%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX214-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:16:21 AM UTC 2026
% Result : Unsatisfiable 213.90s 45.22s
% Output : CNFRefutation 213.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 29
% Syntax : Number of formulae : 256 ( 256 unt; 0 def)
% Number of atoms : 256 ( 255 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 25 ( 25 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-4 aty)
% Number of variables : 449 ( 68 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom,axiom,
! [VAR_0,VAR_1] : aux(VAR_0,VAR_1,btrue) = eps,
file('theBenchmark.p',axiom) ).
cnf(c_1,plain,
aux(A,B,btrue) = eps,
inference(clausify,[status(thm)],[axiom]) ).
fof(axiom_001,axiom,
! [VAR_0,VAR_1] : aux(VAR_0,VAR_1,bfalse) = nil2,
file('theBenchmark.p',axiom_001) ).
cnf(c_2,plain,
aux(A,B,bfalse) = nil2,
inference(clausify,[status(thm)],[axiom_001]) ).
fof(axiom_002,axiom,
! [VAR_0,VAR_1,VAR_2] : aux2(VAR_0,VAR_1,VAR_2,btrue) = x(y(step(VAR_1,VAR_0),VAR_2),step(VAR_2,VAR_0)),
file('theBenchmark.p',axiom_002) ).
cnf(c_3,plain,
aux2(A,B,C,btrue) = x(y(step(B,A),C),step(C,A)),
inference(clausify,[status(thm)],[axiom_002]) ).
fof(axiom_003,axiom,
! [VAR_0,VAR_1,VAR_2] : aux2(VAR_0,VAR_1,VAR_2,bfalse) = x(y(step(VAR_1,VAR_0),VAR_2),nil2),
file('theBenchmark.p',axiom_003) ).
cnf(c_4,plain,
aux2(A,B,C,bfalse) = x(y(step(B,A),C),nil2),
inference(clausify,[status(thm)],[axiom_003]) ).
fof(axiom_061,axiom,
! [VAR_0] : orb(btrue,VAR_0) = btrue,
file('theBenchmark.p',axiom_061) ).
cnf(c_62,plain,
orb(btrue,A) = btrue,
inference(clausify,[status(thm)],[axiom_061]) ).
fof(axiom_062,axiom,
! [VAR_0] : orb(bfalse,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_062) ).
cnf(c_63,plain,
orb(bfalse,A) = A,
inference(clausify,[status(thm)],[axiom_062]) ).
fof(axiom_063,axiom,
! [VAR_0] : andb(btrue,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_063) ).
cnf(c_64,plain,
andb(btrue,A) = A,
inference(clausify,[status(thm)],[axiom_063]) ).
fof(axiom_064,axiom,
! [VAR_0] : andb(bfalse,VAR_0) = bfalse,
file('theBenchmark.p',axiom_064) ).
cnf(c_65,plain,
andb(bfalse,A) = bfalse,
inference(clausify,[status(thm)],[axiom_064]) ).
fof(axiom_065,axiom,
eps2(eps) = btrue,
file('theBenchmark.p',axiom_065) ).
cnf(c_66,plain,
eps2(eps) = btrue,
inference(clausify,[status(thm)],[axiom_065]) ).
cnf(c_67,plain,
btrue = eps2(eps),
inference(copy,[status(thm)],[c_66]) ).
fof(axiom_066,axiom,
! [VAR_0,VAR_1] : eps2(x(VAR_0,VAR_1)) = orb(eps2(VAR_0),eps2(VAR_1)),
file('theBenchmark.p',axiom_066) ).
cnf(c_68,plain,
eps2(x(A,B)) = orb(eps2(A),eps2(B)),
inference(clausify,[status(thm)],[axiom_066]) ).
fof(axiom_067,axiom,
! [VAR_0,VAR_1] : eps2(y(VAR_0,VAR_1)) = andb(eps2(VAR_0),eps2(VAR_1)),
file('theBenchmark.p',axiom_067) ).
cnf(c_69,plain,
eps2(y(A,B)) = andb(eps2(A),eps2(B)),
inference(clausify,[status(thm)],[axiom_067]) ).
fof(axiom_068,axiom,
! [VAR_0] : eps2(star(VAR_0)) = btrue,
file('theBenchmark.p',axiom_068) ).
cnf(c_70,plain,
eps2(star(A)) = btrue,
inference(clausify,[status(thm)],[axiom_068]) ).
cnf(c_71,plain,
eps2(star(A)) = eps2(eps),
inference(paramod,[status(thm)],[c_67,c_70]) ).
fof(axiom_069,axiom,
eps2(nil2) = bfalse,
file('theBenchmark.p',axiom_069) ).
cnf(c_72,plain,
eps2(nil2) = bfalse,
inference(clausify,[status(thm)],[axiom_069]) ).
cnf(c_73,plain,
bfalse = eps2(nil2),
inference(copy,[status(thm)],[c_72]) ).
fof(axiom_071,axiom,
! [VAR_0,VAR_1] : step(atom(VAR_0),VAR_1) = aux(VAR_1,VAR_0,eq(VAR_0,VAR_1)),
file('theBenchmark.p',axiom_071) ).
cnf(c_76,plain,
step(atom(A),B) = aux(B,A,eq(A,B)),
inference(clausify,[status(thm)],[axiom_071]) ).
cnf(c_77,plain,
aux(A,B,eq(B,A)) = step(atom(B),A),
inference(copy,[status(thm)],[c_76]) ).
fof(axiom_072,axiom,
! [VAR_0,VAR_1,VAR_2] : step(x(VAR_0,VAR_1),VAR_2) = x(step(VAR_0,VAR_2),step(VAR_1,VAR_2)),
file('theBenchmark.p',axiom_072) ).
cnf(c_78,plain,
step(x(A,B),C) = x(step(A,C),step(B,C)),
inference(clausify,[status(thm)],[axiom_072]) ).
