TSTP Solution File: SYN159-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN159-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 : Thu Sep 29 23:54:00 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN159-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 01:58:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 tff(n5_type, type, (
% 0.21/0.51 n5: ( $i * $i ) > $o)).
% 0.21/0.51 tff(e_type, type, (
% 0.21/0.51 e: $i)).
% 0.21/0.51 tff(q4_type, type, (
% 0.21/0.51 q4: ( $i * $i ) > $o)).
% 0.21/0.51 tff(b_type, type, (
% 0.21/0.51 b: $i)).
% 0.21/0.51 tff(m3_type, type, (
% 0.21/0.51 m3: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(n2_type, type, (
% 0.21/0.51 n2: $i > $o)).
% 0.21/0.51 tff(p1_type, type, (
% 0.21/0.51 p1: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(k0_type, type, (
% 0.21/0.51 k0: $i > $o)).
% 0.21/0.51 tff(r0_type, type, (
% 0.21/0.51 r0: $i > $o)).
% 0.21/0.51 tff(p2_type, type, (
% 0.21/0.51 p2: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(m1_type, type, (
% 0.21/0.51 m1: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(q2_type, type, (
% 0.21/0.51 q2: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(l1_type, type, (
% 0.21/0.51 l1: ( $i * $i ) > $o)).
% 0.21/0.51 tff(p0_type, type, (
% 0.21/0.51 p0: ( $i * $i ) > $o)).
% 0.21/0.51 tff(m0_type, type, (
% 0.21/0.51 m0: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(c_type, type, (
% 0.21/0.51 c: $i)).
% 0.21/0.51 tff(k3_type, type, (
% 0.21/0.51 k3: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(m2_type, type, (
% 0.21/0.51 m2: $i > $o)).
% 0.21/0.51 tff(k1_type, type, (
% 0.21/0.51 k1: $i > $o)).
% 0.21/0.51 tff(n0_type, type, (
% 0.21/0.51 n0: ( $i * $i ) > $o)).
% 0.21/0.51 tff(d_type, type, (
% 0.21/0.51 d: $i)).
% 0.21/0.51 tff(a_type, type, (
% 0.21/0.51 a: $i)).
% 0.21/0.51 tff(l0_type, type, (
% 0.21/0.51 l0: $i > $o)).
% 0.21/0.51 tff(s0_type, type, (
% 0.21/0.51 s0: $i > $o)).
% 0.21/0.51 tff(r2_type, type, (
% 0.21/0.51 r2: $i > $o)).
% 0.21/0.51 tff(r1_type, type, (
% 0.21/0.51 r1: $i > $o)).
% 0.21/0.51 tff(q1_type, type, (
% 0.21/0.51 q1: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(q0_type, type, (
% 0.21/0.51 q0: ( $i * $i ) > $o)).
% 0.21/0.51 tff(p4_type, type, (
% 0.21/0.51 p4: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(n1_type, type, (
% 0.21/0.51 n1: ( $i * $i * $i ) > $o)).
% 0.21/0.51 tff(n4_type, type, (
% 0.21/0.51 n4: ( $i * $i ) > $o)).
% 0.21/0.51 tff(k4_type, type, (
% 0.21/0.51 k4: $i > $o)).
% 0.21/0.51 tff(n3_type, type, (
% 0.21/0.51 n3: $i > $o)).
% 0.21/0.51 tff(q3_type, type, (
% 0.21/0.51 q3: ( $i * $i ) > $o)).
% 0.21/0.51 tff(1,plain,
% 0.21/0.51 (^[B: $i, A: $i, C: $i] : refl((n2(A) | (~p1(B, C, A))) <=> (n2(A) | (~p1(B, C, A))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(2,plain,
% 0.21/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.51 tff(3,plain,
% 0.21/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A))) <=> ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(4,axiom,(![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_137')).
% 0.21/0.51 tff(5,plain,
% 0.21/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.51 tff(6,plain,(
% 0.21/0.51 ![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[5])).
% 0.21/0.51 tff(7,plain,
% 0.21/0.51 (![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.51 tff(8,plain,
% 0.21/0.51 (p1(e, e, e) <=> p1(e, e, e)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(9,plain,
% 0.21/0.51 (($false | $false | p1(e, e, e)) <=> p1(e, e, e)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(10,plain,
% 0.21/0.51 ((~$true) <=> $false),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(11,axiom,(k0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_28')).
% 0.21/0.51 tff(12,plain,
% 0.21/0.51 (k0(e) <=> $true),
% 0.21/0.51 inference(iff_true,[status(thm)],[11])).
% 0.21/0.51 tff(13,plain,
% 0.21/0.51 ((~k0(e)) <=> (~$true)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.51 tff(14,plain,
% 0.21/0.51 ((~k0(e)) <=> $false),
% 0.21/0.51 inference(transitivity,[status(thm)],[13, 10])).
% 0.21/0.51 tff(15,axiom,(r0(e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_13')).
% 0.21/0.51 tff(16,plain,
% 0.21/0.51 (r0(e) <=> $true),
% 0.21/0.51 inference(iff_true,[status(thm)],[15])).
% 0.21/0.51 tff(17,plain,
% 0.21/0.51 ((~r0(e)) <=> (~$true)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.51 tff(18,plain,
% 0.21/0.51 ((~r0(e)) <=> $false),
% 0.21/0.51 inference(transitivity,[status(thm)],[17, 10])).
% 0.21/0.51 tff(19,plain,
% 0.21/0.51 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ($false | $false | p1(e, e, e))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[18, 14])).
% 0.21/0.51 tff(20,plain,
% 0.21/0.51 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> p1(e, e, e)),
% 0.21/0.51 inference(transitivity,[status(thm)],[19, 9])).
% 0.21/0.51 tff(21,plain,
% 0.21/0.51 (((~r0(e)) | (~k0(e)) | p1(e, e, e)) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(22,plain,
% 0.21/0.51 ((((~r0(e)) | p1(e, e, e)) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(23,plain,
% 0.21/0.51 ((p1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | p1(e, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(24,plain,
% 0.21/0.51 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> (((~r0(e)) | p1(e, e, e)) | (~k0(e)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.51 tff(25,plain,
% 0.21/0.51 (((p1(e, e, e) | (~r0(e))) | (~k0(e))) <=> ((~r0(e)) | (~k0(e)) | p1(e, e, e))),
% 0.21/0.51 inference(transitivity,[status(thm)],[24, 22])).
% 0.21/0.51 tff(26,axiom,((p1(e, e, e) | (~r0(e))) | (~k0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_090')).
% 0.21/0.51 tff(27,plain,
% 0.21/0.51 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.51 tff(28,plain,
% 0.21/0.51 ((~r0(e)) | (~k0(e)) | p1(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.21/0.51 tff(29,plain,
% 0.21/0.51 (p1(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.21/0.51 tff(30,plain,
% 0.21/0.51 (p1(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[29, 8])).
% 0.21/0.51 tff(31,plain,
% 0.21/0.51 (((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(e) | (~p1(e, e, e)))) <=> ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(e) | (~p1(e, e, e)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(32,plain,
% 0.21/0.51 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | (n2(e) | (~p1(e, e, e)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(33,plain,
% 0.21/0.51 ((~![B: $i, A: $i, C: $i] : (n2(A) | (~p1(B, C, A)))) | n2(e) | (~p1(e, e, e))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.51 tff(34,plain,
% 0.21/0.51 (n2(e)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[33, 30, 7])).
% 0.21/0.51 tff(35,plain,
% 0.21/0.51 (^[D: $i, E: $i] : refl((p2(D, E, D) | (~m1(E, D, E))) <=> (p2(D, E, D) | (~m1(E, D, E))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(36,plain,
% 0.21/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.51 tff(37,plain,
% 0.21/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E))) <=> ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(38,axiom,(![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_176')).
% 0.21/0.51 tff(39,plain,
% 0.21/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.51 tff(40,plain,(
% 0.21/0.51 ![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[39])).
