).
% 0.47/0.65 tff(107,plain,
% 0.47/0.65 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.47/0.65 tff(108,plain,
% 0.47/0.65 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.47/0.65 tff(109,plain,(
% 0.47/0.65 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.47/0.65 inference(skolemize,[status(sab)],[108])).
% 0.47/0.65 tff(110,plain,
% 0.47/0.65 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.47/0.65 tff(111,plain,
% 0.47/0.65 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~n0(d, b)) | q3(b, d) | (~q2(d, b, d)))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (~n0(d, b)) | q3(b, d) | (~q2(d, b, d)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(112,plain,
% 0.47/0.65 (((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d)) <=> ((~n0(d, b)) | q3(b, d) | (~q2(d, b, d)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(113,plain,
% 0.47/0.65 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~n0(d, b)) | q3(b, d) | (~q2(d, b, d))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[112])).
% 0.47/0.65 tff(114,plain,
% 0.47/0.65 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (~n0(d, b)) | q3(b, d) | (~q2(d, b, d)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[113, 111])).
% 0.47/0.65 tff(115,plain,
% 0.47/0.65 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(d, b, d)) | (~n0(d, b)) | q3(b, d))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(116,plain,
% 0.47/0.65 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (~n0(d, b)) | q3(b, d) | (~q2(d, b, d))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.47/0.65 tff(117,plain,
% 0.47/0.65 (q3(b, d) | (~q2(d, b, d))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[116, 41, 110])).
% 0.47/0.65 tff(118,plain,
% 0.47/0.65 (q3(b, d)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[117, 100])).
% 0.47/0.65 tff(119,assumption,(~p0(b, b)), introduced(assumption)).
% 0.47/0.65 tff(120,plain,
% 0.47/0.65 (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(121,plain,
% 0.47/0.65 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.47/0.65 inference(quant_intro,[status(thm)],[120])).
% 0.47/0.65 tff(122,plain,
% 0.47/0.65 (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(123,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.47/0.65 tff(124,plain,
% 0.47/0.65 (![X: $i] : p0(b, X)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.47/0.65 tff(125,plain,(
% 0.47/0.65 ![X: $i] : p0(b, X)),
% 0.47/0.65 inference(skolemize,[status(sab)],[124])).
% 0.47/0.65 tff(126,plain,
% 0.47/0.65 (![X: $i] : p0(b, X)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.47/0.65 tff(127,plain,
% 0.47/0.65 ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(128,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[127, 126, 119])).
% 0.47/0.65 tff(129,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(130,plain,
% 0.47/0.65 (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(131,plain,
% 0.47/0.65 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[130])).
% 0.47/0.65 tff(132,plain,
% 0.47/0.65 (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(133,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.47/0.65 tff(134,plain,
% 0.47/0.65 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.47/0.65 tff(135,plain,(
% 0.47/0.65 ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[134])).
% 0.47/0.65 tff(136,plain,
% 0.47/0.65 (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.47/0.65 tff(137,plain,
% 0.47/0.65 (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(138,plain,
% 0.47/0.65 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(139,plain,
% 0.47/0.65 ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.47/0.65 tff(140,plain,
% 0.47/0.65 (s1(b)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[139, 136, 129])).
% 0.47/0.65 tff(141,plain,
% 0.47/0.65 (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(142,plain,
% 0.47/0.65 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[141])).
% 0.47/0.65 tff(143,plain,
% 0.47/0.65 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(144,plain,
% 0.47/0.65 (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(145,plain,
% 0.47/0.65 (![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[144])).
% 0.47/0.65 tff(146,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.47/0.65 tff(147,plain,
% 0.47/0.65 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.47/0.65 tff(148,plain,
% 0.47/0.65 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.47/0.65 tff(149,plain,(
% 0.47/0.65 ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.47/0.65 inference(skolemize,[status(sab)],[148])).
