%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX239-1 : 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 : n014.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 09:16:25 AM UTC 2026
% Result : Unsatisfiable 0.13s 6.02s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of formulae : 103 ( 103 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 5 con; 0-4 aty)
% Number of variables : 172 ( 32 sgn 36 !; 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_005,axiom,
! [VAR_0,VAR_1,VAR_2] : aux3(VAR_0,VAR_1,VAR_2,bfalse) = bfalse,
file('theBenchmark.p',axiom_005) ).
cnf(c_6,plain,
aux3(A,B,C,bfalse) = bfalse,
inference(clausify,[status(thm)],[axiom_005]) ).
fof(axiom_067,axiom,
! [VAR_0] : orb(btrue,VAR_0) = btrue,
file('theBenchmark.p',axiom_067) ).
cnf(c_70,plain,
orb(btrue,A) = btrue,
inference(clausify,[status(thm)],[axiom_067]) ).
fof(axiom_068,axiom,
! [VAR_0] : orb(bfalse,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_068) ).
cnf(c_71,plain,
orb(bfalse,A) = A,
inference(clausify,[status(thm)],[axiom_068]) ).
fof(axiom_071,axiom,
notb(btrue) = bfalse,
file('theBenchmark.p',axiom_071) ).
cnf(c_75,plain,
notb(btrue) = bfalse,
inference(clausify,[status(thm)],[axiom_071]) ).
fof(axiom_073,axiom,
! [VAR_0] : andb(btrue,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_073) ).
cnf(c_77,plain,
andb(btrue,A) = A,
inference(clausify,[status(thm)],[axiom_073]) ).
fof(axiom_075,axiom,
eps2(eps) = btrue,
file('theBenchmark.p',axiom_075) ).
cnf(c_79,plain,
eps2(eps) = btrue,
inference(clausify,[status(thm)],[axiom_075]) ).
fof(axiom_076,axiom,
! [VAR_0,VAR_1] : eps2(x(VAR_0,VAR_1)) = orb(eps2(VAR_0),eps2(VAR_1)),
file('theBenchmark.p',axiom_076) ).
cnf(c_80,plain,
eps2(x(A,B)) = orb(eps2(A),eps2(B)),
inference(clausify,[status(thm)],[axiom_076]) ).
fof(axiom_077,axiom,
! [VAR_0,VAR_1] : eps2(y(VAR_0,VAR_1)) = andb(eps2(VAR_0),eps2(VAR_1)),
file('theBenchmark.p',axiom_077) ).
cnf(c_81,plain,
eps2(y(A,B)) = andb(eps2(A),eps2(B)),
inference(clausify,[status(thm)],[axiom_077]) ).
fof(axiom_078,axiom,
! [VAR_0] : eps2(star(VAR_0)) = btrue,
file('theBenchmark.p',axiom_078) ).
cnf(c_82,plain,
eps2(star(A)) = btrue,
inference(clausify,[status(thm)],[axiom_078]) ).
fof(axiom_079,axiom,
eps2(nil4) = bfalse,
file('theBenchmark.p',axiom_079) ).
cnf(c_83,plain,
eps2(nil4) = bfalse,
inference(clausify,[status(thm)],[axiom_079]) ).
fof(axiom_081,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_081) ).
cnf(c_85,plain,
step(atom(A),B) = aux(B,A,eq(A,B)),
inference(clausify,[status(thm)],[axiom_081]) ).
cnf(c_86,plain,
aux(A,B,eq(B,A)) = step(atom(B),A),
inference(copy,[status(thm)],[c_85]) ).
fof(axiom_082,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_082) ).
cnf(c_87,plain,
step(x(A,B),C) = x(step(A,C),step(B,C)),
inference(clausify,[status(thm)],[axiom_082]) ).
cnf(c_88,plain,
x(step(A,B),step(C,B)) = step(x(A,C),B),
inference(copy,[status(thm)],[c_87]) ).