% 0.21/0.51 tff(41,plain,
% 0.21/0.51 (![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.51 tff(42,plain,
% 0.21/0.51 (m1(e, e, e) <=> m1(e, e, e)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(43,plain,
% 0.21/0.51 (($false | m1(e, e, e)) <=> m1(e, e, e)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(44,plain,
% 0.21/0.51 (((~r0(e)) | m1(e, e, e)) <=> ($false | m1(e, e, e))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.51 tff(45,plain,
% 0.21/0.51 (((~r0(e)) | m1(e, e, e)) <=> m1(e, e, e)),
% 0.21/0.51 inference(transitivity,[status(thm)],[44, 43])).
% 0.21/0.51 tff(46,plain,
% 0.21/0.51 ((m1(e, e, e) | (~r0(e))) <=> ((~r0(e)) | m1(e, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(47,axiom,(m1(e, e, e) | (~r0(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_012')).
% 0.21/0.51 tff(48,plain,
% 0.21/0.51 ((~r0(e)) | m1(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.51 tff(49,plain,
% 0.21/0.51 (m1(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.21/0.51 tff(50,plain,
% 0.21/0.51 (m1(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.51 tff(51,plain,
% 0.21/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(e, e, e)) | p2(e, e, e))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(52,plain,
% 0.21/0.51 ((p2(e, e, e) | (~m1(e, e, e))) <=> ((~m1(e, e, e)) | p2(e, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(53,plain,
% 0.21/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | ((~m1(e, e, e)) | p2(e, e, e)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.51 tff(54,plain,
% 0.21/0.51 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e))),
% 0.21/0.51 inference(transitivity,[status(thm)],[53, 51])).
% 0.21/0.51 tff(55,plain,
% 0.21/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(e, e, e) | (~m1(e, e, e)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(56,plain,
% 0.21/0.51 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (~m1(e, e, e)) | p2(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.51 tff(57,plain,
% 0.21/0.51 (p2(e, e, e)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[56, 50, 41])).
% 0.21/0.51 tff(58,plain,
% 0.21/0.51 (^[D: $i] : refl(((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(59,plain,
% 0.21/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.51 tff(60,plain,
% 0.21/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e)) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(61,plain,
% 0.21/0.51 (^[D: $i] : trans(monotonicity(rewrite((m3(D, e, e) | (~n2(e))) <=> ((~n2(e)) | m3(D, e, e))), (((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> (((~n2(e)) | m3(D, e, e)) | (~p2(D, e, e))))), rewrite((((~n2(e)) | m3(D, e, e)) | (~p2(D, e, e))) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))), (((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(62,plain,
% 0.21/0.51 (![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e))) <=> ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.51 tff(63,axiom,(![D: $i] : ((m3(D, e, e) | (~n2(e))) | (~p2(D, e, e)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_234')).
% 0.21/0.51 tff(64,plain,
% 0.21/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.51 tff(65,plain,
% 0.21/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.51 tff(66,plain,(
% 0.21/0.51 ![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.51 inference(skolemize,[status(sab)],[65])).
% 0.21/0.51 tff(67,plain,
% 0.21/0.51 (![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.51 tff(68,plain,
% 0.21/0.51 (((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | ((~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))) <=> ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | (~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(69,plain,
% 0.21/0.51 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | ((~n2(e)) | (~p2(e, e, e)) | m3(e, e, e))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(70,plain,
% 0.21/0.51 ((~![D: $i] : ((~n2(e)) | (~p2(D, e, e)) | m3(D, e, e))) | (~n2(e)) | (~p2(e, e, e)) | m3(e, e, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.51 tff(71,plain,
% 0.21/0.51 (m3(e, e, e)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[70, 67, 57, 34])).
% 0.21/0.51 tff(72,plain,
% 0.21/0.51 (^[D: $i, E: $i, F: $i, C: $i] : refl(((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(73,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.51 tff(74,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D)) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(75,plain,
% 0.21/0.51 (^[D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((l1(C, D) | (~p0(E, C))) <=> ((~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> (((~p0(E, C)) | l1(C, D)) | (~r0(F))))), rewrite((((~p0(E, C)) | l1(C, D)) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D))), (((l1(C, D) | (~p0(E, C))) | (~r0(F))) <=> ((~r0(F)) | (~p0(E, C)) | l1(C, D)))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> (((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))))), rewrite((((~r0(F)) | (~p0(E, C)) | l1(C, D)) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))), ((((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(76,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E))) <=> ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.51 tff(77,axiom,(![D: $i, E: $i, F: $i, C: $i] : (((l1(C, D) | (~p0(E, C))) | (~r0(F))) | (~m0(D, C, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_003')).
% 0.21/0.51 tff(78,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.51 tff(79,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.21/0.51 tff(80,plain,(
% 0.21/0.51 ![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.51 inference(skolemize,[status(sab)],[79])).
% 0.21/0.51 tff(81,plain,
% 0.21/0.51 (![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.51 tff(82,plain,
% 0.21/0.51 (m0(e, b, c) <=> m0(e, b, c)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(83,axiom,(m0(e, b, c)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_27')).
% 0.21/0.51 tff(84,plain,
% 0.21/0.51 (m0(e, b, c)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.51 tff(85,plain,
% 0.21/0.51 (p0(c, b) <=> p0(c, b)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(86,axiom,(p0(c, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_18')).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 (p0(c, b)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 (r0(b) <=> r0(b)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(89,axiom,(r0(b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_9')).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 (r0(b)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 (((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e)) <=> ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 (((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))) <=> ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e))),
% 0.21/0.51 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | ((~m0(e, b, c)) | (~r0(b)) | (~p0(c, b)) | l1(b, e))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 ((~![D: $i, E: $i, F: $i, C: $i] : ((~m0(D, C, E)) | (~r0(F)) | (~p0(E, C)) | l1(C, D))) | (~r0(b)) | (~p0(c, b)) | (~m0(e, b, c)) | l1(b, e)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (l1(b, e)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[96, 90, 87, 84, 81])).
% 0.21/0.52 tff(98,plain,
% 0.21/0.52 (^[H: $i, G: $i] : refl(((~l1(H, G)) | q2(G, G, H)) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(99,plain,
% 0.21/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.52 tff(100,plain,
% 0.21/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H)) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(101,plain,
% 0.21/0.52 (^[H: $i, G: $i] : rewrite((q2(G, G, H) | (~l1(H, G))) <=> ((~l1(H, G)) | q2(G, G, H)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(102,plain,
% 0.21/0.52 (![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G))) <=> ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.52 tff(103,axiom,(![H: $i, G: $i] : (q2(G, G, H) | (~l1(H, G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_186')).
% 0.21/0.52 tff(104,plain,
% 0.21/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.52 tff(105,plain,
% 0.21/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.21/0.52 tff(106,plain,(
% 0.21/0.52 ![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.52 inference(skolemize,[status(sab)],[105])).
% 0.21/0.52 tff(107,plain,
% 0.21/0.52 (![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.21/0.52 tff(108,plain,
% 0.21/0.52 (((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))) <=> ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(109,plain,
% 0.21/0.52 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | ((~l1(b, e)) | q2(e, e, b))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(110,plain,
% 0.21/0.52 ((~![H: $i, G: $i] : ((~l1(H, G)) | q2(G, G, H))) | (~l1(b, e)) | q2(e, e, b)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.52 tff(111,plain,
% 0.21/0.52 (q2(e, e, b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[110, 107, 97])).
% 0.21/0.52 tff(112,plain,
% 0.21/0.52 (^[B: $i, C: $i] : refl(((~p0(C, B)) | p1(B, B, B)) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(113,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[112])).
% 0.21/0.52 tff(114,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B)) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(115,plain,
% 0.21/0.52 (^[B: $i, C: $i] : rewrite((p1(B, B, B) | (~p0(C, B))) <=> ((~p0(C, B)) | p1(B, B, B)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(116,plain,
% 0.21/0.52 (![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B))) <=> ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.52 tff(117,axiom,(![B: $i, C: $i] : (p1(B, B, B) | (~p0(C, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_085')).
