%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN143-10 : TPTP v9.2.1. Released v7.3.0.
% 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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:36:15 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.83s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 23 RR)
% Number of literals : 84 ( 83 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-4 aty)
% Number of variables : 124 ( 49 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule_050,axiom,
ifeq(l0(X1),true,ifeq(p0(b,X2),true,ifeq(s0(b),true,n1(X1,X2,X1),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_050) ).
cnf(axiom_14,axiom,
p0(b,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
cnf(axiom_5,axiom,
s0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(rule_002,axiom,
ifeq(n0(X1,X2),true,l1(X2,X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
cnf(axiom_37,axiom,
n0(b,a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
cnf(axiom_20,axiom,
l0(a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
cnf(rule_085,axiom,
ifeq(p0(X1,X2),true,p1(X2,X2,X2),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_085) ).
cnf(rule_126,axiom,
ifeq(s1(X1),true,ifeq(q0(X2,X3),true,s1(X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_126) ).
cnf(axiom_17,axiom,
q0(X1,d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
cnf(rule_125,axiom,
ifeq(p0(X1,X1),true,s1(X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_125) ).
cnf(rule_054,axiom,
ifeq(n1(X1,X2,X1),true,ifeq(l0(X3),true,ifeq(l1(X3,X1),true,n1(X1,X2,X2),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_054) ).
cnf(rule_177,axiom,
ifeq(p1(X1,X1,X1),true,ifeq(k0(X2),true,q2(X1,X2,X2),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_177) ).
cnf(rule_182,axiom,
ifeq(q2(X1,X2,X3),true,ifeq(p1(X3,X3,X2),true,ifeq(n1(X1,X3,X2),true,q2(X3,X1,X3),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_182) ).
cnf(axiom_32,axiom,
k0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
cnf(rule_137,axiom,
ifeq(p1(X1,X2,X3),true,n2(X3),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_137) ).
cnf(rule_133,axiom,
ifeq(s1(X1),true,ifeq(p0(X2,X2),true,ifeq(m0(X3,X1,X4),true,l2(X4,X4),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_133) ).
cnf(axiom_28,axiom,
k0(e) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
cnf(rule_189,axiom,
ifeq(q2(b,X1,b),true,ifeq(s1(b),true,s2(X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_189) ).
cnf(rule_244,axiom,
ifeq(n2(X1),true,p3(X1,X1,X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_244) ).
cnf(axiom_19,axiom,
m0(X1,d,X2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
cnf(rule_299,axiom,
ifeq(p3(X1,X2,X3),true,ifeq(l1(X4,X2),true,s4(X4),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_299) ).
cnf(axiom_34,axiom,
n0(c,d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
cnf(rule_273,axiom,
ifeq(s2(X1),true,ifeq(q2(X2,X1,X2),true,ifeq(m0(X2,X3,X4),true,s3(X1,X4),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_273) ).
cnf(rule_279,axiom,
ifeq(s3(a,X1),true,ifeq(l2(X2,X3),true,m4(X1,X3),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_279) ).
cnf(rule_305,axiom,
ifeq(s4(X1),true,ifeq(m4(e,e),true,m5(X1,X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_305) ).
cnf(prove_this,negated_conjecture,
m5(d,d) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(c_0_27,axiom,
ifeq(l0(X1),true,ifeq(p0(b,X2),true,ifeq(s0(b),true,n1(X1,X2,X1),true),true),true) = true,
rule_050 ).
cnf(c_0_28,axiom,
p0(b,X1) = true,
axiom_14 ).
cnf(c_0_29,axiom,
s0(b) = true,
axiom_5 ).
cnf(c_0_30,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_31,axiom,
ifeq(n0(X1,X2),true,l1(X2,X2),true) = true,
rule_002 ).
cnf(c_0_32,axiom,
n0(b,a) = true,
axiom_37 ).
cnf(c_0_33,plain,
ifeq(l0(X1),true,n1(X1,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_30]) ).
cnf(c_0_34,axiom,
l0(a) = true,
axiom_20 ).
cnf(c_0_35,axiom,
ifeq(p0(X1,X2),true,p1(X2,X2,X2),true) = true,
rule_085 ).
cnf(c_0_36,axiom,
ifeq(s1(X1),true,ifeq(q0(X2,X3),true,s1(X2),true),true) = true,
rule_126 ).
cnf(c_0_37,axiom,
q0(X1,d) = true,
axiom_17 ).
cnf(c_0_38,axiom,
ifeq(p0(X1,X1),true,s1(X1),true) = true,
rule_125 ).
cnf(c_0_39,axiom,
ifeq(n1(X1,X2,X1),true,ifeq(l0(X3),true,ifeq(l1(X3,X1),true,n1(X1,X2,X2),true),true),true) = true,
rule_054 ).
cnf(c_0_40,plain,
l1(a,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30]) ).
cnf(c_0_41,plain,
n1(a,X1,a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]) ).
cnf(c_0_42,axiom,
ifeq(p1(X1,X1,X1),true,ifeq(k0(X2),true,q2(X1,X2,X2),true),true) = true,
rule_177 ).