% 0.47/0.65 tff(150,plain,
% 0.47/0.65 (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.47/0.65 tff(151,plain,
% 0.47/0.65 (q0(d, d) <=> q0(d, d)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(152,axiom,(q0(d, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.47/0.65 tff(153,plain,
% 0.47/0.65 (q0(d, d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.47/0.65 tff(154,plain,
% 0.47/0.65 (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(155,plain,
% 0.47/0.65 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(d, d)) | (~s1(b)) | s1(d))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(156,plain,
% 0.47/0.65 ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (~q0(d, d)) | (~s1(b)) | s1(d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.47/0.65 tff(157,plain,
% 0.47/0.65 (s1(d)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[156, 153, 150, 140])).
% 0.47/0.65 tff(158,plain,
% 0.47/0.65 (k0(e) <=> k0(e)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(159,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.47/0.65 tff(160,plain,
% 0.47/0.65 (k0(e)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.47/0.65 tff(161,plain,
% 0.47/0.65 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(162,plain,
% 0.47/0.65 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(163,plain,
% 0.47/0.65 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(164,plain,
% 0.47/0.65 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[163])).
% 0.47/0.65 tff(165,plain,
% 0.47/0.65 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.47/0.65 inference(transitivity,[status(thm)],[164, 162])).
% 0.47/0.65 tff(166,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.47/0.65 tff(167,plain,
% 0.47/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.47/0.65 tff(168,plain,
% 0.47/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[167, 161])).
% 0.47/0.65 tff(169,plain,
% 0.47/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.47/0.65 tff(170,plain,
% 0.47/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[169, 161])).
% 0.47/0.65 tff(171,plain,
% 0.47/0.65 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[170, 161])).
% 0.47/0.65 tff(172,plain,
% 0.47/0.65 (q1(d, d, d)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[171, 61, 160])).
% 0.47/0.65 tff(173,plain,
% 0.47/0.65 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(174,plain,
% 0.47/0.65 (((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d)) <=> ((~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(175,plain,
% 0.47/0.65 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[174])).
% 0.47/0.65 tff(176,plain,
% 0.47/0.65 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[175, 173])).
% 0.47/0.65 tff(177,plain,
% 0.47/0.65 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | ((~q0(d, d)) | (~s0(d)) | (~q1(d, d, d)) | r1(d))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(178,plain,
% 0.47/0.65 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))) | (~s0(d)) | (~q0(d, d)) | r1(d) | (~q1(d, d, d))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.47/0.65 tff(179,plain,
% 0.47/0.65 (r1(d)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[178, 61, 153, 172, 55])).
% 0.47/0.65 tff(180,plain,
% 0.47/0.65 (((~r1(d)) | s2(d) | (~s1(d))) <=> ((~r1(d)) | s2(d) | (~s1(d)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(181,plain,
% 0.47/0.65 (((s2(d) | (~r1(d))) | (~s1(d))) <=> ((~r1(d)) | s2(d) | (~s1(d)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(182,axiom,((s2(d) | (~r1(d))) | (~s1(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_191')).
% 0.47/0.65 tff(183,plain,
% 0.47/0.65 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.47/0.65 tff(184,plain,
% 0.47/0.65 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[183, 180])).
% 0.47/0.65 tff(185,plain,
% 0.47/0.65 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.47/0.65 tff(186,plain,
% 0.47/0.65 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[185, 180])).
% 0.47/0.65 tff(187,plain,
% 0.47/0.65 ((~r1(d)) | s2(d) | (~s1(d))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[186, 180])).
% 0.47/0.65 tff(188,plain,
% 0.47/0.65 (s2(d) | (~s1(d))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[187, 179])).
% 0.47/0.65 tff(189,plain,
% 0.47/0.65 (s2(d)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[188, 157])).
% 0.47/0.65 tff(190,plain,
% 0.47/0.65 (^[B: $i, D: $i, C: $i] : refl(((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C)) <=> ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C)))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(191,plain,
% 0.47/0.65 (![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C)) <=> ![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[190])).