% 0.21/0.52 tff(118,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.52 tff(119,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.21/0.52 tff(120,plain,(
% 0.21/0.52 ![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.52 inference(skolemize,[status(sab)],[119])).
% 0.21/0.52 tff(121,plain,
% 0.21/0.52 (![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.21/0.52 tff(122,plain,
% 0.21/0.52 (((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))) <=> ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(123,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | ((~p0(c, b)) | p1(b, b, b))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(124,plain,
% 0.21/0.52 ((~![B: $i, C: $i] : ((~p0(C, B)) | p1(B, B, B))) | (~p0(c, b)) | p1(b, b, b)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.52 tff(125,plain,
% 0.21/0.52 (p1(b, b, b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[124, 87, 121])).
% 0.21/0.52 tff(126,plain,
% 0.21/0.52 (^[B: $i, D: $i, E: $i, C: $i] : refl(((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(127,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.52 tff(128,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(129,plain,
% 0.21/0.52 (^[B: $i, D: $i, E: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((k3(B, B, C) | (~p1(C, D, B))) <=> ((~p1(C, D, B)) | k3(B, B, C))), (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) <=> (((~p1(C, D, B)) | k3(B, B, C)) | (~m2(E))))), rewrite((((~p1(C, D, B)) | k3(B, B, C)) | (~m2(E))) <=> ((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))), (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) <=> ((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)))), ((((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> (((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) | (~m2(D))))), rewrite((((~m2(E)) | (~p1(C, D, B)) | k3(B, B, C)) | (~m2(D))) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))), ((((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(130,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, C: $i] : (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D))) <=> ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.52 tff(131,axiom,(![B: $i, D: $i, E: $i, C: $i] : (((k3(B, B, C) | (~p1(C, D, B))) | (~m2(E))) | (~m2(D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_201')).
% 0.21/0.52 tff(132,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.52 tff(133,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.21/0.52 tff(134,plain,(
% 0.21/0.52 ![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.52 inference(skolemize,[status(sab)],[133])).
% 0.21/0.52 tff(135,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.21/0.52 tff(136,plain,
% 0.21/0.52 (^[I: $i, J: $i] : refl((k1(I) | (~n0(J, I))) <=> (k1(I) | (~n0(J, I))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(137,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[136])).
% 0.21/0.52 tff(138,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I))) <=> ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(139,axiom,(![I: $i, J: $i] : (k1(I) | (~n0(J, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_001')).
% 0.21/0.52 tff(140,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.52 tff(141,plain,(
% 0.21/0.52 ![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[140])).
% 0.21/0.52 tff(142,plain,
% 0.21/0.52 (![I: $i, J: $i] : (k1(I) | (~n0(J, I)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.21/0.52 tff(143,plain,
% 0.21/0.52 (n0(d, b) <=> n0(d, b)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(144,axiom,(n0(d, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_7')).
% 0.21/0.52 tff(145,plain,
% 0.21/0.52 (n0(d, b)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.21/0.52 tff(146,plain,
% 0.21/0.52 (((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))) <=> ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(147,plain,
% 0.21/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | (k1(b) | (~n0(d, b)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(148,plain,
% 0.21/0.52 ((~![I: $i, J: $i] : (k1(I) | (~n0(J, I)))) | k1(b) | (~n0(d, b))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.52 tff(149,plain,
% 0.21/0.52 (k1(b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[148, 145, 142])).
% 0.21/0.52 tff(150,plain,
% 0.21/0.52 ((m2(b) | (~k1(b))) <=> (m2(b) | (~k1(b)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(151,axiom,(m2(b) | (~k1(b))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_136')).
% 0.21/0.52 tff(152,plain,
% 0.21/0.52 (m2(b) | (~k1(b))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.52 tff(153,plain,
% 0.21/0.52 (m2(b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.21/0.52 tff(154,plain,
% 0.21/0.52 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(155,plain,
% 0.21/0.52 (((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b)) <=> ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(156,plain,
% 0.21/0.52 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~p1(b, b, b)) | (~m2(b)) | k3(b, b, b)))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.52 tff(157,plain,
% 0.21/0.52 (((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))) <=> ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b))),
% 0.21/0.52 inference(transitivity,[status(thm)],[156, 154])).
% 0.21/0.52 tff(158,plain,
% 0.21/0.52 ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | ((~m2(b)) | (~m2(b)) | (~p1(b, b, b)) | k3(b, b, b))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(159,plain,
% 0.21/0.52 ((~![B: $i, D: $i, E: $i, C: $i] : ((~m2(D)) | (~m2(E)) | (~p1(C, D, B)) | k3(B, B, C))) | (~p1(b, b, b)) | (~m2(b)) | k3(b, b, b)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.52 tff(160,plain,
% 0.21/0.52 (k3(b, b, b)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[159, 153, 135, 125])).
% 0.21/0.52 tff(161,plain,
% 0.21/0.52 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(162,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[161])).
% 0.21/0.52 tff(163,plain,
% 0.21/0.52 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(164,plain,
% 0.21/0.52 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((q4(B, C) | (~k3(D, D, B))) <=> ((~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> (((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))))), rewrite((((~k3(D, D, B)) | q4(B, C)) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) <=> ((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> (((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))))), rewrite((((~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C)) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))), ((((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(165,plain,
% 0.21/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[164])).
% 0.21/0.53 tff(166,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : (((q4(B, C) | (~k3(D, D, B))) | (~q2(E, C, B))) | (~m3(E, F, E)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_295')).
% 0.21/0.53 tff(167,plain,
% 0.21/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.53 tff(168,plain,
% 0.21/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.21/0.53 tff(169,plain,(
% 0.21/0.53 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.21/0.53 inference(skolemize,[status(sab)],[168])).
% 0.21/0.53 tff(170,plain,
% 0.21/0.53 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.21/0.53 tff(171,plain,
% 0.21/0.53 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(172,plain,
% 0.21/0.53 (((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e)) <=> ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(173,plain,
% 0.21/0.53 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[172])).
% 0.21/0.53 tff(174,plain,
% 0.21/0.53 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e))),
% 0.21/0.53 inference(transitivity,[status(thm)],[173, 171])).
% 0.21/0.53 tff(175,plain,
% 0.21/0.53 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(e, e, e)) | (~q2(e, e, b)) | (~k3(b, b, b)) | q4(b, e))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(176,plain,
% 0.21/0.53 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(b, b, b)) | (~m3(e, e, e)) | (~q2(e, e, b)) | q4(b, e)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.53 tff(177,plain,
% 0.21/0.53 (q4(b, e)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[176, 170, 160, 111, 71])).
% 0.21/0.53 tff(178,plain,
% 0.21/0.53 (^[D: $i, C: $i] : refl((n5(C, C) | (~q4(D, C))) <=> (n5(C, C) | (~q4(D, C))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(179,plain,
% 0.21/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[178])).
% 0.21/0.53 tff(180,plain,
% 0.21/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C))) <=> ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(181,axiom,(![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_313')).
% 0.21/0.53 tff(182,plain,
% 0.21/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.21/0.53 tff(183,plain,(
% 0.21/0.53 ![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[182])).
% 0.21/0.53 tff(184,plain,
% 0.21/0.53 (![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.21/0.53 tff(185,plain,
% 0.21/0.53 (((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | (n5(e, e) | (~q4(b, e)))) <=> ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | n5(e, e) | (~q4(b, e)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(186,plain,
% 0.21/0.53 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | (n5(e, e) | (~q4(b, e)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(187,plain,
% 0.21/0.53 ((~![D: $i, C: $i] : (n5(C, C) | (~q4(D, C)))) | n5(e, e) | (~q4(b, e))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.21/0.53 tff(188,plain,
% 0.21/0.53 (n5(e, e)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[187, 184, 177])).