fof(axiom_073,axiom,
! [VAR_0,VAR_1,VAR_2] : step(y(VAR_0,VAR_1),VAR_2) = aux2(VAR_2,VAR_0,VAR_1,eps2(VAR_0)),
file('theBenchmark.p',axiom_073) ).
cnf(c_79,plain,
step(y(A,B),C) = aux2(C,A,B,eps2(A)),
inference(clausify,[status(thm)],[axiom_073]) ).
cnf(c_80,plain,
aux2(A,B,C,eps2(B)) = step(y(B,C),A),
inference(copy,[status(thm)],[c_79]) ).
fof(axiom_074,axiom,
! [VAR_0,VAR_1] : step(star(VAR_0),VAR_1) = y(step(VAR_0,VAR_1),star(VAR_0)),
file('theBenchmark.p',axiom_074) ).
cnf(c_81,plain,
step(star(A),B) = y(step(A,B),star(A)),
inference(clausify,[status(thm)],[axiom_074]) ).
fof(axiom_075,axiom,
! [VAR_0] : step(nil2,VAR_0) = nil2,
file('theBenchmark.p',axiom_075) ).
cnf(c_82,plain,
step(nil2,A) = nil2,
inference(clausify,[status(thm)],[axiom_075]) ).
fof(axiom_076,axiom,
! [VAR_0] : step(eps,VAR_0) = nil2,
file('theBenchmark.p',axiom_076) ).
cnf(c_83,plain,
step(eps,A) = nil2,
inference(clausify,[status(thm)],[axiom_076]) ).
fof(axiom_077,axiom,
! [VAR_0] : rec(VAR_0,nil) = eps2(VAR_0),
file('theBenchmark.p',axiom_077) ).
cnf(c_84,plain,
rec(A,nil) = eps2(A),
inference(clausify,[status(thm)],[axiom_077]) ).
cnf(c_85,plain,
eps2(A) = rec(A,nil),
inference(copy,[status(thm)],[c_84]) ).
fof(axiom_078,axiom,
! [VAR_0,VAR_1,VAR_2] : rec(VAR_0,cons(VAR_1,VAR_2)) = rec(step(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',axiom_078) ).
cnf(c_86,plain,
rec(A,cons(B,C)) = rec(step(A,B),C),
inference(clausify,[status(thm)],[axiom_078]) ).
cnf(c_87,plain,
rec(step(A,B),C) = rec(A,cons(B,C)),
inference(copy,[status(thm)],[c_86]) ).
fof(axiom_079,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : prop_star_plus_easy(VAR_0,VAR_1,VAR_2,VAR_3) = eq2(rec(star(x(VAR_0,VAR_1)),cons(VAR_2,cons(VAR_3,nil))),rec(x(star(VAR_0),star(VAR_1)),cons(VAR_2,cons(VAR_3,nil)))),
file('theBenchmark.p',axiom_079) ).
cnf(c_88,plain,
prop_star_plus_easy(A,B,C,D) = eq2(rec(star(x(A,B)),cons(C,cons(D,nil))),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),
inference(clausify,[status(thm)],[axiom_079]) ).
fof(axiom_080,axiom,
eq(a,b) = bfalse,
file('theBenchmark.p',axiom_080) ).
cnf(c_89,plain,
eq(a,b) = bfalse,
inference(clausify,[status(thm)],[axiom_080]) ).
cnf(c_6401,plain,
eq(a,b) = eps2(nil2),
inference(paramod,[status(thm)],[c_73,c_89]) ).
cnf(c_6402,plain,
eq(a,b) = rec(nil2,nil),
inference(paramod,[status(thm)],[c_85,c_6401]) ).
cnf(c_90,plain,
rec(nil2,nil) = eq(a,b),
inference(copy,[status(thm)],[c_6402]) ).
fof(axiom_081,axiom,
eq(a,c) = bfalse,
file('theBenchmark.p',axiom_081) ).
cnf(c_91,plain,
eq(a,c) = bfalse,
inference(clausify,[status(thm)],[axiom_081]) ).
cnf(c_6403,plain,
eq(a,c) = eps2(nil2),
inference(paramod,[status(thm)],[c_73,c_91]) ).
cnf(c_6404,plain,
eq(a,c) = rec(nil2,nil),
inference(paramod,[status(thm)],[c_85,c_6403]) ).
cnf(c_92,plain,
eq(a,c) = eq(a,b),
inference(paramod,[status(thm)],[c_90,c_6404]) ).
fof(axiom_084,axiom,
eq(c,a) = bfalse,
file('theBenchmark.p',axiom_084) ).
cnf(c_97,plain,
eq(c,a) = bfalse,
inference(clausify,[status(thm)],[axiom_084]) ).
cnf(c_6405,plain,
eq(c,a) = eps2(nil2),
inference(paramod,[status(thm)],[c_73,c_97]) ).
cnf(c_6406,plain,
eq(c,a) = rec(nil2,nil),
inference(paramod,[status(thm)],[c_85,c_6405]) ).
cnf(c_98,plain,
eq(c,a) = eq(a,b),
inference(paramod,[status(thm)],[c_90,c_6406]) ).
fof(axiom_087,axiom,
eq2(btrue,bfalse) = bfalse,
file('theBenchmark.p',axiom_087) ).
cnf(c_103,plain,
eq2(btrue,bfalse) = bfalse,
inference(clausify,[status(thm)],[axiom_087]) ).
cnf(c_6407,plain,
eq2(eps2(eps),bfalse) = bfalse,
inference(paramod,[status(thm)],[c_67,c_103]) ).
cnf(c_6408,plain,
eq2(rec(eps,nil),bfalse) = bfalse,
inference(paramod,[status(thm)],[c_85,c_6407]) ).
cnf(c_6409,plain,
eq2(rec(eps,nil),eps2(nil2)) = bfalse,
inference(paramod,[status(thm)],[c_73,c_6408]) ).