fof(axiom_084,axiom,
! [VAR_0,VAR_1] : step(star(VAR_0),VAR_1) = y(step(VAR_0,VAR_1),star(VAR_0)),
file('theBenchmark.p',axiom_084) ).
cnf(c_91,plain,
step(star(A),B) = y(step(A,B),star(A)),
inference(clausify,[status(thm)],[axiom_084]) ).
cnf(c_92,plain,
y(step(A,B),star(A)) = step(star(A),B),
inference(copy,[status(thm)],[c_91]) ).
fof(axiom_086,axiom,
! [VAR_0] : step(eps,VAR_0) = nil4,
file('theBenchmark.p',axiom_086) ).
cnf(c_94,plain,
step(eps,A) = nil4,
inference(clausify,[status(thm)],[axiom_086]) ).
fof(axiom_087,axiom,
! [VAR_0] : rec(VAR_0,nil2) = eps2(VAR_0),
file('theBenchmark.p',axiom_087) ).
cnf(c_95,plain,
rec(A,nil2) = eps2(A),
inference(clausify,[status(thm)],[axiom_087]) ).
cnf(c_96,plain,
eps2(A) = rec(A,nil2),
inference(copy,[status(thm)],[c_95]) ).
fof(axiom_088,axiom,
! [VAR_0,VAR_1,VAR_2] : rec(VAR_0,cons2(VAR_1,VAR_2)) = rec(step(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',axiom_088) ).
cnf(c_97,plain,
rec(A,cons2(B,C)) = rec(step(A,B),C),
inference(clausify,[status(thm)],[axiom_088]) ).
cnf(c_98,plain,
rec(step(A,B),C) = rec(A,cons2(B,C)),
inference(copy,[status(thm)],[c_97]) ).
fof(axiom_095,axiom,
! [VAR_0,VAR_1] : reck2(atom(VAR_0),cons2(VAR_1,nil2)) = eq(VAR_0,VAR_1),
file('theBenchmark.p',axiom_095) ).
cnf(c_105,plain,
reck2(atom(A),cons2(B,nil2)) = eq(A,B),
inference(clausify,[status(thm)],[axiom_095]) ).
cnf(c_106,plain,
eq(A,B) = reck2(atom(A),cons2(B,nil2)),
inference(copy,[status(thm)],[c_105]) ).
fof(axiom_100,axiom,
! [VAR_0,VAR_1,VAR_2] : reck2(star(VAR_0),cons2(VAR_1,VAR_2)) = aux3(VAR_0,VAR_1,VAR_2,notb(eps2(VAR_0))),
file('theBenchmark.p',axiom_100) ).
cnf(c_112,plain,
reck2(star(A),cons2(B,C)) = aux3(A,B,C,notb(eps2(A))),
inference(clausify,[status(thm)],[axiom_100]) ).
cnf(c_2657,plain,
reck2(star(A),cons2(B,C)) = aux3(A,B,C,notb(rec(A,nil2))),
inference(paramod,[status(thm)],[c_96,c_112]) ).
cnf(c_113,plain,
aux3(A,B,C,notb(rec(A,nil2))) = reck2(star(A),cons2(B,C)),
inference(copy,[status(thm)],[c_2657]) ).
fof(axiom_101,axiom,
! [VAR_0,VAR_1] : prop_same(VAR_0,VAR_1) = eq2(rec(VAR_0,VAR_1),reck2(VAR_0,VAR_1)),
file('theBenchmark.p',axiom_101) ).
cnf(c_114,plain,
prop_same(A,B) = eq2(rec(A,B),reck2(A,B)),
inference(clausify,[status(thm)],[axiom_101]) ).
fof(axiom_109,axiom,
eq2(btrue,bfalse) = bfalse,
file('theBenchmark.p',axiom_109) ).
cnf(c_128,plain,
eq2(btrue,bfalse) = bfalse,
inference(clausify,[status(thm)],[axiom_109]) ).