% 0.47/0.65 tff(192,plain,
% 0.47/0.65 (![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C)) <=> ![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(193,plain,
% 0.47/0.65 (^[B: $i, D: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((q3(B, C) | (~n1(D, B, C))) <=> ((~n1(D, B, C)) | q3(B, C))), (((q3(B, C) | (~n1(D, B, C))) | (~s2(B))) <=> (((~n1(D, B, C)) | q3(B, C)) | (~s2(B))))), rewrite((((~n1(D, B, C)) | q3(B, C)) | (~s2(B))) <=> ((~n1(D, B, C)) | (~s2(B)) | q3(B, C))), (((q3(B, C) | (~n1(D, B, C))) | (~s2(B))) <=> ((~n1(D, B, C)) | (~s2(B)) | q3(B, C)))), ((((q3(B, C) | (~n1(D, B, C))) | (~s2(B))) | (~q3(C, B))) <=> (((~n1(D, B, C)) | (~s2(B)) | q3(B, C)) | (~q3(C, B))))), rewrite((((~n1(D, B, C)) | (~s2(B)) | q3(B, C)) | (~q3(C, B))) <=> ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))), ((((q3(B, C) | (~n1(D, B, C))) | (~s2(B))) | (~q3(C, B))) <=> ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(194,plain,
% 0.47/0.65 (![B: $i, D: $i, C: $i] : (((q3(B, C) | (~n1(D, B, C))) | (~s2(B))) | (~q3(C, B))) <=> ![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[193])).
% 0.47/0.65 tff(195,axiom,(![B: $i, D: $i, C: $i] : (((q3(B, C) | (~n1(D, B, C))) | (~s2(B))) | (~q3(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_257')).
% 0.47/0.65 tff(196,plain,
% 0.47/0.65 (![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.47/0.65 tff(197,plain,
% 0.47/0.65 (![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.47/0.65 tff(198,plain,(
% 0.47/0.65 ![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))),
% 0.47/0.65 inference(skolemize,[status(sab)],[197])).
% 0.47/0.65 tff(199,plain,
% 0.47/0.65 (![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.47/0.65 tff(200,plain,
% 0.47/0.65 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(201,plain,
% 0.47/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[200])).
% 0.47/0.65 tff(202,plain,
% 0.47/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(203,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.47/0.65 tff(204,plain,
% 0.47/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.47/0.65 tff(205,plain,(
% 0.47/0.65 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[204])).
% 0.47/0.65 tff(206,plain,
% 0.47/0.65 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.47/0.65 tff(207,plain,
% 0.47/0.65 (n0(b, a) <=> n0(b, a)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(208,axiom,(n0(b, a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_37')).
% 0.47/0.65 tff(209,plain,
% 0.47/0.65 (n0(b, a)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.47/0.65 tff(210,plain,
% 0.47/0.65 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(211,plain,
% 0.47/0.65 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(a) | (~n0(b, a)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(212,plain,
% 0.47/0.65 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(a) | (~n0(b, a))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.47/0.65 tff(213,plain,
% 0.47/0.65 (k1(a)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[212, 209, 206])).
% 0.47/0.65 tff(214,plain,
% 0.47/0.65 (n0(d, e) <=> n0(d, e)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(215,axiom,(n0(d, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_3')).
% 0.47/0.65 tff(216,plain,
% 0.47/0.65 (n0(d, e)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.47/0.65 tff(217,plain,
% 0.47/0.65 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(218,plain,
% 0.47/0.65 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(e) | (~n0(d, e)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(219,plain,
% 0.47/0.65 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(e) | (~n0(d, e))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.47/0.65 tff(220,plain,
% 0.47/0.65 (k1(e)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[219, 216, 206])).
% 0.47/0.65 tff(221,assumption,(~m1(d, e, e)), introduced(assumption)).
% 0.47/0.65 tff(222,plain,
% 0.47/0.65 (^[B: $i, A: $i] : refl(((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)) <=> ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(223,plain,
% 0.47/0.65 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)) <=> ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[222])).
