%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN159-1 : TPTP v9.2.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 : Tue May 5 05:36:18 PM UTC 2026
% Result : Unsatisfiable 1.46s 1.75s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 67
% Syntax : Number of clauses : 222 ( 91 unt; 0 nHn; 171 RR)
% Number of literals : 449 ( 0 equ; 229 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 36 ( 35 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 320 ( 110 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule_021,axiom,
( m1(X1,X2,X1)
| ~ l0(X1)
| ~ k0(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_021) ).
cnf(axiom_28,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
cnf(axiom_24,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
cnf(rule_126,axiom,
( s1(X1)
| ~ q0(X1,X2)
| ~ s1(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_126) ).
cnf(axiom_17,axiom,
q0(X1,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_17) ).
cnf(rule_125,axiom,
( s1(X1)
| ~ p0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_125) ).
cnf(axiom_14,axiom,
p0(b,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_14) ).
cnf(rule_176,axiom,
( p2(X1,X2,X1)
| ~ m1(X2,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_176) ).
cnf(rule_007,axiom,
( m1(X1,X2,X1)
| ~ p0(X3,X2)
| ~ r0(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_007) ).
cnf(rule_155,axiom,
( p2(X1,X2,X2)
| ~ k1(X3)
| ~ p2(e,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_155) ).
cnf(rule_001,axiom,
( k1(X1)
| ~ n0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_001) ).
cnf(axiom_26,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
cnf(axiom_13,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
cnf(rule_107,axiom,
( q1(e,X1,X1)
| ~ m0(X1,d,X1)
| ~ m0(e,d,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_107) ).
cnf(axiom_19,axiom,
m0(X1,d,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_19) ).
cnf(rule_192,axiom,
( k3(X1,X2,X1)
| ~ s1(X2)
| ~ p2(X3,X2,X4)
| ~ n0(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_192) ).
cnf(rule_029,axiom,
( m1(X1,X2,X1)
| ~ p0(X1,X2)
| ~ s0(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_029) ).
cnf(axiom_5,axiom,
s0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_5) ).
cnf(rule_127,axiom,
( k2(X1,X2)
| ~ m1(X3,X2,X1)
| ~ k1(X4)
| ~ k2(X4,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_127) ).
cnf(rule_129,axiom,
( k2(X1,X1)
| ~ q1(X2,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_129) ).
cnf(rule_057,axiom,
( n1(X1,X1,X1)
| ~ r0(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_057) ).
cnf(axiom_30,axiom,
n0(e,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
cnf(rule_005,axiom,
( m1(X1,X2,X1)
| ~ m0(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_005) ).
cnf(rule_088,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_088) ).
cnf(axiom_20,axiom,
l0(a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
cnf(rule_179,axiom,
( q2(X1,X1,X1)
| ~ k1(X2)
| ~ n1(X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_179) ).
cnf(axiom_3,axiom,
n0(d,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_3) ).
cnf(axiom_11,axiom,
n0(e,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_11) ).
cnf(axiom_34,axiom,
n0(c,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
cnf(rule_085,axiom,
( p1(X1,X1,X1)
| ~ p0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_085) ).
cnf(rule_082,axiom,
( p1(X1,X2,X3)
| ~ m0(X3,X1,X4)
| ~ p1(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_082) ).
cnf(axiom_12,axiom,
m0(a,X1,a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_12) ).
cnf(rule_255,axiom,
( q3(X1,X2)
| ~ q2(X3,X1,X2)
| ~ n0(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_255) ).
cnf(rule_133,axiom,
( l2(X1,X1)
| ~ p0(X2,X2)
| ~ s1(X3)
| ~ m0(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_133) ).
cnf(rule_090,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_090) ).
cnf(rule_202,axiom,
( k3(X1,X1,X2)
| ~ q0(X3,X2)
| ~ k2(X1,X4)
| ~ k3(X2,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_202) ).
cnf(rule_137,axiom,
( n2(X1)
| ~ p1(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_137) ).
cnf(rule_154,axiom,
( p2(X1,X1,X1)
| ~ q1(X1,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_154) ).