cnf(c_6410,plain,
eq2(rec(eps,nil),rec(nil2,nil)) = bfalse,
inference(paramod,[status(thm)],[c_85,c_6409]) ).
cnf(c_6411,plain,
eq2(rec(eps,nil),eq(a,b)) = bfalse,
inference(paramod,[status(thm)],[c_90,c_6410]) ).
cnf(c_6412,plain,
eq2(rec(eps,nil),eq(a,b)) = eps2(nil2),
inference(paramod,[status(thm)],[c_73,c_6411]) ).
cnf(c_6413,plain,
eq2(rec(eps,nil),eq(a,b)) = rec(nil2,nil),
inference(paramod,[status(thm)],[c_85,c_6412]) ).
cnf(c_104,plain,
eq2(rec(eps,nil),eq(a,b)) = eq(a,b),
inference(paramod,[status(thm)],[c_90,c_6413]) ).
fof(axiom_088,axiom,
! [VAR_0] : eq(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_088) ).
cnf(c_105,plain,
eq(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_088]) ).
cnf(c_6414,plain,
eq(A,A) = eps2(eps),
inference(paramod,[status(thm)],[c_67,c_105]) ).
cnf(c_6415,plain,
eq(A,A) = rec(eps,nil),
inference(paramod,[status(thm)],[c_85,c_6414]) ).
cnf(c_106,plain,
rec(eps,nil) = eq(A,A),
inference(copy,[status(thm)],[c_6415]) ).
fof(axiom_089,axiom,
! [VAR_0] : eq2(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_089) ).
cnf(c_107,plain,
eq2(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_089]) ).
cnf(c_6416,plain,
eq2(A,A) = eps2(eps),
inference(paramod,[status(thm)],[c_67,c_107]) ).
cnf(c_108,plain,
eq2(A,A) = rec(eps,nil),
inference(paramod,[status(thm)],[c_85,c_6416]) ).
fof(goal,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : eq2(prop_star_plus_easy(VAR_0,VAR_1,VAR_2,VAR_3),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_109,plain,
eq2(prop_star_plus_easy(A,B,C,D),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_6417,plain,
eq2(eq2(rec(star(x(A,B)),cons(C,cons(D,nil))),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),bfalse) != btrue,
inference(paramod,[status(thm)],[c_88,c_109]) ).
cnf(c_6418,plain,
eq2(eq2(rec(star(x(A,B)),cons(C,cons(D,nil))),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),eps2(nil2)) != btrue,
inference(paramod,[status(thm)],[c_73,c_6417]) ).
cnf(c_6419,plain,
eq2(eq2(rec(star(x(A,B)),cons(C,cons(D,nil))),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),rec(nil2,nil)) != btrue,
inference(paramod,[status(thm)],[c_85,c_6418]) ).
cnf(c_6420,plain,
eq2(eq2(rec(star(x(A,B)),cons(C,cons(D,nil))),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),eq(a,b)) != btrue,
inference(paramod,[status(thm)],[c_90,c_6419]) ).
cnf(c_6421,plain,
eq2(eq2(rec(star(x(A,B)),cons(C,cons(D,nil))),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),eq(a,b)) != eps2(eps),
inference(paramod,[status(thm)],[c_67,c_6420]) ).
cnf(c_110,plain,
eq2(eq2(rec(star(x(A,B)),cons(C,cons(D,nil))),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_85,c_6421]) ).
cnf(c_6422,plain,
andb(eps2(eps),A) = A,
inference(paramod,[status(thm)],[c_67,c_64]) ).
cnf(c_111,plain,
andb(rec(eps,nil),A) = A,
inference(paramod,[status(thm)],[c_85,c_6422]) ).
cnf(c_6423,plain,
orb(eps2(eps),A) = btrue,
inference(paramod,[status(thm)],[c_67,c_62]) ).
cnf(c_6424,plain,
orb(rec(eps,nil),A) = btrue,
inference(paramod,[status(thm)],[c_85,c_6423]) ).
cnf(c_6425,plain,
orb(rec(eps,nil),A) = eps2(eps),
inference(paramod,[status(thm)],[c_67,c_6424]) ).
cnf(c_112,plain,
orb(rec(eps,nil),A) = rec(eps,nil),
inference(paramod,[status(thm)],[c_85,c_6425]) ).
cnf(c_6426,plain,
aux2(A,B,C,eps2(eps)) = x(y(step(B,A),C),step(C,A)),
inference(paramod,[status(thm)],[c_67,c_3]) ).
cnf(c_113,plain,
aux2(A,B,C,rec(eps,nil)) = x(y(step(B,A),C),step(C,A)),
inference(paramod,[status(thm)],[c_85,c_6426]) ).
cnf(c_6427,plain,
aux(A,B,eps2(eps)) = eps,
inference(paramod,[status(thm)],[c_67,c_1]) ).
cnf(c_114,plain,
aux(A,B,rec(eps,nil)) = eps,
inference(paramod,[status(thm)],[c_85,c_6427]) ).
cnf(c_6428,plain,
andb(eps2(nil2),A) = bfalse,
inference(paramod,[status(thm)],[c_73,c_65]) ).
cnf(c_6429,plain,
andb(rec(nil2,nil),A) = bfalse,
inference(paramod,[status(thm)],[c_85,c_6428]) ).
cnf(c_6430,plain,
andb(eq(a,b),A) = bfalse,
inference(paramod,[status(thm)],[c_90,c_6429]) ).
cnf(c_6431,plain,
andb(eq(a,b),A) = eps2(nil2),
inference(paramod,[status(thm)],[c_73,c_6430]) ).
cnf(c_6432,plain,
andb(eq(a,b),A) = rec(nil2,nil),
inference(paramod,[status(thm)],[c_85,c_6431]) ).
cnf(c_115,plain,
andb(eq(a,b),A) = eq(a,b),
inference(paramod,[status(thm)],[c_90,c_6432]) ).