% 0.21/0.53 tff(189,plain,
% 0.21/0.53 (^[I: $i] : refl((m3(I, I, I) | (~p2(I, I, I))) <=> (m3(I, I, I) | (~p2(I, I, I))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(190,plain,
% 0.21/0.53 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[189])).
% 0.21/0.53 tff(191,plain,
% 0.21/0.53 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I))) <=> ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(192,axiom,(![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_238')).
% 0.21/0.53 tff(193,plain,
% 0.21/0.53 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.21/0.53 tff(194,plain,(
% 0.21/0.53 ![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[193])).
% 0.21/0.53 tff(195,plain,
% 0.21/0.53 (![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.21/0.53 tff(196,plain,
% 0.21/0.53 (m1(a, a, a) <=> m1(a, a, a)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(197,plain,
% 0.21/0.53 ((m1(a, a, a) | $false | $false) <=> m1(a, a, a)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(198,axiom,(l0(a)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_20')).
% 0.21/0.53 tff(199,plain,
% 0.21/0.53 (l0(a) <=> $true),
% 0.21/0.53 inference(iff_true,[status(thm)],[198])).
% 0.21/0.53 tff(200,plain,
% 0.21/0.53 ((~l0(a)) <=> (~$true)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[199])).
% 0.21/0.53 tff(201,plain,
% 0.21/0.53 ((~l0(a)) <=> $false),
% 0.21/0.53 inference(transitivity,[status(thm)],[200, 10])).
% 0.21/0.53 tff(202,axiom,(s0(d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_1')).
% 0.21/0.53 tff(203,plain,
% 0.21/0.53 (s0(d) <=> $true),
% 0.21/0.53 inference(iff_true,[status(thm)],[202])).
% 0.21/0.53 tff(204,plain,
% 0.21/0.53 ((~s0(d)) <=> (~$true)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[203])).
% 0.21/0.53 tff(205,plain,
% 0.21/0.53 ((~s0(d)) <=> $false),
% 0.21/0.53 inference(transitivity,[status(thm)],[204, 10])).
% 0.21/0.53 tff(206,plain,
% 0.21/0.53 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | $false | $false)),
% 0.21/0.53 inference(monotonicity,[status(thm)],[205, 201])).
% 0.21/0.53 tff(207,plain,
% 0.21/0.53 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> m1(a, a, a)),
% 0.21/0.53 inference(transitivity,[status(thm)],[206, 197])).
% 0.21/0.53 tff(208,plain,
% 0.21/0.53 ((m1(a, a, a) | (~s0(d)) | (~l0(a))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(209,plain,
% 0.21/0.53 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(210,plain,
% 0.21/0.53 ((m1(a, a, a) | (~l0(a))) <=> (m1(a, a, a) | (~l0(a)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(211,plain,
% 0.21/0.53 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> ((m1(a, a, a) | (~l0(a))) | (~s0(d)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[210])).
% 0.21/0.53 tff(212,plain,
% 0.21/0.53 (((m1(a, a, a) | (~l0(a))) | (~s0(d))) <=> (m1(a, a, a) | (~s0(d)) | (~l0(a)))),
% 0.21/0.53 inference(transitivity,[status(thm)],[211, 209])).
% 0.21/0.53 tff(213,axiom,((m1(a, a, a) | (~l0(a))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_023')).
% 0.21/0.53 tff(214,plain,
% 0.21/0.53 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.21/0.53 tff(215,plain,
% 0.21/0.53 (m1(a, a, a) | (~s0(d)) | (~l0(a))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[214, 208])).
% 0.21/0.53 tff(216,plain,
% 0.21/0.53 (m1(a, a, a)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[215, 207])).
% 0.21/0.53 tff(217,plain,
% 0.21/0.53 (m1(a, a, a)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[216, 196])).
% 0.21/0.53 tff(218,plain,
% 0.21/0.53 (((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))) <=> ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(219,plain,
% 0.21/0.53 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | (p2(a, a, a) | (~m1(a, a, a)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(220,plain,
% 0.21/0.53 ((~![D: $i, E: $i] : (p2(D, E, D) | (~m1(E, D, E)))) | p2(a, a, a) | (~m1(a, a, a))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.53 tff(221,plain,
% 0.21/0.53 (p2(a, a, a)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[220, 217, 41])).
% 0.21/0.53 tff(222,plain,
% 0.21/0.53 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(223,plain,
% 0.21/0.53 ((m3(a, a, a) | (~p2(a, a, a))) <=> ((~p2(a, a, a)) | m3(a, a, a))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(224,plain,
% 0.21/0.53 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | ((~p2(a, a, a)) | m3(a, a, a)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[223])).
% 0.21/0.53 tff(225,plain,
% 0.21/0.53 (((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))) <=> ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a))),
% 0.21/0.53 inference(transitivity,[status(thm)],[224, 222])).
% 0.21/0.53 tff(226,plain,
% 0.21/0.53 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (m3(a, a, a) | (~p2(a, a, a)))),
% 0.21/0.53 inference(quant_inst,[status(thm)],[])).
% 0.21/0.53 tff(227,plain,
% 0.21/0.53 ((~![I: $i] : (m3(I, I, I) | (~p2(I, I, I)))) | (~p2(a, a, a)) | m3(a, a, a)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.21/0.53 tff(228,plain,
% 0.21/0.53 (m3(a, a, a)),
% 0.21/0.53 inference(unit_resolution,[status(thm)],[227, 221, 195])).
% 0.21/0.53 tff(229,plain,
% 0.21/0.53 (^[I: $i] : refl((q2(I, I, I) | (~p1(I, I, I))) <=> (q2(I, I, I) | (~p1(I, I, I))))),
% 0.21/0.53 inference(bind,[status(th)],[])).
% 0.21/0.53 tff(230,plain,
% 0.21/0.53 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.53 inference(quant_intro,[status(thm)],[229])).
% 0.21/0.53 tff(231,plain,
% 0.21/0.53 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I))) <=> ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(232,axiom,(![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_181')).
% 0.21/0.53 tff(233,plain,
% 0.21/0.53 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.21/0.53 tff(234,plain,(
% 0.21/0.53 ![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.53 inference(skolemize,[status(sab)],[233])).
% 0.21/0.53 tff(235,plain,
% 0.21/0.53 (![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.21/0.53 tff(236,plain,
% 0.21/0.53 (p1(a, a, a) <=> p1(a, a, a)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(237,plain,
% 0.21/0.53 (($false | p1(a, a, a)) <=> p1(a, a, a)),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(238,plain,
% 0.21/0.53 (((~l0(a)) | p1(a, a, a)) <=> ($false | p1(a, a, a))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[201])).
% 0.21/0.53 tff(239,plain,
% 0.21/0.53 (((~l0(a)) | p1(a, a, a)) <=> p1(a, a, a)),
% 0.21/0.53 inference(transitivity,[status(thm)],[238, 237])).
% 0.21/0.53 tff(240,plain,
% 0.21/0.53 ((p1(a, a, a) | (~l0(a))) <=> ((~l0(a)) | p1(a, a, a))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(241,axiom,(p1(a, a, a) | (~l0(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_088')).
% 0.21/0.53 tff(242,plain,
% 0.21/0.53 ((~l0(a)) | p1(a, a, a)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.21/0.53 tff(243,plain,
% 0.21/0.53 (p1(a, a, a)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[242, 239])).
% 0.21/0.53 tff(244,plain,
% 0.21/0.53 (p1(a, a, a)),
% 0.21/0.53 inference(modus_ponens,[status(thm)],[243, 236])).
% 0.21/0.53 tff(245,plain,
% 0.21/0.53 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(246,plain,
% 0.21/0.53 ((q2(a, a, a) | (~p1(a, a, a))) <=> ((~p1(a, a, a)) | q2(a, a, a))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(247,plain,
% 0.21/0.54 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | ((~p1(a, a, a)) | q2(a, a, a)))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[246])).