% 0.47/0.65 tff(224,plain,
% 0.47/0.65 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B)) <=> ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(225,plain,
% 0.47/0.65 (^[B: $i, A: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1(A, B, B) | (~k1(a))) <=> ((~k1(a)) | m1(A, B, B))), (((m1(A, B, B) | (~k1(a))) | (~k1(B))) <=> (((~k1(a)) | m1(A, B, B)) | (~k1(B))))), rewrite((((~k1(a)) | m1(A, B, B)) | (~k1(B))) <=> ((~k1(a)) | (~k1(B)) | m1(A, B, B))), (((m1(A, B, B) | (~k1(a))) | (~k1(B))) <=> ((~k1(a)) | (~k1(B)) | m1(A, B, B)))), ((((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A))) <=> (((~k1(a)) | (~k1(B)) | m1(A, B, B)) | (~q0(A, A))))), rewrite((((~k1(a)) | (~k1(B)) | m1(A, B, B)) | (~q0(A, A))) <=> ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))), ((((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A))) <=> ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(226,plain,
% 0.47/0.65 (![B: $i, A: $i] : (((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A))) <=> ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[225])).
% 0.47/0.65 tff(227,axiom,(![B: $i, A: $i] : (((m1(A, B, B) | (~k1(a))) | (~k1(B))) | (~q0(A, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_034')).
% 0.47/0.65 tff(228,plain,
% 0.47/0.65 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.47/0.65 tff(229,plain,
% 0.47/0.65 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.47/0.65 tff(230,plain,(
% 0.47/0.65 ![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.47/0.65 inference(skolemize,[status(sab)],[229])).
% 0.47/0.65 tff(231,plain,
% 0.47/0.65 (![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[230, 223])).
% 0.47/0.65 tff(232,plain,
% 0.47/0.65 (((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))) <=> ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | (~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(233,plain,
% 0.47/0.65 (((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e)) <=> ((~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(234,plain,
% 0.47/0.65 (((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e))) <=> ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[233])).
% 0.47/0.65 tff(235,plain,
% 0.47/0.65 (((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e))) <=> ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | (~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[234, 232])).
% 0.47/0.65 tff(236,plain,
% 0.47/0.65 ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | ((~k1(a)) | (~q0(d, d)) | (~k1(e)) | m1(d, e, e))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(237,plain,
% 0.47/0.65 ((~![B: $i, A: $i] : ((~k1(a)) | (~q0(A, A)) | (~k1(B)) | m1(A, B, B))) | (~k1(a)) | (~q0(d, d)) | m1(d, e, e) | (~k1(e))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.47/0.65 tff(238,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[237, 153, 231, 221, 220, 213])).
% 0.47/0.65 tff(239,plain,(m1(d, e, e)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.66 tff(240,plain,
% 0.47/0.66 (q0(b, e) <=> q0(b, e)),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(241,axiom,(q0(b, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_21')).
% 0.47/0.66 tff(242,plain,
% 0.47/0.66 (q0(b, e)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.47/0.66 tff(243,plain,
% 0.47/0.66 (((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b))) <=> ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(244,plain,
% 0.47/0.66 ((((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b)) | (~k0(b))) <=> ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(245,plain,
% 0.47/0.66 ((((~q0(b, e)) | n1(d, d, b)) | (~m1(d, e, e))) <=> ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(246,plain,
% 0.47/0.66 ((n1(d, d, b) | (~q0(b, e))) <=> ((~q0(b, e)) | n1(d, d, b))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(247,plain,
% 0.47/0.66 (((n1(d, d, b) | (~q0(b, e))) | (~m1(d, e, e))) <=> (((~q0(b, e)) | n1(d, d, b)) | (~m1(d, e, e)))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[246])).
% 0.47/0.66 tff(248,plain,
% 0.47/0.66 (((n1(d, d, b) | (~q0(b, e))) | (~m1(d, e, e))) <=> ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b))),
% 0.47/0.66 inference(transitivity,[status(thm)],[247, 245])).
% 0.47/0.66 tff(249,plain,
% 0.47/0.66 ((((n1(d, d, b) | (~q0(b, e))) | (~m1(d, e, e))) | (~k0(b))) <=> (((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b)) | (~k0(b)))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[248])).
% 0.47/0.66 tff(250,plain,
% 0.47/0.66 ((((n1(d, d, b) | (~q0(b, e))) | (~m1(d, e, e))) | (~k0(b))) <=> ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[249, 244])).
% 0.47/0.66 tff(251,axiom,(((n1(d, d, b) | (~q0(b, e))) | (~m1(d, e, e))) | (~k0(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_060')).
% 0.47/0.66 tff(252,plain,
% 0.47/0.66 ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.47/0.66 tff(253,plain,
% 0.47/0.66 ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[252, 243])).