cnf(c_6433,plain,
orb(eps2(nil2),A) = A,
inference(paramod,[status(thm)],[c_73,c_63]) ).
cnf(c_6434,plain,
orb(rec(nil2,nil),A) = A,
inference(paramod,[status(thm)],[c_85,c_6433]) ).
cnf(c_116,plain,
orb(eq(a,b),A) = A,
inference(paramod,[status(thm)],[c_90,c_6434]) ).
cnf(c_6435,plain,
aux2(A,B,C,eps2(nil2)) = x(y(step(B,A),C),nil2),
inference(paramod,[status(thm)],[c_73,c_4]) ).
cnf(c_6436,plain,
aux2(A,B,C,rec(nil2,nil)) = x(y(step(B,A),C),nil2),
inference(paramod,[status(thm)],[c_85,c_6435]) ).
cnf(c_117,plain,
aux2(A,B,C,eq(a,b)) = x(y(step(B,A),C),nil2),
inference(paramod,[status(thm)],[c_90,c_6436]) ).
cnf(c_6437,plain,
aux(A,B,eps2(nil2)) = nil2,
inference(paramod,[status(thm)],[c_73,c_2]) ).
cnf(c_6438,plain,
aux(A,B,rec(nil2,nil)) = nil2,
inference(paramod,[status(thm)],[c_85,c_6437]) ).
cnf(c_118,plain,
aux(A,B,eq(a,b)) = nil2,
inference(paramod,[status(thm)],[c_90,c_6438]) ).
cnf(c_119,plain,
aux2(A,B,C,rec(B,nil)) = step(y(B,C),A),
inference(paramod,[status(thm)],[c_85,c_80]) ).
cnf(c_6439,plain,
rec(star(A),nil) = eps2(eps),
inference(paramod,[status(thm)],[c_85,c_71]) ).
cnf(c_122,plain,
rec(star(A),nil) = rec(eps,nil),
inference(paramod,[status(thm)],[c_85,c_6439]) ).
cnf(c_6440,plain,
rec(y(A,B),nil) = andb(eps2(A),eps2(B)),
inference(paramod,[status(thm)],[c_85,c_69]) ).
cnf(c_6441,plain,
rec(y(A,B),nil) = andb(rec(A,nil),eps2(B)),
inference(paramod,[status(thm)],[c_85,c_6440]) ).
cnf(c_6442,plain,
rec(y(A,B),nil) = andb(rec(A,nil),rec(B,nil)),
inference(paramod,[status(thm)],[c_85,c_6441]) ).
cnf(c_123,plain,
andb(rec(A,nil),rec(B,nil)) = rec(y(A,B),nil),
inference(copy,[status(thm)],[c_6442]) ).
cnf(c_6443,plain,
rec(x(A,B),nil) = orb(eps2(A),eps2(B)),
inference(paramod,[status(thm)],[c_85,c_68]) ).
cnf(c_6444,plain,
rec(x(A,B),nil) = orb(rec(A,nil),eps2(B)),
inference(paramod,[status(thm)],[c_85,c_6443]) ).
cnf(c_6445,plain,
rec(x(A,B),nil) = orb(rec(A,nil),rec(B,nil)),
inference(paramod,[status(thm)],[c_85,c_6444]) ).
cnf(c_124,plain,
orb(rec(A,nil),rec(B,nil)) = rec(x(A,B),nil),
inference(copy,[status(thm)],[c_6445]) ).
cnf(c_126,plain,
rec(x(step(A,B),step(C,B)),D) = rec(x(A,C),cons(B,D)),
inference(paramod,[status(thm)],[c_78,c_87]) ).
cnf(c_6446,plain,
rec(y(step(A,B),star(A)),C) = rec(star(A),cons(B,C)),
inference(paramod,[status(thm)],[c_81,c_87]) ).
cnf(c_127,plain,
rec(star(A),cons(B,C)) = rec(y(step(A,B),star(A)),C),
inference(copy,[status(thm)],[c_6446]) ).
cnf(c_6447,plain,
aux(c,a,eq(a,b)) = step(atom(a),c),
inference(paramod,[status(thm)],[c_92,c_77]) ).
cnf(c_6448,plain,
nil2 = step(atom(a),c),
inference(paramod,[status(thm)],[c_118,c_6447]) ).
cnf(c_131,plain,
step(atom(a),c) = nil2,
inference(copy,[status(thm)],[c_6448]) ).
cnf(c_6449,plain,
aux(a,c,eq(a,b)) = step(atom(c),a),
inference(paramod,[status(thm)],[c_98,c_77]) ).
cnf(c_6450,plain,
nil2 = step(atom(c),a),
inference(paramod,[status(thm)],[c_118,c_6449]) ).
cnf(c_135,plain,
step(atom(c),a) = nil2,
inference(copy,[status(thm)],[c_6450]) ).
cnf(c_6451,plain,
aux(A,A,rec(eps,nil)) = step(atom(A),A),
inference(paramod,[status(thm)],[c_106,c_77]) ).
cnf(c_6452,plain,
eps = step(atom(A),A),
inference(paramod,[status(thm)],[c_114,c_6451]) ).
cnf(c_139,plain,
step(atom(A),A) = eps,
inference(copy,[status(thm)],[c_6452]) ).
cnf(c_6453,plain,
eq2(eq2(rec(step(star(x(A,B)),C),cons(D,nil)),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_87,c_110]) ).
cnf(c_6454,plain,
eq2(eq2(rec(y(step(x(A,B),C),star(x(A,B))),cons(D,nil)),rec(x(star(A),star(B)),cons(C,cons(D,nil)))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_81,c_6453]) ).
cnf(c_143,plain,
eq2(eq2(rec(y(x(step(A,B),step(C,B)),star(x(A,C))),cons(D,nil)),rec(x(star(A),star(C)),cons(B,cons(D,nil)))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_78,c_6454]) ).