% 0.21/0.54 tff(248,plain,
% 0.21/0.54 (((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))) <=> ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a))),
% 0.21/0.54 inference(transitivity,[status(thm)],[247, 245])).
% 0.21/0.54 tff(249,plain,
% 0.21/0.54 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (q2(a, a, a) | (~p1(a, a, a)))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(250,plain,
% 0.21/0.54 ((~![I: $i] : (q2(I, I, I) | (~p1(I, I, I)))) | (~p1(a, a, a)) | q2(a, a, a)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.21/0.54 tff(251,plain,
% 0.21/0.54 (q2(a, a, a)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[250, 244, 235])).
% 0.21/0.54 tff(252,plain,
% 0.21/0.54 (^[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)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(253,plain,
% 0.21/0.54 (![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))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[252])).
% 0.21/0.54 tff(254,plain,
% 0.21/0.54 (![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))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(255,plain,
% 0.21/0.54 (^[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))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(256,plain,
% 0.21/0.54 (![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))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[255])).
% 0.21/0.54 tff(257,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')).
% 0.21/0.54 tff(258,plain,
% 0.21/0.54 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.21/0.54 tff(259,plain,
% 0.21/0.54 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.21/0.54 tff(260,plain,(
% 0.21/0.54 ![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.54 inference(skolemize,[status(sab)],[259])).
% 0.21/0.54 tff(261,plain,
% 0.21/0.54 (![B: $i, A: $i, J: $i, C: $i] : ((~p0(C, J)) | (~n0(B, A)) | q1(J, A, J))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[260, 253])).
% 0.21/0.54 tff(262,plain,
% 0.21/0.54 (p0(b, d) <=> p0(b, d)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(263,axiom,(p0(b, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_10')).
% 0.21/0.54 tff(264,plain,
% 0.21/0.54 (p0(b, d)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.21/0.54 tff(265,plain,
% 0.21/0.54 (((~![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))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(266,plain,
% 0.21/0.54 ((~![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))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(267,plain,
% 0.21/0.54 ((~![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)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.21/0.54 tff(268,plain,
% 0.21/0.54 (q1(d, b, d)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[267, 145, 264, 261])).
% 0.21/0.54 tff(269,plain,
% 0.21/0.54 (^[D: $i, E: $i] : refl(((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(270,plain,
% 0.21/0.54 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[269])).
% 0.21/0.54 tff(271,plain,
% 0.21/0.54 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(272,plain,
% 0.21/0.54 (^[D: $i, E: $i] : trans(monotonicity(trans(monotonicity(iff_true(asserted(s0(d)), (s0(d) <=> $true)), ((~s0(d)) <=> (~$true))), rewrite((~$true) <=> $false), ((~s0(d)) <=> $false)), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)))), rewrite(((~q0(D, E)) | $false | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))), (((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(273,plain,
% 0.21/0.54 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D)) <=> ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[272])).
% 0.21/0.54 tff(274,plain,
% 0.21/0.54 (^[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))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(275,plain,
% 0.21/0.54 (![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))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[274])).
% 0.21/0.54 tff(276,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')).
% 0.21/0.54 tff(277,plain,
% 0.21/0.54 (![D: $i, E: $i] : ((~q0(D, E)) | (~s0(d)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.21/0.54 tff(278,plain,
% 0.21/0.54 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.21/0.54 tff(279,plain,
% 0.21/0.54 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.21/0.54 tff(280,plain,(
% 0.21/0.54 ![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(skolemize,[status(sab)],[279])).
% 0.21/0.54 tff(281,plain,
% 0.21/0.54 (![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[280, 270])).
% 0.21/0.54 tff(282,plain,
% 0.21/0.54 (q0(a, b) <=> q0(a, b)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(283,axiom,(q0(a, b)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.21/0.54 tff(284,plain,
% 0.21/0.54 (q0(a, b)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.21/0.54 tff(285,plain,
% 0.21/0.54 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(286,plain,
% 0.21/0.54 (((~q0(a, b)) | (~q1(d, b, d)) | r1(a)) <=> (r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(287,plain,
% 0.21/0.54 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(a) | (~q1(d, b, d)) | (~q0(a, b))))),
% 0.21/0.54 inference(monotonicity,[status(thm)],[286])).
% 0.21/0.54 tff(288,plain,
% 0.21/0.54 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b)))),
% 0.21/0.54 inference(transitivity,[status(thm)],[287, 285])).
% 0.21/0.54 tff(289,plain,
% 0.21/0.54 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(a, b)) | (~q1(d, b, d)) | r1(a))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(290,plain,
% 0.21/0.54 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(a) | (~q1(d, b, d)) | (~q0(a, b))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.21/0.54 tff(291,plain,
% 0.21/0.54 (r1(a)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[290, 284, 281, 268])).
% 0.21/0.54 tff(292,plain,
% 0.21/0.54 (^[G: $i] : refl(((~l0(G)) | (~r1(G)) | r2(G)) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(293,plain,
% 0.21/0.54 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[292])).
% 0.21/0.54 tff(294,plain,
% 0.21/0.54 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G)) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(295,plain,
% 0.21/0.54 (^[G: $i] : rewrite(((r2(G) | (~r1(G))) | (~l0(G))) <=> ((~l0(G)) | (~r1(G)) | r2(G)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(296,plain,
% 0.21/0.54 (![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G))) <=> ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[295])).
% 0.21/0.54 tff(297,axiom,(![G: $i] : ((r2(G) | (~r1(G))) | (~l0(G)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_188')).
% 0.21/0.54 tff(298,plain,
% 0.21/0.54 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.21/0.54 tff(299,plain,
% 0.21/0.54 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.21/0.54 tff(300,plain,(
% 0.21/0.54 ![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.54 inference(skolemize,[status(sab)],[299])).
% 0.21/0.54 tff(301,plain,
% 0.21/0.54 (![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.21/0.54 tff(302,plain,
% 0.21/0.54 (l0(a) <=> l0(a)),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(303,plain,
% 0.21/0.54 (l0(a)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[198, 302])).
% 0.21/0.54 tff(304,plain,
% 0.21/0.54 (((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))) <=> ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(305,plain,
% 0.21/0.55 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | ((~l0(a)) | (~r1(a)) | r2(a))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(306,plain,
% 0.21/0.55 ((~![G: $i] : ((~l0(G)) | (~r1(G)) | r2(G))) | (~l0(a)) | (~r1(a)) | r2(a)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.21/0.55 tff(307,plain,
% 0.21/0.55 (r2(a)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[306, 303, 301, 291])).
% 0.21/0.55 tff(308,plain,
% 0.21/0.55 (((~r2(a)) | k3(a, a, a)) <=> ((~r2(a)) | k3(a, a, a))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(309,plain,
% 0.21/0.55 ((k3(a, a, a) | (~r2(a))) <=> ((~r2(a)) | k3(a, a, a))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(310,axiom,(k3(a, a, a) | (~r2(a))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_204')).
% 0.21/0.55 tff(311,plain,
% 0.21/0.55 ((~r2(a)) | k3(a, a, a)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.21/0.55 tff(312,plain,
% 0.21/0.55 ((~r2(a)) | k3(a, a, a)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[311, 308])).
% 0.21/0.55 tff(313,plain,
% 0.21/0.55 (k3(a, a, a)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[312, 307])).
% 0.21/0.55 tff(314,plain,
% 0.21/0.55 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(315,plain,
% 0.21/0.55 (((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a)) <=> ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(316,plain,
% 0.21/0.55 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a)))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[315])).
% 0.21/0.55 tff(317,plain,
% 0.21/0.55 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a))),
% 0.21/0.55 inference(transitivity,[status(thm)],[316, 314])).
% 0.21/0.55 tff(318,plain,
% 0.21/0.55 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | ((~m3(a, a, a)) | (~q2(a, a, a)) | (~k3(a, a, a)) | q4(a, a))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(319,plain,
% 0.21/0.55 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~m3(E, F, E)) | (~q2(E, C, B)) | (~k3(D, D, B)) | q4(B, C))) | (~k3(a, a, a)) | (~q2(a, a, a)) | (~m3(a, a, a)) | q4(a, a)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.21/0.55 tff(320,plain,
% 0.21/0.55 (q4(a, a)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[319, 313, 170, 251, 228])).