fof(axiom_110,axiom,
! [VAR_0] : eq(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_110) ).
cnf(c_129,plain,
eq(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_110]) ).
cnf(c_130,plain,
reck2(atom(A),cons2(A,nil2)) = btrue,
inference(paramod,[status(thm)],[c_106,c_129]) ).
fof(axiom_111,axiom,
! [VAR_0] : eq2(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_111) ).
cnf(c_131,plain,
eq2(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_111]) ).
fof(goal,axiom,
! [VAR_0,VAR_1] : eq2(prop_same(VAR_0,VAR_1),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_132,plain,
eq2(prop_same(A,B),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_133,plain,
eq2(eq2(rec(A,B),reck2(A,B)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_114,c_132]) ).
cnf(c_136,plain,
rec(nil4,nil2) = bfalse,
inference(paramod,[status(thm)],[c_96,c_83]) ).
cnf(c_137,plain,
rec(star(A),nil2) = btrue,
inference(paramod,[status(thm)],[c_96,c_82]) ).
cnf(c_2658,plain,
rec(y(A,B),nil2) = andb(eps2(A),eps2(B)),
inference(paramod,[status(thm)],[c_96,c_81]) ).
cnf(c_2659,plain,
rec(y(A,B),nil2) = andb(rec(A,nil2),eps2(B)),
inference(paramod,[status(thm)],[c_96,c_2658]) ).
cnf(c_138,plain,
rec(y(A,B),nil2) = andb(rec(A,nil2),rec(B,nil2)),
inference(paramod,[status(thm)],[c_96,c_2659]) ).
cnf(c_2660,plain,
rec(x(A,B),nil2) = orb(eps2(A),eps2(B)),
inference(paramod,[status(thm)],[c_96,c_80]) ).
cnf(c_2661,plain,
rec(x(A,B),nil2) = orb(rec(A,nil2),eps2(B)),
inference(paramod,[status(thm)],[c_96,c_2660]) ).
cnf(c_139,plain,
rec(x(A,B),nil2) = orb(rec(A,nil2),rec(B,nil2)),
inference(paramod,[status(thm)],[c_96,c_2661]) ).
cnf(c_140,plain,
rec(eps,nil2) = btrue,
inference(paramod,[status(thm)],[c_96,c_79]) ).
cnf(c_141,plain,
aux(A,B,reck2(atom(B),cons2(A,nil2))) = step(atom(B),A),
inference(paramod,[status(thm)],[c_106,c_86]) ).
cnf(c_198,plain,
rec(nil4,A) = rec(eps,cons2(B,A)),
inference(paramod,[status(thm)],[c_94,c_98]) ).
cnf(c_2662,plain,
rec(step(star(A),B),nil2) = andb(rec(step(A,B),nil2),rec(star(A),nil2)),
inference(paramod,[status(thm)],[c_92,c_138]) ).
cnf(c_2663,plain,
rec(star(A),cons2(B,nil2)) = andb(rec(step(A,B),nil2),rec(star(A),nil2)),
inference(paramod,[status(thm)],[c_98,c_2662]) ).
cnf(c_2664,plain,
rec(star(A),cons2(B,nil2)) = andb(rec(A,cons2(B,nil2)),rec(star(A),nil2)),
inference(paramod,[status(thm)],[c_98,c_2663]) ).
cnf(c_225,plain,
rec(star(A),cons2(B,nil2)) = andb(rec(A,cons2(B,nil2)),btrue),
inference(paramod,[status(thm)],[c_137,c_2664]) ).
cnf(c_2665,plain,
rec(step(x(A,B),C),nil2) = orb(rec(step(A,C),nil2),rec(step(B,C),nil2)),
inference(paramod,[status(thm)],[c_88,c_139]) ).