cnf(c_147,plain,
andb(eq(A,A),B) = B,
inference(paramod,[status(thm)],[c_106,c_111]) ).
cnf(c_148,plain,
orb(eq(A,A),B) = rec(eps,nil),
inference(paramod,[status(thm)],[c_106,c_112]) ).
cnf(c_6455,plain,
aux2(A,eps,B,rec(eps,nil)) = x(y(nil2,B),step(B,A)),
inference(paramod,[status(thm)],[c_83,c_113]) ).
cnf(c_149,plain,
step(y(eps,A),B) = x(y(nil2,A),step(A,B)),
inference(paramod,[status(thm)],[c_119,c_6455]) ).
cnf(c_157,plain,
aux2(A,step(B,C),D,rec(B,cons(C,nil))) = step(y(step(B,C),D),A),
inference(paramod,[status(thm)],[c_87,c_119]) ).
cnf(c_6456,plain,
aux2(A,nil2,B,eq(a,b)) = step(y(nil2,B),A),
inference(paramod,[status(thm)],[c_90,c_119]) ).
cnf(c_6457,plain,
x(y(step(nil2,A),B),nil2) = step(y(nil2,B),A),
inference(paramod,[status(thm)],[c_117,c_6456]) ).
cnf(c_6458,plain,
x(y(nil2,B),nil2) = step(y(nil2,B),A),
inference(paramod,[status(thm)],[c_82,c_6457]) ).
cnf(c_158,plain,
step(y(nil2,A),B) = x(y(nil2,A),nil2),
inference(copy,[status(thm)],[c_6458]) ).
cnf(c_6459,plain,
andb(eq(a,b),rec(A,nil)) = rec(y(nil2,A),nil),
inference(paramod,[status(thm)],[c_90,c_123]) ).
cnf(c_6460,plain,
eq(a,b) = rec(y(nil2,A),nil),
inference(paramod,[status(thm)],[c_115,c_6459]) ).
cnf(c_163,plain,
rec(y(nil2,A),nil) = eq(a,b),
inference(copy,[status(thm)],[c_6460]) ).
cnf(c_6461,plain,
andb(eq(A,A),rec(B,nil)) = rec(y(eps,B),nil),
inference(paramod,[status(thm)],[c_106,c_123]) ).
cnf(c_6462,plain,
rec(B,nil) = rec(y(eps,B),nil),
inference(paramod,[status(thm)],[c_147,c_6461]) ).
cnf(c_165,plain,
rec(y(eps,A),nil) = rec(A,nil),
inference(copy,[status(thm)],[c_6462]) ).
cnf(c_6463,plain,
andb(rec(A,nil),rec(eps,nil)) = rec(y(A,star(B)),nil),
inference(paramod,[status(thm)],[c_122,c_123]) ).
cnf(c_6464,plain,
rec(y(A,eps),nil) = rec(y(A,star(B)),nil),
inference(paramod,[status(thm)],[c_123,c_6463]) ).
cnf(c_170,plain,
rec(y(A,star(B)),nil) = rec(y(A,eps),nil),
inference(copy,[status(thm)],[c_6464]) ).
cnf(c_6465,plain,
orb(eq(a,b),rec(A,nil)) = rec(x(nil2,A),nil),
inference(paramod,[status(thm)],[c_90,c_124]) ).
cnf(c_6466,plain,
rec(A,nil) = rec(x(nil2,A),nil),
inference(paramod,[status(thm)],[c_116,c_6465]) ).
cnf(c_173,plain,
rec(x(nil2,A),nil) = rec(A,nil),
inference(copy,[status(thm)],[c_6466]) ).
cnf(c_6467,plain,
orb(eq(A,A),rec(B,nil)) = rec(x(eps,B),nil),
inference(paramod,[status(thm)],[c_106,c_124]) ).
cnf(c_6468,plain,
rec(eps,nil) = rec(x(eps,B),nil),
inference(paramod,[status(thm)],[c_148,c_6467]) ).
cnf(c_175,plain,
rec(x(eps,A),nil) = rec(eps,nil),
inference(copy,[status(thm)],[c_6468]) ).
cnf(c_6469,plain,
rec(x(y(step(A,B),star(A)),step(C,B)),D) = rec(x(star(A),C),cons(B,D)),
inference(paramod,[status(thm)],[c_81,c_126]) ).
cnf(c_183,plain,
rec(x(star(A),B),cons(C,D)) = rec(x(y(step(A,C),star(A)),step(B,C)),D),
inference(copy,[status(thm)],[c_6469]) ).
cnf(c_185,plain,
rec(x(nil2,step(A,B)),C) = rec(x(nil2,A),cons(B,C)),
inference(paramod,[status(thm)],[c_82,c_126]) ).
cnf(c_237,plain,
eq2(eq2(rec(y(x(step(A,B),eps),star(x(A,atom(B)))),cons(C,nil)),rec(x(star(A),star(atom(B))),cons(B,cons(C,nil)))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_139,c_143]) ).
cnf(c_6470,plain,
eps2(y(step(A,B),star(A))) = rec(star(A),cons(B,nil)),
inference(paramod,[status(thm)],[c_127,c_85]) ).
cnf(c_6471,plain,
rec(y(step(A,B),star(A)),nil) = rec(star(A),cons(B,nil)),
inference(paramod,[status(thm)],[c_85,c_6470]) ).
cnf(c_6472,plain,
rec(y(step(A,B),eps),nil) = rec(star(A),cons(B,nil)),
inference(paramod,[status(thm)],[c_170,c_6471]) ).
cnf(c_242,plain,
rec(star(A),cons(B,nil)) = rec(y(step(A,B),eps),nil),
inference(copy,[status(thm)],[c_6472]) ).
cnf(c_6473,plain,
orb(eq(a,b),rec(A,nil)) = rec(x(y(nil2,B),A),nil),
inference(paramod,[status(thm)],[c_163,c_124]) ).