cnf(rule_298,axiom,
( r4(X1)
| ~ n3(X1)
| ~ q3(X2,X3)
| ~ p0(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_298) ).
cnf(rule_236,axiom,
( m3(X1,X1,X1)
| ~ n2(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_236) ).
cnf(rule_274,axiom,
( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_274) ).
cnf(rule_240,axiom,
( n3(X1)
| ~ p2(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_240) ).
cnf(rule_003,axiom,
( l1(X1,X2)
| ~ p0(X3,X1)
| ~ r0(X4)
| ~ m0(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_003) ).
cnf(axiom_27,axiom,
m0(e,b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
cnf(axiom_18,axiom,
p0(c,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
cnf(rule_201,axiom,
( k3(X1,X1,X2)
| ~ p1(X2,X3,X1)
| ~ m2(X4)
| ~ m2(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_201) ).
cnf(rule_136,axiom,
( m2(b)
| ~ k1(b) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_136) ).
cnf(rule_124,axiom,
( r1(X1)
| ~ q0(X1,X2)
| ~ s0(d)
| ~ q1(d,X2,d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_124) ).
cnf(axiom_1,axiom,
s0(d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
cnf(rule_117,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_117) ).
cnf(rule_277,axiom,
( l4(X1)
| ~ p3(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_277) ).
cnf(rule_246,axiom,
( p3(X1,X1,X1)
| ~ l2(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_246) ).
cnf(rule_234,axiom,
( m3(X1,e,e)
| ~ n2(e)
| ~ p2(X1,e,e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_234) ).
cnf(rule_284,axiom,
( n4(X1,X1)
| ~ k4(X2)
| ~ m3(X1,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_284) ).
cnf(rule_186,axiom,
( q2(X1,X1,X2)
| ~ l1(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_186) ).
cnf(axiom_9,axiom,
r0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
cnf(rule_286,axiom,
( p4(X1,X1,X1)
| ~ q3(X2,X3)
| ~ n3(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_286) ).
cnf(rule_314,axiom,
( n5(X1,X1)
| ~ r4(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_314) ).
cnf(rule_295,axiom,
( q4(X1,X2)
| ~ k3(X3,X3,X1)
| ~ q2(X4,X2,X1)
| ~ m3(X4,X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_295) ).
cnf(rule_181,axiom,
( q2(X1,X1,X1)
| ~ p1(X1,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_181) ).
cnf(axiom_21,axiom,
q0(b,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_21) ).
cnf(rule_296,axiom,
( q4(X1,X1)
| ~ r1(X1)
| ~ l4(X2)
| ~ q4(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_296) ).
cnf(rule_242,axiom,
( p3(X1,X2,X3)
| ~ r2(X2)
| ~ k3(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_242) ).
cnf(rule_188,axiom,
( r2(X1)
| ~ r1(X1)
| ~ l0(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_188) ).
cnf(rule_307,axiom,
( n5(X1,X2)
| ~ q4(X3,X4)
| ~ n4(X1,X4)
| ~ p4(X5,X5,X2)
| ~ n5(X5,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_307) ).
cnf(rule_281,axiom,
( n4(X1,X2)
| ~ p3(X1,X2,X2)
| ~ n4(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_281) ).
cnf(prove_this,negated_conjecture,
~ n5(a,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_67,axiom,
( m1(X1,X2,X1)
| ~ l0(X1)
| ~ k0(X2) ),
rule_021 ).
cnf(c_0_68,axiom,
k0(e),
axiom_28 ).
cnf(c_0_69,plain,
( m1(X1,e,X1)
| ~ l0(X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,axiom,
l0(c),
axiom_24 ).
cnf(c_0_71,axiom,
( s1(X1)
| ~ q0(X1,X2)
| ~ s1(X3) ),
rule_126 ).
cnf(c_0_72,axiom,
q0(X1,d),
axiom_17 ).
cnf(c_0_73,axiom,
( s1(X1)
| ~ p0(X1,X1) ),
rule_125 ).
cnf(c_0_74,axiom,
p0(b,X1),
axiom_14 ).