% 0.21/0.55 tff(321,plain,
% 0.21/0.55 (^[I: $i, A: $i, J: $i] : refl(((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)) <=> ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(322,plain,
% 0.21/0.55 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)) <=> ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[321])).
% 0.21/0.55 tff(323,plain,
% 0.21/0.55 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I)) <=> ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(324,plain,
% 0.21/0.55 (^[I: $i, A: $i, J: $i] : trans(monotonicity(rewrite((k3(I, I, I) | (~r1(I))) <=> ((~r1(I)) | k3(I, I, I))), (((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A))) <=> (((~r1(I)) | k3(I, I, I)) | (~p2(J, A, A))))), rewrite((((~r1(I)) | k3(I, I, I)) | (~p2(J, A, A))) <=> ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))), (((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A))) <=> ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(325,plain,
% 0.21/0.55 (![I: $i, A: $i, J: $i] : ((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A))) <=> ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[324])).
% 0.21/0.55 tff(326,axiom,(![I: $i, A: $i, J: $i] : ((k3(I, I, I) | (~r1(I))) | (~p2(J, A, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_213')).
% 0.21/0.55 tff(327,plain,
% 0.21/0.55 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.21/0.55 tff(328,plain,
% 0.21/0.55 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[327, 323])).
% 0.21/0.55 tff(329,plain,(
% 0.21/0.55 ![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.21/0.55 inference(skolemize,[status(sab)],[328])).
% 0.21/0.55 tff(330,plain,
% 0.21/0.55 (![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[329, 322])).
% 0.21/0.55 tff(331,plain,
% 0.21/0.55 (q1(d, d, d) <=> q1(d, d, d)),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(332,plain,
% 0.21/0.55 (($false | $false | q1(d, d, d)) <=> q1(d, d, d)),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(333,plain,
% 0.21/0.55 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ($false | $false | q1(d, d, d))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[205, 14])).
% 0.21/0.55 tff(334,plain,
% 0.21/0.55 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> q1(d, d, d)),
% 0.21/0.55 inference(transitivity,[status(thm)],[333, 332])).
% 0.21/0.55 tff(335,plain,
% 0.21/0.55 (((~s0(d)) | (~k0(e)) | q1(d, d, d)) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(336,plain,
% 0.21/0.55 ((((~k0(e)) | q1(d, d, d)) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(337,plain,
% 0.21/0.55 ((q1(d, d, d) | (~k0(e))) <=> ((~k0(e)) | q1(d, d, d))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(338,plain,
% 0.21/0.55 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> (((~k0(e)) | q1(d, d, d)) | (~s0(d)))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[337])).
% 0.21/0.55 tff(339,plain,
% 0.21/0.55 (((q1(d, d, d) | (~k0(e))) | (~s0(d))) <=> ((~s0(d)) | (~k0(e)) | q1(d, d, d))),
% 0.21/0.55 inference(transitivity,[status(thm)],[338, 336])).
% 0.21/0.55 tff(340,axiom,((q1(d, d, d) | (~k0(e))) | (~s0(d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_117')).
% 0.21/0.55 tff(341,plain,
% 0.21/0.55 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.21/0.55 tff(342,plain,
% 0.21/0.55 ((~s0(d)) | (~k0(e)) | q1(d, d, d)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[341, 335])).
% 0.21/0.55 tff(343,plain,
% 0.21/0.55 (q1(d, d, d)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[342, 334])).
% 0.21/0.55 tff(344,plain,
% 0.21/0.55 (q1(d, d, d)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[343, 331])).
% 0.21/0.55 tff(345,plain,
% 0.21/0.55 (q0(e, d) <=> q0(e, d)),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(346,axiom,(q0(e, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_2')).
% 0.21/0.55 tff(347,plain,
% 0.21/0.55 (q0(e, d)),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.21/0.55 tff(348,plain,
% 0.21/0.55 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(e) | (~q1(d, d, d)) | (~q0(e, d)))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(349,plain,
% 0.21/0.55 (((~q0(e, d)) | (~q1(d, d, d)) | r1(e)) <=> (r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(350,plain,
% 0.21/0.55 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | (r1(e) | (~q1(d, d, d)) | (~q0(e, d))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[349])).
% 0.21/0.55 tff(351,plain,
% 0.21/0.55 (((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))) <=> ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[350, 348])).
% 0.21/0.55 tff(352,plain,
% 0.21/0.55 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | ((~q0(e, d)) | (~q1(d, d, d)) | r1(e))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(353,plain,
% 0.21/0.55 ((~![D: $i, E: $i] : ((~q0(D, E)) | (~q1(d, E, d)) | r1(D))) | r1(e) | (~q1(d, d, d)) | (~q0(e, d))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.21/0.55 tff(354,plain,
% 0.21/0.55 (r1(e)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[353, 347, 344, 281])).
% 0.21/0.55 tff(355,plain,
% 0.21/0.55 (^[B: $i] : refl((p2(B, B, B) | (~n1(d, d, B))) <=> (p2(B, B, B) | (~n1(d, d, B))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(356,plain,
% 0.21/0.55 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[355])).
% 0.21/0.55 tff(357,plain,
% 0.21/0.55 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B))) <=> ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(358,axiom,(![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_153')).
% 0.21/0.55 tff(359,plain,
% 0.21/0.55 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.21/0.55 tff(360,plain,(
% 0.21/0.55 ![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[359])).
% 0.21/0.55 tff(361,plain,
% 0.21/0.55 (![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.21/0.55 tff(362,plain,
% 0.21/0.55 (n1(d, d, d) <=> n1(d, d, d)),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(363,plain,
% 0.21/0.55 ((n1(d, d, d) | $false) <=> n1(d, d, d)),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(364,axiom,(q0(d, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_25')).
% 0.21/0.55 tff(365,plain,
% 0.21/0.55 (q0(d, d) <=> $true),
% 0.21/0.55 inference(iff_true,[status(thm)],[364])).
% 0.21/0.55 tff(366,plain,
% 0.21/0.55 ((~q0(d, d)) <=> (~$true)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[365])).
% 0.21/0.55 tff(367,plain,
% 0.21/0.55 ((~q0(d, d)) <=> $false),
% 0.21/0.55 inference(transitivity,[status(thm)],[366, 10])).
% 0.21/0.55 tff(368,plain,
% 0.21/0.55 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | $false)),
% 0.21/0.55 inference(monotonicity,[status(thm)],[367])).
% 0.21/0.55 tff(369,plain,
% 0.21/0.55 ((n1(d, d, d) | (~q0(d, d))) <=> n1(d, d, d)),
% 0.21/0.55 inference(transitivity,[status(thm)],[368, 363])).
% 0.21/0.56 tff(370,plain,
% 0.21/0.56 ((n1(d, d, d) | (~q0(d, d))) <=> (n1(d, d, d) | (~q0(d, d)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(371,axiom,(n1(d, d, d) | (~q0(d, d))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_045')).
% 0.21/0.56 tff(372,plain,
% 0.21/0.56 (n1(d, d, d) | (~q0(d, d))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.21/0.56 tff(373,plain,
% 0.21/0.56 (n1(d, d, d) | (~q0(d, d))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[372, 370])).
% 0.21/0.56 tff(374,plain,
% 0.21/0.56 (n1(d, d, d)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[373, 369])).
% 0.21/0.56 tff(375,plain,
% 0.21/0.56 (n1(d, d, d)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[374, 362])).
% 0.21/0.56 tff(376,plain,
% 0.21/0.56 (((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))) <=> ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(377,plain,
% 0.21/0.56 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | (p2(d, d, d) | (~n1(d, d, d)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(378,plain,
% 0.21/0.56 ((~![B: $i] : (p2(B, B, B) | (~n1(d, d, B)))) | p2(d, d, d) | (~n1(d, d, d))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.21/0.56 tff(379,plain,
% 0.21/0.56 (p2(d, d, d)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[378, 375, 361])).