cnf(c_6474,plain,
rec(A,nil) = rec(x(y(nil2,B),A),nil),
inference(paramod,[status(thm)],[c_116,c_6473]) ).
cnf(c_313,plain,
rec(x(y(nil2,A),B),nil) = rec(B,nil),
inference(copy,[status(thm)],[c_6474]) ).
cnf(c_6475,plain,
andb(rec(A,nil),rec(B,nil)) = rec(y(x(nil2,A),B),nil),
inference(paramod,[status(thm)],[c_173,c_123]) ).
cnf(c_6476,plain,
rec(y(A,B),nil) = rec(y(x(nil2,A),B),nil),
inference(paramod,[status(thm)],[c_123,c_6475]) ).
cnf(c_321,plain,
rec(y(x(nil2,A),B),nil) = rec(y(A,B),nil),
inference(copy,[status(thm)],[c_6476]) ).
cnf(c_6477,plain,
andb(rec(eps,nil),rec(A,nil)) = rec(y(x(eps,B),A),nil),
inference(paramod,[status(thm)],[c_175,c_123]) ).
cnf(c_6478,plain,
rec(y(eps,A),nil) = rec(y(x(eps,B),A),nil),
inference(paramod,[status(thm)],[c_123,c_6477]) ).
cnf(c_6479,plain,
rec(A,nil) = rec(y(x(eps,B),A),nil),
inference(paramod,[status(thm)],[c_165,c_6478]) ).
cnf(c_326,plain,
rec(y(x(eps,A),B),nil) = rec(B,nil),
inference(copy,[status(thm)],[c_6479]) ).
cnf(c_6480,plain,
andb(rec(A,nil),rec(B,nil)) = rec(y(A,x(y(nil2,C),B)),nil),
inference(paramod,[status(thm)],[c_313,c_123]) ).
cnf(c_6481,plain,
rec(y(A,B),nil) = rec(y(A,x(y(nil2,C),B)),nil),
inference(paramod,[status(thm)],[c_123,c_6480]) ).
cnf(c_441,plain,
rec(y(A,x(y(nil2,B),C)),nil) = rec(y(A,C),nil),
inference(copy,[status(thm)],[c_6481]) ).
cnf(c_6482,plain,
orb(rec(A,nil),rec(B,nil)) = rec(x(x(y(nil2,C),A),B),nil),
inference(paramod,[status(thm)],[c_313,c_124]) ).
cnf(c_6483,plain,
rec(x(A,B),nil) = rec(x(x(y(nil2,C),A),B),nil),
inference(paramod,[status(thm)],[c_124,c_6482]) ).
cnf(c_442,plain,
rec(x(x(y(nil2,A),B),C),nil) = rec(x(B,C),nil),
inference(copy,[status(thm)],[c_6483]) ).
cnf(c_520,plain,
rec(x(y(nil2,A),step(A,B)),C) = rec(y(eps,A),cons(B,C)),
inference(paramod,[status(thm)],[c_149,c_87]) ).
cnf(c_6484,plain,
orb(rec(y(A,B),nil),rec(C,nil)) = rec(x(y(x(nil2,A),B),C),nil),
inference(paramod,[status(thm)],[c_321,c_124]) ).
cnf(c_6485,plain,
rec(x(y(A,B),C),nil) = rec(x(y(x(nil2,A),B),C),nil),
inference(paramod,[status(thm)],[c_124,c_6484]) ).
cnf(c_587,plain,
rec(x(y(x(nil2,A),B),C),nil) = rec(x(y(A,B),C),nil),
inference(copy,[status(thm)],[c_6485]) ).
cnf(c_610,plain,
rec(star(x(A,B)),cons(C,nil)) = rec(y(x(step(A,C),step(B,C)),eps),nil),
inference(paramod,[status(thm)],[c_78,c_242]) ).
cnf(c_6486,plain,
rec(star(atom(c)),cons(a,nil)) = rec(y(nil2,eps),nil),
inference(paramod,[status(thm)],[c_135,c_242]) ).
cnf(c_616,plain,
rec(star(atom(c)),cons(a,nil)) = eq(a,b),
inference(paramod,[status(thm)],[c_163,c_6486]) ).
cnf(c_6487,plain,
eps2(x(nil2,step(A,B))) = rec(x(nil2,A),cons(B,nil)),
inference(paramod,[status(thm)],[c_185,c_85]) ).
cnf(c_6488,plain,
rec(x(nil2,step(A,B)),nil) = rec(x(nil2,A),cons(B,nil)),
inference(paramod,[status(thm)],[c_85,c_6487]) ).
cnf(c_6489,plain,
rec(step(A,B),nil) = rec(x(nil2,A),cons(B,nil)),
inference(paramod,[status(thm)],[c_173,c_6488]) ).
cnf(c_688,plain,
rec(x(nil2,A),cons(B,nil)) = rec(step(A,B),nil),
inference(copy,[status(thm)],[c_6489]) ).
cnf(c_6490,plain,
rec(x(nil2,eps),A) = rec(x(nil2,atom(B)),cons(B,A)),
inference(paramod,[status(thm)],[c_139,c_185]) ).
cnf(c_696,plain,
rec(x(nil2,atom(A)),cons(A,B)) = rec(x(nil2,eps),B),
inference(copy,[status(thm)],[c_6490]) ).
cnf(c_706,plain,
rec(x(nil2,A),cons(B,nil)) = rec(A,cons(B,nil)),
inference(paramod,[status(thm)],[c_688,c_87]) ).
cnf(c_6491,plain,
rec(x(nil2,y(eps,A)),cons(B,nil)) = rec(x(y(nil2,A),step(A,B)),nil),
inference(paramod,[status(thm)],[c_149,c_688]) ).
cnf(c_6492,plain,
rec(y(eps,A),cons(B,nil)) = rec(x(y(nil2,A),step(A,B)),nil),
inference(paramod,[status(thm)],[c_706,c_6491]) ).