cnf(c_0_75,axiom,
( p2(X1,X2,X1)
| ~ m1(X2,X1,X2) ),
rule_176 ).
cnf(c_0_76,plain,
m1(c,e,c),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,axiom,
( m1(X1,X2,X1)
| ~ p0(X3,X2)
| ~ r0(X1) ),
rule_007 ).
cnf(c_0_78,plain,
( s1(X1)
| ~ s1(X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_79,plain,
s1(b),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,axiom,
( p2(X1,X2,X2)
| ~ k1(X3)
| ~ p2(e,X1,X2) ),
rule_155 ).
cnf(c_0_81,plain,
p2(e,c,e),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,axiom,
( k1(X1)
| ~ n0(X2,X1) ),
rule_001 ).
cnf(c_0_83,axiom,
n0(d,c),
axiom_26 ).
cnf(c_0_84,plain,
( m1(X1,X2,X1)
| ~ r0(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_74]) ).
cnf(c_0_85,axiom,
r0(e),
axiom_13 ).
cnf(c_0_86,axiom,
( q1(e,X1,X1)
| ~ m0(X1,d,X1)
| ~ m0(e,d,X1) ),
rule_107 ).
cnf(c_0_87,axiom,
m0(X1,d,X2),
axiom_19 ).
cnf(c_0_88,axiom,
( k3(X1,X2,X1)
| ~ s1(X2)
| ~ p2(X3,X2,X4)
| ~ n0(X1,X4) ),
rule_192 ).
cnf(c_0_89,plain,
s1(X1),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_90,plain,
( p2(c,e,e)
| ~ k1(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_91,plain,
k1(c),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_92,axiom,
( m1(X1,X2,X1)
| ~ p0(X1,X2)
| ~ s0(X1) ),
rule_029 ).
cnf(c_0_93,axiom,
s0(b),
axiom_5 ).
cnf(c_0_94,axiom,
( k2(X1,X2)
| ~ m1(X3,X2,X1)
| ~ k1(X4)
| ~ k2(X4,X2) ),
rule_127 ).
cnf(c_0_95,plain,
m1(e,X1,e),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_96,axiom,
( k2(X1,X1)
| ~ q1(X2,X1,X1) ),
rule_129 ).
cnf(c_0_97,plain,
q1(e,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87]),c_0_87])]) ).
cnf(c_0_98,axiom,
( n1(X1,X1,X1)
| ~ r0(X1) ),
rule_057 ).
cnf(c_0_99,axiom,
n0(e,e),
axiom_30 ).
cnf(c_0_100,plain,
( k3(X1,X2,X1)
| ~ p2(X3,X2,X4)
| ~ n0(X1,X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]) ).
cnf(c_0_101,plain,
p2(c,e,e),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_102,axiom,
( m1(X1,X2,X1)
| ~ m0(X2,X2,X1) ),
rule_005 ).
cnf(c_0_103,plain,
m1(b,X1,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_74]),c_0_93])]) ).
cnf(c_0_104,plain,
( k2(e,X1)
| ~ k2(X2,X1)
| ~ k1(X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_105,plain,
k2(X1,X1),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_106,axiom,
( p1(a,a,a)
| ~ l0(a) ),
rule_088 ).
cnf(c_0_107,axiom,
l0(a),
axiom_20 ).
cnf(c_0_108,axiom,
( q2(X1,X1,X1)
| ~ k1(X2)
| ~ n1(X1,X1,X2) ),
rule_179 ).
cnf(c_0_109,plain,
n1(e,e,e),
inference(spm,[status(thm)],[c_0_98,c_0_85]) ).
cnf(c_0_110,plain,
k1(e),
inference(spm,[status(thm)],[c_0_82,c_0_99]) ).
cnf(c_0_111,plain,
( k3(X1,e,X1)
| ~ n0(X1,e) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_112,axiom,
n0(d,e),
axiom_3 ).
cnf(c_0_113,plain,
m1(X1,d,X1),
inference(spm,[status(thm)],[c_0_102,c_0_87]) ).
cnf(c_0_114,plain,
( k2(b,X1)
| ~ k2(X2,X1)
| ~ k1(X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_103]) ).