% 0.21/0.56 tff(380,plain,
% 0.21/0.56 (((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))) <=> ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | (~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(381,plain,
% 0.21/0.56 (((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e)) <=> ((~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(382,plain,
% 0.21/0.56 (((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e))) <=> ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~r1(e)) | k3(e, e, e) | (~p2(d, d, d))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[381])).
% 0.21/0.56 tff(383,plain,
% 0.21/0.56 (((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e))) <=> ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | (~r1(e)) | k3(e, e, e) | (~p2(d, d, d)))),
% 0.21/0.56 inference(transitivity,[status(thm)],[382, 380])).
% 0.21/0.56 tff(384,plain,
% 0.21/0.56 ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | ((~p2(d, d, d)) | (~r1(e)) | k3(e, e, e))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(385,plain,
% 0.21/0.56 ((~![I: $i, A: $i, J: $i] : ((~p2(J, A, A)) | (~r1(I)) | k3(I, I, I))) | (~r1(e)) | k3(e, e, e) | (~p2(d, d, d))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.21/0.56 tff(386,plain,
% 0.21/0.56 (k3(e, e, e)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[385, 379, 354, 330])).
% 0.21/0.56 tff(387,plain,
% 0.21/0.56 (^[B: $i, C: $i] : refl((p4(B, C, B) | (~k3(B, B, C))) <=> (p4(B, C, B) | (~k3(B, B, C))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(388,plain,
% 0.21/0.56 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[387])).
% 0.21/0.56 tff(389,plain,
% 0.21/0.56 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C))) <=> ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(390,axiom,(![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_287')).
% 0.21/0.56 tff(391,plain,
% 0.21/0.56 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.21/0.56 tff(392,plain,(
% 0.21/0.56 ![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[391])).
% 0.21/0.56 tff(393,plain,
% 0.21/0.56 (![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[392, 388])).
% 0.21/0.56 tff(394,plain,
% 0.21/0.56 (((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(e, e, e) | (~k3(e, e, e)))) <=> ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(e, e, e) | (~k3(e, e, e)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(395,plain,
% 0.21/0.56 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | (p4(e, e, e) | (~k3(e, e, e)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(396,plain,
% 0.21/0.56 ((~![B: $i, C: $i] : (p4(B, C, B) | (~k3(B, B, C)))) | p4(e, e, e) | (~k3(e, e, e))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.21/0.56 tff(397,plain,
% 0.21/0.56 (p4(e, e, e)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[396, 393, 386])).
% 0.21/0.56 tff(398,assumption,(~n4(a, a)), introduced(assumption)).
% 0.21/0.56 tff(399,plain,
% 0.21/0.56 (^[I: $i, H: $i] : refl((n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(400,plain,
% 0.21/0.56 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[399])).
% 0.21/0.56 tff(401,plain,
% 0.21/0.56 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(402,plain,
% 0.21/0.56 (^[I: $i, H: $i] : trans(monotonicity(rewrite((n4(H, H) | (~k4(I))) <=> (n4(H, H) | (~k4(I)))), (((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> ((n4(H, H) | (~k4(I))) | (~m3(H, H, H))))), rewrite(((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))), (((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(403,plain,
% 0.21/0.56 (![I: $i, H: $i] : ((n4(H, H) | (~k4(I))) | (~m3(H, H, H))) <=> ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[402])).
% 0.21/0.56 tff(404,axiom,(![I: $i, H: $i] : ((n4(H, H) | (~k4(I))) | (~m3(H, H, H)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_284')).
% 0.21/0.56 tff(405,plain,
% 0.21/0.56 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.21/0.56 tff(406,plain,
% 0.21/0.56 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[405, 401])).
% 0.21/0.56 tff(407,plain,(
% 0.21/0.56 ![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[406])).
% 0.21/0.56 tff(408,plain,
% 0.21/0.56 (![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[407, 400])).
% 0.21/0.56 tff(409,plain,
% 0.21/0.56 (^[D: $i, E: $i, F: $i] : refl((n3(D) | (~p2(E, F, D))) <=> (n3(D) | (~p2(E, F, D))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(410,plain,
% 0.21/0.56 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[409])).
% 0.21/0.56 tff(411,plain,
% 0.21/0.56 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D))) <=> ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(412,axiom,(![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_240')).
% 0.21/0.56 tff(413,plain,
% 0.21/0.56 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.21/0.56 tff(414,plain,(
% 0.21/0.56 ![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.56 inference(skolemize,[status(sab)],[413])).
% 0.21/0.56 tff(415,plain,
% 0.21/0.56 (![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[414, 410])).
% 0.21/0.56 tff(416,plain,
% 0.21/0.56 (((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(e) | (~p2(e, e, e)))) <=> ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(e) | (~p2(e, e, e)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(417,plain,
% 0.21/0.56 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | (n3(e) | (~p2(e, e, e)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(418,plain,
% 0.21/0.56 ((~![D: $i, E: $i, F: $i] : (n3(D) | (~p2(E, F, D)))) | n3(e) | (~p2(e, e, e))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.21/0.56 tff(419,plain,
% 0.21/0.56 (n3(e)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[418, 415, 57])).
% 0.21/0.56 tff(420,plain,
% 0.21/0.56 (^[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)))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(421,plain,
% 0.21/0.56 (![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))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[420])).
% 0.21/0.56 tff(422,plain,
% 0.21/0.56 (![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))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(423,plain,
% 0.21/0.56 (^[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))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(424,plain,
% 0.21/0.56 (![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))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[423])).
% 0.21/0.56 tff(425,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')).
% 0.21/0.56 tff(426,plain,
% 0.21/0.56 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.21/0.56 tff(427,plain,
% 0.21/0.56 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[426, 422])).
% 0.21/0.56 tff(428,plain,(
% 0.21/0.56 ![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.56 inference(skolemize,[status(sab)],[427])).
% 0.21/0.56 tff(429,plain,
% 0.21/0.56 (![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[428, 421])).
% 0.21/0.56 tff(430,plain,
% 0.21/0.56 (n0(e, e) <=> n0(e, e)),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(431,axiom,(n0(e, e)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_30')).
% 0.21/0.56 tff(432,plain,
% 0.21/0.56 (n0(e, e)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.21/0.56 tff(433,plain,
% 0.21/0.56 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(434,plain,
% 0.21/0.56 (((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b)) <=> (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(435,plain,
% 0.21/0.56 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | (q3(e, b) | (~n0(e, e)) | (~q2(e, e, b))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[434])).
% 0.21/0.56 tff(436,plain,
% 0.21/0.56 (((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))) <=> ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b)))),
% 0.21/0.56 inference(transitivity,[status(thm)],[435, 433])).
% 0.21/0.56 tff(437,plain,
% 0.21/0.56 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | ((~q2(e, e, b)) | (~n0(e, e)) | q3(e, b))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(438,plain,
% 0.21/0.56 ((~![I: $i, H: $i, G: $i] : ((~q2(I, G, H)) | (~n0(I, G)) | q3(G, H))) | q3(e, b) | (~n0(e, e)) | (~q2(e, e, b))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.21/0.56 tff(439,plain,
% 0.21/0.56 (q3(e, b)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[438, 432, 429, 111])).
% 0.21/0.56 tff(440,plain,
% 0.21/0.56 (((~q3(e, b)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | k4(c) | (~n3(e)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(441,plain,
% 0.21/0.56 (((~q3(e, b)) | $false | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | k4(c) | (~n3(e)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(442,axiom,(n0(c, d)), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','axiom_34')).
% 0.21/0.56 tff(443,plain,
% 0.21/0.56 (n0(c, d) <=> $true),
% 0.21/0.56 inference(iff_true,[status(thm)],[442])).