cnf(c_708,plain,
rec(y(eps,A),cons(B,nil)) = rec(step(A,B),nil),
inference(paramod,[status(thm)],[c_313,c_6492]) ).
cnf(c_724,plain,
rec(y(eps,A),cons(B,nil)) = rec(A,cons(B,nil)),
inference(paramod,[status(thm)],[c_708,c_87]) ).
cnf(c_6493,plain,
aux2(A,step(x(nil2,atom(B)),B),C,rec(x(nil2,eps),nil)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_696,c_157]) ).
cnf(c_6494,plain,
aux2(A,x(step(nil2,B),step(atom(B),B)),C,rec(x(nil2,eps),nil)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_78,c_6493]) ).
cnf(c_6495,plain,
aux2(A,x(nil2,step(atom(B),B)),C,rec(x(nil2,eps),nil)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_82,c_6494]) ).
cnf(c_6496,plain,
aux2(A,x(nil2,eps),C,rec(x(nil2,eps),nil)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_139,c_6495]) ).
cnf(c_6497,plain,
aux2(A,x(nil2,eps),C,rec(eps,nil)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_173,c_6496]) ).
cnf(c_6498,plain,
x(y(step(x(nil2,eps),A),C),step(C,A)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_113,c_6497]) ).
cnf(c_6499,plain,
x(y(x(step(nil2,A),step(eps,A)),C),step(C,A)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_78,c_6498]) ).
cnf(c_6500,plain,
x(y(x(nil2,step(eps,A)),C),step(C,A)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_82,c_6499]) ).
cnf(c_6501,plain,
x(y(x(nil2,nil2),C),step(C,A)) = step(y(step(x(nil2,atom(B)),B),C),A),
inference(paramod,[status(thm)],[c_83,c_6500]) ).
cnf(c_6502,plain,
x(y(x(nil2,nil2),C),step(C,A)) = step(y(x(step(nil2,B),step(atom(B),B)),C),A),
inference(paramod,[status(thm)],[c_78,c_6501]) ).
cnf(c_6503,plain,
x(y(x(nil2,nil2),C),step(C,A)) = step(y(x(nil2,step(atom(B),B)),C),A),
inference(paramod,[status(thm)],[c_82,c_6502]) ).
cnf(c_6504,plain,
x(y(x(nil2,nil2),C),step(C,A)) = step(y(x(nil2,eps),C),A),
inference(paramod,[status(thm)],[c_139,c_6503]) ).
cnf(c_750,plain,
step(y(x(nil2,eps),A),B) = x(y(x(nil2,nil2),A),step(A,B)),
inference(copy,[status(thm)],[c_6504]) ).
cnf(c_930,plain,
rec(x(star(atom(a)),A),cons(c,B)) = rec(x(y(nil2,star(atom(a))),step(A,c)),B),
inference(paramod,[status(thm)],[c_131,c_183]) ).
cnf(c_6505,plain,
orb(rec(y(A,B),nil),rec(C,nil)) = rec(x(y(A,x(y(nil2,D),B)),C),nil),
inference(paramod,[status(thm)],[c_441,c_124]) ).
cnf(c_6506,plain,
rec(x(y(A,B),C),nil) = rec(x(y(A,x(y(nil2,D),B)),C),nil),
inference(paramod,[status(thm)],[c_124,c_6505]) ).
cnf(c_1043,plain,
rec(x(y(A,x(y(nil2,B),C)),D),nil) = rec(x(y(A,C),D),nil),
inference(copy,[status(thm)],[c_6506]) ).
cnf(c_6507,plain,
rec(x(y(nil2,A),step(x(y(nil2,B),A),C)),nil) = rec(y(eps,x(y(nil2,B),A)),cons(C,nil)),
inference(paramod,[status(thm)],[c_1043,c_520]) ).
cnf(c_6508,plain,
rec(x(y(nil2,A),x(step(y(nil2,B),C),step(A,C))),nil) = rec(y(eps,x(y(nil2,B),A)),cons(C,nil)),
inference(paramod,[status(thm)],[c_78,c_6507]) ).
cnf(c_6509,plain,
rec(x(y(nil2,A),x(x(y(nil2,B),nil2),step(A,C))),nil) = rec(y(eps,x(y(nil2,B),A)),cons(C,nil)),
inference(paramod,[status(thm)],[c_158,c_6508]) ).
cnf(c_6510,plain,
rec(x(x(y(nil2,B),nil2),step(A,C)),nil) = rec(y(eps,x(y(nil2,B),A)),cons(C,nil)),
inference(paramod,[status(thm)],[c_313,c_6509]) ).
cnf(c_6511,plain,
rec(x(nil2,step(A,C)),nil) = rec(y(eps,x(y(nil2,B),A)),cons(C,nil)),
inference(paramod,[status(thm)],[c_442,c_6510]) ).
cnf(c_6512,plain,
rec(step(A,C),nil) = rec(y(eps,x(y(nil2,B),A)),cons(C,nil)),
inference(paramod,[status(thm)],[c_173,c_6511]) ).
cnf(c_6513,plain,
rec(step(A,C),nil) = rec(x(y(nil2,B),A),cons(C,nil)),
inference(paramod,[status(thm)],[c_724,c_6512]) ).
cnf(c_3133,plain,
rec(x(y(nil2,A),B),cons(C,nil)) = rec(step(B,C),nil),
inference(copy,[status(thm)],[c_6513]) ).
cnf(c_3138,plain,
rec(x(y(nil2,A),B),cons(C,nil)) = rec(B,cons(C,nil)),
inference(paramod,[status(thm)],[c_3133,c_87]) ).
cnf(c_6514,plain,
rec(x(y(nil2,A),y(x(nil2,eps),B)),cons(C,nil)) = rec(x(y(x(nil2,nil2),B),step(B,C)),nil),
inference(paramod,[status(thm)],[c_750,c_3133]) ).