cnf(c_0_115,plain,
( k2(e,X1)
| ~ k1(X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_116,axiom,
n0(e,b),
axiom_11 ).
cnf(c_0_117,axiom,
n0(c,d),
axiom_34 ).
cnf(c_0_118,axiom,
( p1(X1,X1,X1)
| ~ p0(X2,X1) ),
rule_085 ).
cnf(c_0_119,axiom,
( p1(X1,X2,X3)
| ~ m0(X3,X1,X4)
| ~ p1(X3,X1,X4) ),
rule_082 ).
cnf(c_0_120,plain,
p1(a,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).
cnf(c_0_121,axiom,
m0(a,X1,a),
axiom_12 ).
cnf(c_0_122,axiom,
( q3(X1,X2)
| ~ q2(X3,X1,X2)
| ~ n0(X3,X1) ),
rule_255 ).
cnf(c_0_123,plain,
q2(e,e,e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110])]) ).
cnf(c_0_124,axiom,
( l2(X1,X1)
| ~ p0(X2,X2)
| ~ s1(X3)
| ~ m0(X4,X3,X1) ),
rule_133 ).
cnf(c_0_125,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
rule_090 ).
cnf(c_0_126,axiom,
( k3(X1,X1,X2)
| ~ q0(X3,X2)
| ~ k2(X1,X4)
| ~ k3(X2,X5,X4) ),
rule_202 ).
cnf(c_0_127,plain,
k3(d,e,d),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_128,plain,
( k2(X1,d)
| ~ k2(X2,d)
| ~ k1(X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_113]) ).
cnf(c_0_129,plain,
( k2(b,X1)
| ~ k1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_110])]) ).
cnf(c_0_130,plain,
k1(b),
inference(spm,[status(thm)],[c_0_82,c_0_116]) ).
cnf(c_0_131,plain,
k1(d),
inference(spm,[status(thm)],[c_0_82,c_0_117]) ).
cnf(c_0_132,axiom,
( n2(X1)
| ~ p1(X2,X3,X1) ),
rule_137 ).
cnf(c_0_133,plain,
p1(X1,X1,X1),
inference(spm,[status(thm)],[c_0_118,c_0_74]) ).
cnf(c_0_134,axiom,
( p2(X1,X1,X1)
| ~ q1(X1,X1,X1) ),
rule_154 ).
cnf(c_0_135,plain,
p1(a,X1,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121])]) ).
cnf(c_0_136,axiom,
( r4(X1)
| ~ n3(X1)
| ~ q3(X2,X3)
| ~ p0(X4,X1) ),
rule_298 ).
cnf(c_0_137,plain,
q3(e,e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_99])]) ).
cnf(c_0_138,plain,
( l2(X1,X1)
| ~ p0(X2,X2)
| ~ m0(X3,X4,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_89])]) ).
cnf(c_0_139,plain,
p1(e,e,e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_85]),c_0_68])]) ).
cnf(c_0_140,plain,
( k3(X1,X1,d)
| ~ k2(X1,d) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_72])]) ).
cnf(c_0_141,plain,
k2(X1,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]),c_0_131])]) ).
cnf(c_0_142,axiom,
( m3(X1,X1,X1)
| ~ n2(X1) ),
rule_236 ).
cnf(c_0_143,plain,
n2(X1),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_144,axiom,
( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) ),
rule_274 ).
cnf(c_0_145,axiom,
( n3(X1)
| ~ p2(X2,X3,X1) ),
rule_240 ).
cnf(c_0_146,plain,
p2(e,e,e),
inference(spm,[status(thm)],[c_0_134,c_0_97]) ).
cnf(c_0_147,axiom,
( l1(X1,X2)
| ~ p0(X3,X1)
| ~ r0(X4)
| ~ m0(X2,X1,X3) ),
rule_003 ).
cnf(c_0_148,axiom,
m0(e,b,c),
axiom_27 ).
cnf(c_0_149,axiom,
p0(c,b),
axiom_18 ).
cnf(c_0_150,axiom,
( k3(X1,X1,X2)
| ~ p1(X2,X3,X1)
| ~ m2(X4)
| ~ m2(X3) ),
rule_201 ).