cnf(c_0_43,plain,
p1(X1,X1,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_30]) ).
cnf(c_0_44,plain,
ifeq(s1(X1),true,s1(X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_30]) ).
cnf(c_0_45,plain,
s1(b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28]),c_0_30]) ).
cnf(c_0_46,axiom,
ifeq(q2(X1,X2,X3),true,ifeq(p1(X3,X3,X2),true,ifeq(n1(X1,X3,X2),true,q2(X3,X1,X3),true),true),true) = true,
rule_182 ).
cnf(c_0_47,plain,
n1(a,X1,X1) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_34]),c_0_30]),c_0_30]),c_0_41]),c_0_30]) ).
cnf(c_0_48,plain,
ifeq(k0(X1),true,q2(X2,X1,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_30]) ).
cnf(c_0_49,axiom,
k0(b) = true,
axiom_32 ).
cnf(c_0_50,axiom,
ifeq(p1(X1,X2,X3),true,n2(X3),true) = true,
rule_137 ).
cnf(c_0_51,axiom,
ifeq(s1(X1),true,ifeq(p0(X2,X2),true,ifeq(m0(X3,X1,X4),true,l2(X4,X4),true),true),true) = true,
rule_133 ).
cnf(c_0_52,plain,
s1(X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_30]) ).
cnf(c_0_53,axiom,
k0(e) = true,
axiom_28 ).
cnf(c_0_54,axiom,
ifeq(q2(b,X1,b),true,ifeq(s1(b),true,s2(X1),true),true) = true,
rule_189 ).
cnf(c_0_55,plain,
ifeq(q2(a,X1,X1),true,q2(X1,a,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_43]),c_0_30]),c_0_30]) ).
cnf(c_0_56,plain,
q2(X1,b,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_30]) ).
cnf(c_0_57,axiom,
ifeq(n2(X1),true,p3(X1,X1,X1),true) = true,
rule_244 ).
cnf(c_0_58,plain,
n2(X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_43]),c_0_30]) ).
cnf(c_0_59,plain,
ifeq(p0(X1,X1),true,ifeq(m0(X2,X3,X4),true,l2(X4,X4),true),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_30]) ).
cnf(c_0_60,axiom,
m0(X1,d,X2) = true,
axiom_19 ).
cnf(c_0_61,plain,
q2(X1,e,e) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_53]),c_0_30]) ).
cnf(c_0_62,plain,
ifeq(q2(b,X1,b),true,s2(X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_45]),c_0_30]) ).
cnf(c_0_63,plain,
q2(b,a,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_30]) ).
cnf(c_0_64,axiom,
ifeq(p3(X1,X2,X3),true,ifeq(l1(X4,X2),true,s4(X4),true),true) = true,
rule_299 ).
cnf(c_0_65,plain,
p3(X1,X1,X1) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_30]) ).
cnf(c_0_66,axiom,
n0(c,d) = true,
axiom_34 ).
cnf(c_0_67,plain,
ifeq(p0(X1,X1),true,l2(X2,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_30]) ).
cnf(c_0_68,axiom,
ifeq(s2(X1),true,ifeq(q2(X2,X1,X2),true,ifeq(m0(X2,X3,X4),true,s3(X1,X4),true),true),true) = true,
rule_273 ).
cnf(c_0_69,plain,
q2(e,a,e) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_61]),c_0_30]) ).
cnf(c_0_70,plain,
s2(a) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_30]) ).
cnf(c_0_71,plain,
ifeq(l1(X1,X2),true,s4(X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_30]) ).
cnf(c_0_72,plain,
l1(d,d) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_66]),c_0_30]) ).
cnf(c_0_73,axiom,
ifeq(s3(a,X1),true,ifeq(l2(X2,X3),true,m4(X1,X3),true),true) = true,
rule_279 ).
cnf(c_0_74,plain,
l2(X1,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_28]),c_0_30]) ).
cnf(c_0_75,plain,
ifeq(m0(e,X1,X2),true,s3(a,X2),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_30]),c_0_30]) ).
cnf(c_0_76,axiom,
ifeq(s4(X1),true,ifeq(m4(e,e),true,m5(X1,X1),true),true) = true,
rule_305 ).
cnf(c_0_77,plain,
s4(d) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_30]) ).
cnf(c_0_78,plain,
ifeq(s3(a,X1),true,m4(X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_30]) ).
cnf(c_0_79,plain,
s3(a,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_60]),c_0_30]) ).
cnf(c_0_80,plain,
ifeq(m4(e,e),true,m5(d,d),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_30]) ).
cnf(c_0_81,plain,
m4(X1,X2) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_30]) ).
cnf(c_0_82,negated_conjecture,
m5(d,d) != true,
prove_this ).
cnf(c_0_83,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_30]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN143-10 : TPTP v9.2.1. Released v7.3.0.
% 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
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 08:15:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.66/1.83 % Version : CSE_E---1.7
% 1.66/1.83 % Problem : theBenchmark.p
% 1.66/1.83 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.83 % SZS output start CNFRefutation
% See solution above
% 1.66/1.83 % Total time : 1.375s
%------------------------------------------------------------------------------