cnf(c_6515,plain,
rec(y(x(nil2,eps),B),cons(C,nil)) = rec(x(y(x(nil2,nil2),B),step(B,C)),nil),
inference(paramod,[status(thm)],[c_3138,c_6514]) ).
cnf(c_6516,plain,
rec(y(x(nil2,eps),B),cons(C,nil)) = rec(x(y(nil2,B),step(B,C)),nil),
inference(paramod,[status(thm)],[c_587,c_6515]) ).
cnf(c_3147,plain,
rec(y(x(nil2,eps),A),cons(B,nil)) = rec(step(A,B),nil),
inference(paramod,[status(thm)],[c_313,c_6516]) ).
cnf(c_3305,plain,
rec(y(x(nil2,eps),A),cons(B,nil)) = rec(A,cons(B,nil)),
inference(paramod,[status(thm)],[c_3147,c_87]) ).
cnf(c_3959,plain,
rec(star(x(A,atom(c))),cons(a,nil)) = rec(y(x(step(A,a),nil2),eps),nil),
inference(paramod,[status(thm)],[c_135,c_610]) ).
cnf(c_6517,plain,
eq2(eq2(rec(y(x(step(atom(a),c),eps),star(x(atom(a),atom(c)))),cons(A,nil)),rec(x(y(nil2,star(atom(a))),step(star(atom(c)),c)),cons(A,nil))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_930,c_237]) ).
cnf(c_6518,plain,
eq2(eq2(rec(y(x(nil2,eps),star(x(atom(a),atom(c)))),cons(A,nil)),rec(x(y(nil2,star(atom(a))),step(star(atom(c)),c)),cons(A,nil))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_131,c_6517]) ).
cnf(c_6519,plain,
eq2(eq2(rec(star(x(atom(a),atom(c))),cons(A,nil)),rec(x(y(nil2,star(atom(a))),step(star(atom(c)),c)),cons(A,nil))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_3305,c_6518]) ).
cnf(c_6520,plain,
eq2(eq2(rec(star(x(atom(a),atom(c))),cons(A,nil)),rec(x(y(nil2,star(atom(a))),y(step(atom(c),c),star(atom(c)))),cons(A,nil))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_81,c_6519]) ).
cnf(c_6521,plain,
eq2(eq2(rec(star(x(atom(a),atom(c))),cons(A,nil)),rec(x(y(nil2,star(atom(a))),y(eps,star(atom(c)))),cons(A,nil))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_139,c_6520]) ).
cnf(c_6522,plain,
eq2(eq2(rec(star(x(atom(a),atom(c))),cons(A,nil)),rec(y(eps,star(atom(c))),cons(A,nil))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_3138,c_6521]) ).
cnf(c_6306,plain,
eq2(eq2(rec(star(x(atom(a),atom(c))),cons(A,nil)),rec(star(atom(c)),cons(A,nil))),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_724,c_6522]) ).
cnf(c_6523,plain,
eq2(eq2(rec(star(x(atom(a),atom(c))),cons(a,nil)),eq(a,b)),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_616,c_6306]) ).
cnf(c_6524,plain,
eq2(eq2(rec(y(x(step(atom(a),a),nil2),eps),nil),eq(a,b)),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_3959,c_6523]) ).
cnf(c_6525,plain,
eq2(eq2(rec(y(x(eps,nil2),eps),nil),eq(a,b)),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_139,c_6524]) ).
cnf(c_6526,plain,
eq2(eq2(rec(eps,nil),eq(a,b)),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_326,c_6525]) ).
cnf(c_6527,plain,
eq2(eq(a,b),eq(a,b)) != rec(eps,nil),
inference(paramod,[status(thm)],[c_104,c_6526]) ).
cnf(c_6528,plain,
rec(eps,nil) != rec(eps,nil),
inference(paramod,[status(thm)],[c_108,c_6527]) ).
cnf(c_6400,plain,
$false,
inference(copy,[status(thm)],[c_6528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX214-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.37 % Computer : n020.cluster.edu
% 0.04/0.37 % Model : x86_64 x86_64
% 0.04/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.37 % Memory : 8046.5625MB
% 0.04/0.37 % OS : Linux 6.8.0-71-generic
% 0.04/0.37 % CPULimit : 300
% 0.04/0.37 % WCLimit : 300
% 0.04/0.37 % DateTime : Sat Sep 26 16:57:50 UTC 2026
% 0.04/0.37 % CPUTime :
% 0.04/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.37 % Process 2060817 was started by sandbox on n020,
% 0.04/0.37 % Sat Sep 26 16:57:50 2026
% 0.04/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.38
% 0.04/0.38 % From the command line: assign(max_seconds, 300).
% 213.90/45.22
% 213.90/45.22 % given #500 (F,wt=30): 1928 eq2(eq2(rec(y(x(nil2,eps),star(x(nil2,atom(A)))),cons(A,nil)),eq(B,B)),eq(a,b)) != rec(eps,nil). [para(106(a,1),1856(a,1,1,2))].
% 213.90/45.22
% 213.90/45.22 % given #1000 (T,wt=20): 4620 rec(x(y(x(nil2,eps),A),atom(B)),cons(B,nil)) = rec(x(step(A,B),eps),nil). [para(750(a,1),4533(a,1,1,1)),rewrite([1954(10),442(8),4619(15)]),flip(a)].
% 213.90/45.22
% 213.90/45.22 % SZS status Unsatisfiable for theBenchmark
% 213.90/45.22
% 213.90/45.22 % Proof 1 at 3.73 (+ 0.70) seconds.
% 213.90/45.22 % Length of proof is 99.
% 213.90/45.22 % Level of proof is 14.
% 213.90/45.22 % Maximum clause weight is 46.000.
% 213.90/45.22 % Given clauses 1039.
% 213.90/45.22
% 213.90/45.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------