cnf(c_0_151,plain,
p1(X1,X2,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_135]),c_0_121])]) ).
cnf(c_0_152,axiom,
( m2(b)
| ~ k1(b) ),
rule_136 ).
cnf(c_0_153,plain,
( r4(X1)
| ~ n3(X1)
| ~ p0(X2,X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_154,axiom,
( r1(X1)
| ~ q0(X1,X2)
| ~ s0(d)
| ~ q1(d,X2,d) ),
rule_124 ).
cnf(c_0_155,axiom,
s0(d),
axiom_1 ).
cnf(c_0_156,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
rule_117 ).
cnf(c_0_157,axiom,
( l4(X1)
| ~ p3(X2,X3,X1) ),
rule_277 ).
cnf(c_0_158,axiom,
( p3(X1,X1,X1)
| ~ l2(X1,X1) ),
rule_246 ).
cnf(c_0_159,plain,
( l2(X1,X1)
| ~ p0(X2,X2) ),
inference(spm,[status(thm)],[c_0_138,c_0_87]) ).
cnf(c_0_160,axiom,
( m3(X1,e,e)
| ~ n2(e)
| ~ p2(X1,e,e) ),
rule_234 ).
cnf(c_0_161,plain,
n2(e),
inference(spm,[status(thm)],[c_0_132,c_0_139]) ).
cnf(c_0_162,plain,
k3(X1,X1,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).
cnf(c_0_163,axiom,
( n4(X1,X1)
| ~ k4(X2)
| ~ m3(X1,X1,X1) ),
rule_284 ).
cnf(c_0_164,plain,
m3(X1,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143])]) ).
cnf(c_0_165,plain,
( k4(c)
| ~ q3(e,b)
| ~ n3(e) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_117])]) ).
cnf(c_0_166,plain,
n3(e),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_167,axiom,
( q2(X1,X1,X2)
| ~ l1(X2,X1) ),
rule_186 ).
cnf(c_0_168,plain,
( l1(b,e)
| ~ r0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_149])]) ).
cnf(c_0_169,axiom,
r0(b),
axiom_9 ).
cnf(c_0_170,plain,
( k3(a,a,X1)
| ~ m2(X2)
| ~ m2(X3) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_171,plain,
m2(b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_130])]) ).
cnf(c_0_172,axiom,
( p4(X1,X1,X1)
| ~ q3(X2,X3)
| ~ n3(X1) ),
rule_286 ).
cnf(c_0_173,plain,
p2(X1,e,X1),
inference(spm,[status(thm)],[c_0_75,c_0_95]) ).
cnf(c_0_174,axiom,
( n5(X1,X1)
| ~ r4(X1) ),
rule_314 ).
cnf(c_0_175,plain,
( r4(X1)
| ~ n3(X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_74]) ).
cnf(c_0_176,plain,
( r1(X1)
| ~ q1(d,X2,d)
| ~ q0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155])]) ).
cnf(c_0_177,plain,
q1(d,d,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_155]),c_0_68])]) ).
cnf(c_0_178,plain,
( l4(X1)
| ~ l2(X1,X1) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_179,plain,
l2(X1,X1),
inference(spm,[status(thm)],[c_0_159,c_0_74]) ).
cnf(c_0_180,axiom,
( q4(X1,X2)
| ~ k3(X3,X3,X1)
| ~ q2(X4,X2,X1)
| ~ m3(X4,X5,X4) ),
rule_295 ).
cnf(c_0_181,plain,
( m3(X1,e,e)
| ~ p2(X1,e,e) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_161])]) ).
cnf(c_0_182,axiom,
( q2(X1,X1,X1)
| ~ p1(X1,X1,X1) ),
rule_181 ).
cnf(c_0_183,plain,
( k3(X1,X1,X2)
| ~ q0(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_162]),c_0_141])]) ).
cnf(c_0_184,axiom,
q0(b,e),
axiom_21 ).
cnf(c_0_185,plain,
( n4(X1,X1)
| ~ k4(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]) ).