% 0.47/0.66 tff(254,plain,
% 0.47/0.66 ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[253, 243])).
% 0.47/0.66 tff(255,plain,
% 0.47/0.66 ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[254, 243])).
% 0.47/0.66 tff(256,plain,
% 0.47/0.66 ((~m1(d, e, e)) | (~q0(b, e)) | n1(d, d, b) | (~k0(b))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[255, 243])).
% 0.47/0.66 tff(257,plain,
% 0.47/0.66 ((~m1(d, e, e)) | n1(d, d, b)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[256, 242, 92])).
% 0.47/0.66 tff(258,plain,
% 0.47/0.66 (n1(d, d, b)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[257, 239])).
% 0.47/0.66 tff(259,plain,
% 0.47/0.66 (((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | ((~s2(d)) | q3(d, b) | (~n1(d, d, b)) | (~q3(b, d)))) <=> ((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | (~s2(d)) | q3(d, b) | (~n1(d, d, b)) | (~q3(b, d)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(260,plain,
% 0.47/0.66 (((~n1(d, d, b)) | (~s2(d)) | (~q3(b, d)) | q3(d, b)) <=> ((~s2(d)) | q3(d, b) | (~n1(d, d, b)) | (~q3(b, d)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(261,plain,
% 0.47/0.66 (((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | ((~n1(d, d, b)) | (~s2(d)) | (~q3(b, d)) | q3(d, b))) <=> ((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | ((~s2(d)) | q3(d, b) | (~n1(d, d, b)) | (~q3(b, d))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[260])).
% 0.47/0.66 tff(262,plain,
% 0.47/0.66 (((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | ((~n1(d, d, b)) | (~s2(d)) | (~q3(b, d)) | q3(d, b))) <=> ((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | (~s2(d)) | q3(d, b) | (~n1(d, d, b)) | (~q3(b, d)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[261, 259])).
% 0.47/0.66 tff(263,plain,
% 0.47/0.66 ((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | ((~n1(d, d, b)) | (~s2(d)) | (~q3(b, d)) | q3(d, b))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(264,plain,
% 0.47/0.67 ((~![B: $i, D: $i, C: $i] : ((~n1(D, B, C)) | (~s2(B)) | (~q3(C, B)) | q3(B, C))) | (~s2(d)) | q3(d, b) | (~n1(d, d, b)) | (~q3(b, d))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.47/0.67 tff(265,plain,
% 0.47/0.67 ((~s2(d)) | q3(d, b) | (~q3(b, d))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[264, 258, 199])).
% 0.47/0.67 tff(266,plain,
% 0.47/0.67 (q3(d, b) | (~q3(b, d))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[265, 189])).
% 0.47/0.67 tff(267,plain,
% 0.47/0.67 (q3(d, b)),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[266, 118])).
% 0.47/0.67 tff(268,plain,
% 0.47/0.67 (^[X: $i] : refl((~q3(d, X)) <=> (~q3(d, X)))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(269,plain,
% 0.47/0.67 (![X: $i] : (~q3(d, X)) <=> ![X: $i] : (~q3(d, X))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[268])).
% 0.47/0.67 tff(270,plain,
% 0.47/0.67 (![X: $i] : (~q3(d, X)) <=> ![X: $i] : (~q3(d, X))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(271,axiom,(![X: $i] : (~q3(d, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.47/0.67 tff(272,plain,
% 0.47/0.67 (![X: $i] : (~q3(d, X))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.47/0.67 tff(273,plain,(
% 0.47/0.67 ![X: $i] : (~q3(d, X))),
% 0.47/0.67 inference(skolemize,[status(sab)],[272])).
% 0.47/0.67 tff(274,plain,
% 0.47/0.67 (![X: $i] : (~q3(d, X))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[273, 269])).
% 0.47/0.67 tff(275,plain,
% 0.47/0.67 ((~![X: $i] : (~q3(d, X))) | (~q3(d, b))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(276,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[275, 274, 267])).
% 0.47/0.67 % SZS output end Proof
% 0.47/0.67 % E exiting
%------------------------------------------------------------------------------