% 0.21/0.56 tff(444,plain,
% 0.21/0.56 ((~n0(c, d)) <=> (~$true)),
% 0.46/0.57 inference(monotonicity,[status(thm)],[443])).
% 0.46/0.57 tff(445,plain,
% 0.46/0.57 ((~n0(c, d)) <=> $false),
% 0.46/0.57 inference(transitivity,[status(thm)],[444, 10])).
% 0.46/0.57 tff(446,plain,
% 0.46/0.57 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | $false | k4(c) | (~n3(e)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[445])).
% 0.46/0.57 tff(447,plain,
% 0.46/0.57 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | k4(c) | (~n3(e)))),
% 0.46/0.57 inference(transitivity,[status(thm)],[446, 441])).
% 0.46/0.57 tff(448,plain,
% 0.46/0.57 (((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(449,plain,
% 0.46/0.57 ((((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(450,plain,
% 0.46/0.57 (((k4(c) | (~n0(c, d))) | (~q3(e, b))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(451,plain,
% 0.46/0.57 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> (((~q3(e, b)) | (~n0(c, d)) | k4(c)) | (~n3(e)))),
% 0.46/0.57 inference(monotonicity,[status(thm)],[450])).
% 0.46/0.57 tff(452,plain,
% 0.46/0.57 ((((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))) <=> ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e)))),
% 0.46/0.57 inference(transitivity,[status(thm)],[451, 449])).
% 0.46/0.57 tff(453,axiom,(((k4(c) | (~n0(c, d))) | (~q3(e, b))) | (~n3(e))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_274')).
% 0.46/0.57 tff(454,plain,
% 0.46/0.57 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.46/0.57 tff(455,plain,
% 0.46/0.57 ((~q3(e, b)) | (~n0(c, d)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[454, 448])).
% 0.46/0.57 tff(456,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[455, 447])).
% 0.46/0.57 tff(457,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[456, 440])).
% 0.46/0.57 tff(458,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[457, 440])).
% 0.46/0.57 tff(459,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[458, 440])).
% 0.46/0.57 tff(460,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[459, 440])).
% 0.46/0.57 tff(461,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[460, 440])).
% 0.46/0.57 tff(462,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[461, 440])).
% 0.46/0.57 tff(463,plain,
% 0.46/0.57 ((~q3(e, b)) | k4(c) | (~n3(e))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[462, 440])).
% 0.46/0.57 tff(464,plain,
% 0.46/0.57 (k4(c)),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[463, 439, 419])).
% 0.46/0.57 tff(465,plain,
% 0.46/0.57 (((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(a, a) | (~m3(a, a, a)) | (~k4(c)))) <=> ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(a, a) | (~m3(a, a, a)) | (~k4(c)))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(466,plain,
% 0.46/0.57 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | (n4(a, a) | (~m3(a, a, a)) | (~k4(c)))),
% 0.46/0.57 inference(quant_inst,[status(thm)],[])).
% 0.46/0.57 tff(467,plain,
% 0.46/0.57 ((~![I: $i, H: $i] : (n4(H, H) | (~m3(H, H, H)) | (~k4(I)))) | n4(a, a) | (~m3(a, a, a)) | (~k4(c))),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.46/0.57 tff(468,plain,
% 0.46/0.57 ($false),
% 0.46/0.57 inference(unit_resolution,[status(thm)],[467, 464, 408, 398, 228])).
% 0.46/0.57 tff(469,plain,(n4(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.46/0.57 tff(470,plain,
% 0.46/0.57 ((~n5(a, e)) <=> (~n5(a, e))),
% 0.46/0.57 inference(rewrite,[status(thm)],[])).
% 0.46/0.57 tff(471,axiom,(~n5(a, e)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.46/0.57 tff(472,plain,
% 0.46/0.57 (~n5(a, e)),
% 0.46/0.57 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.46/0.57 tff(473,plain,
% 0.46/0.57 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : refl(((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)))),
% 0.46/0.57 inference(bind,[status(th)],[])).
% 0.46/0.57 tff(474,plain,
% 0.46/0.57 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[473])).
% 0.46/0.58 tff(475,plain,
% 0.46/0.58 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(476,plain,
% 0.46/0.58 (^[B: $i, D: $i, E: $i, F: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((n5(B, C) | (~q4(D, E))) <=> ((~q4(D, E)) | n5(B, C))), (((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) <=> (((~q4(D, E)) | n5(B, C)) | (~n4(B, E))))), rewrite((((~q4(D, E)) | n5(B, C)) | (~n4(B, E))) <=> ((~n4(B, E)) | (~q4(D, E)) | n5(B, C))), (((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) <=> ((~n4(B, E)) | (~q4(D, E)) | n5(B, C)))), ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) <=> (((~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~p4(F, F, C))))), rewrite((((~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~p4(F, F, C))) <=> ((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))), ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) <=> ((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)))), (((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> (((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~n5(F, C))))), rewrite((((~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C)) | (~n5(F, C))) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))), (((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))))),
% 0.46/0.58 inference(bind,[status(th)],[])).
% 0.46/0.58 tff(477,plain,
% 0.46/0.58 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C))) <=> ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.46/0.58 inference(quant_intro,[status(thm)],[476])).
% 0.46/0.58 tff(478,axiom,(![B: $i, D: $i, E: $i, F: $i, C: $i] : ((((n5(B, C) | (~q4(D, E))) | (~n4(B, E))) | (~p4(F, F, C))) | (~n5(F, C)))), file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax','rule_307')).
% 0.46/0.58 tff(479,plain,
% 0.46/0.58 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.46/0.58 tff(480,plain,
% 0.46/0.58 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[479, 475])).
% 0.46/0.58 tff(481,plain,(
% 0.46/0.58 ![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.46/0.58 inference(skolemize,[status(sab)],[480])).
% 0.46/0.58 tff(482,plain,
% 0.46/0.58 (![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))),
% 0.46/0.58 inference(modus_ponens,[status(thm)],[481, 474])).
% 0.46/0.58 tff(483,plain,
% 0.46/0.58 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~p4(e, e, e)) | (~n5(e, e)))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~p4(e, e, e)) | (~n5(e, e)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(484,plain,
% 0.46/0.58 (((~n5(e, e)) | (~p4(e, e, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e)) <=> (n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~p4(e, e, e)) | (~n5(e, e)))),
% 0.46/0.58 inference(rewrite,[status(thm)],[])).
% 0.46/0.58 tff(485,plain,
% 0.46/0.58 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(e, e)) | (~p4(e, e, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | (n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~p4(e, e, e)) | (~n5(e, e))))),
% 0.46/0.58 inference(monotonicity,[status(thm)],[484])).
% 0.48/0.60 tff(486,plain,
% 0.48/0.60 (((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(e, e)) | (~p4(e, e, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e))) <=> ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~p4(e, e, e)) | (~n5(e, e)))),
% 0.48/0.60 inference(transitivity,[status(thm)],[485, 483])).
% 0.48/0.60 tff(487,plain,
% 0.48/0.60 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | ((~n5(e, e)) | (~p4(e, e, e)) | (~n4(a, a)) | (~q4(a, a)) | n5(a, e))),
% 0.48/0.60 inference(quant_inst,[status(thm)],[])).
% 0.48/0.60 tff(488,plain,
% 0.48/0.60 ((~![B: $i, D: $i, E: $i, F: $i, C: $i] : ((~n5(F, C)) | (~p4(F, F, C)) | (~n4(B, E)) | (~q4(D, E)) | n5(B, C))) | n5(a, e) | (~n4(a, a)) | (~q4(a, a)) | (~p4(e, e, e)) | (~n5(e, e))),
% 0.48/0.60 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.48/0.60 tff(489,plain,
% 0.48/0.60 ($false),
% 0.48/0.60 inference(unit_resolution,[status(thm)],[488, 482, 472, 469, 397, 320, 188])).
% 0.48/0.60 % SZS output end Proof
%------------------------------------------------------------------------------