cnf(c_0_186,plain,
( k4(c)
| ~ q3(e,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166])]) ).
cnf(c_0_187,plain,
( q3(X1,X2)
| ~ l1(X2,X1)
| ~ n0(X1,X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_167]) ).
cnf(c_0_188,plain,
l1(b,e),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_189,plain,
( k3(a,a,X1)
| ~ m2(X2) ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_190,plain,
( p4(X1,X1,X1)
| ~ n3(X1) ),
inference(spm,[status(thm)],[c_0_172,c_0_137]) ).
cnf(c_0_191,plain,
n3(X1),
inference(spm,[status(thm)],[c_0_145,c_0_173]) ).
cnf(c_0_192,plain,
( n5(X1,X1)
| ~ n3(X1) ),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_193,axiom,
( q4(X1,X1)
| ~ r1(X1)
| ~ l4(X2)
| ~ q4(X2,X3) ),
rule_296 ).
cnf(c_0_194,plain,
r1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_72])]) ).
cnf(c_0_195,plain,
l4(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_179])]) ).
cnf(c_0_196,plain,
( q4(X1,X2)
| ~ k3(X3,X3,X1)
| ~ q2(e,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_146])]) ).
cnf(c_0_197,plain,
q2(X1,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_133])]) ).
cnf(c_0_198,plain,
k3(X1,X1,e),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_199,plain,
( n4(X1,X1)
| ~ q3(e,b) ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_200,plain,
q3(e,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_99])]) ).
cnf(c_0_201,axiom,
( p3(X1,X2,X3)
| ~ r2(X2)
| ~ k3(X2,X3,X1) ),
rule_242 ).
cnf(c_0_202,plain,
k3(a,a,X1),
inference(spm,[status(thm)],[c_0_189,c_0_171]) ).
cnf(c_0_203,axiom,
( r2(X1)
| ~ r1(X1)
| ~ l0(X1) ),
rule_188 ).
cnf(c_0_204,axiom,
( n5(X1,X2)
| ~ q4(X3,X4)
| ~ n4(X1,X4)
| ~ p4(X5,X5,X2)
| ~ n5(X5,X2) ),
rule_307 ).
cnf(c_0_205,plain,
p4(X1,X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_191])]) ).
cnf(c_0_206,plain,
n5(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_191])]) ).
cnf(c_0_207,plain,
( q4(X1,X1)
| ~ q4(X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_194])]),c_0_195])]) ).
cnf(c_0_208,plain,
q4(e,e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_198])]) ).
cnf(c_0_209,axiom,
( n4(X1,X2)
| ~ p3(X1,X2,X2)
| ~ n4(X1,X1) ),
rule_281 ).
cnf(c_0_210,plain,
n4(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_200])]) ).
cnf(c_0_211,plain,
( p3(X1,a,a)
| ~ r2(a) ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_212,plain,
( r2(X1)
| ~ l0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_194])]) ).
cnf(c_0_213,plain,
( n5(X1,X2)
| ~ q4(X3,X4)
| ~ n4(X1,X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_206])]) ).
cnf(c_0_214,plain,
q4(X1,X1),
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_215,plain,
( n4(X1,X2)
| ~ p3(X1,X2,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_210])]) ).
cnf(c_0_216,plain,
p3(X1,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_107])]) ).
cnf(c_0_217,plain,
( n5(X1,X2)
| ~ n4(X1,X3) ),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_218,plain,
n4(X1,a),
inference(spm,[status(thm)],[c_0_215,c_0_216]) ).
cnf(c_0_219,negated_conjecture,
~ n5(a,e),
prove_this ).
cnf(c_0_220,plain,
n5(X1,X2),
inference(spm,[status(thm)],[c_0_217,c_0_218]) ).
cnf(c_0_221,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_220])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN159-1 : TPTP v9.2.1. Released v1.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n004.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 08:16:32 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.46/1.75 % Version : CSE_E---1.7
% 1.46/1.75 % Problem : theBenchmark.p
% 1.46/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.46/1.75 % SZS output start CNFRefutation
% See solution above
% 1.46/1.76 % Total time : 1.371s
%------------------------------------------------------------------------------