cnf(c_2666,plain,
rec(x(A,B),cons2(C,nil2)) = orb(rec(step(A,C),nil2),rec(step(B,C),nil2)),
inference(paramod,[status(thm)],[c_98,c_2665]) ).
cnf(c_2667,plain,
rec(x(A,B),cons2(C,nil2)) = orb(rec(A,cons2(C,nil2)),rec(step(B,C),nil2)),
inference(paramod,[status(thm)],[c_98,c_2666]) ).
cnf(c_229,plain,
rec(x(A,B),cons2(C,nil2)) = orb(rec(A,cons2(C,nil2)),rec(B,cons2(C,nil2))),
inference(paramod,[status(thm)],[c_98,c_2667]) ).
cnf(c_230,plain,
aux3(x(A,B),C,D,notb(orb(rec(A,nil2),rec(B,nil2)))) = reck2(star(x(A,B)),cons2(C,D)),
inference(paramod,[status(thm)],[c_139,c_113]) ).
cnf(c_2668,plain,
aux(A,A,btrue) = step(atom(A),A),
inference(paramod,[status(thm)],[c_130,c_141]) ).
cnf(c_2669,plain,
eps = step(atom(A),A),
inference(paramod,[status(thm)],[c_1,c_2668]) ).
cnf(c_241,plain,
step(atom(A),A) = eps,
inference(copy,[status(thm)],[c_2669]) ).
cnf(c_2670,plain,
rec(eps,A) = rec(atom(B),cons2(B,A)),
inference(paramod,[status(thm)],[c_241,c_98]) ).
cnf(c_297,plain,
rec(atom(A),cons2(A,B)) = rec(eps,B),
inference(copy,[status(thm)],[c_2670]) ).
cnf(c_2671,plain,
eps2(nil4) = rec(eps,cons2(A,nil2)),
inference(paramod,[status(thm)],[c_198,c_96]) ).
cnf(c_2672,plain,
rec(nil4,nil2) = rec(eps,cons2(A,nil2)),
inference(paramod,[status(thm)],[c_96,c_2671]) ).
cnf(c_2673,plain,
bfalse = rec(eps,cons2(A,nil2)),
inference(paramod,[status(thm)],[c_136,c_2672]) ).
cnf(c_365,plain,
rec(eps,cons2(A,nil2)) = bfalse,
inference(copy,[status(thm)],[c_2673]) ).
cnf(c_2674,plain,
aux3(x(eps,A),B,C,notb(orb(btrue,rec(A,nil2)))) = reck2(star(x(eps,A)),cons2(B,C)),
inference(paramod,[status(thm)],[c_140,c_230]) ).
cnf(c_2675,plain,
aux3(x(eps,A),B,C,notb(btrue)) = reck2(star(x(eps,A)),cons2(B,C)),
inference(paramod,[status(thm)],[c_70,c_2674]) ).
cnf(c_2676,plain,
aux3(x(eps,A),B,C,bfalse) = reck2(star(x(eps,A)),cons2(B,C)),
inference(paramod,[status(thm)],[c_75,c_2675]) ).
cnf(c_2677,plain,
bfalse = reck2(star(x(eps,A)),cons2(B,C)),
inference(paramod,[status(thm)],[c_6,c_2676]) ).
cnf(c_2499,plain,
reck2(star(x(eps,A)),cons2(B,C)) = bfalse,
inference(copy,[status(thm)],[c_2677]) ).
cnf(c_2520,plain,
eq2(eq2(rec(star(x(eps,A)),cons2(B,C)),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_2499,c_133]) ).
cnf(c_2678,plain,
eq2(eq2(andb(rec(x(eps,A),cons2(B,nil2)),btrue),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_225,c_2520]) ).
cnf(c_2679,plain,
eq2(eq2(andb(orb(rec(eps,cons2(B,nil2)),rec(A,cons2(B,nil2))),btrue),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_229,c_2678]) ).
cnf(c_2680,plain,
eq2(eq2(andb(orb(bfalse,rec(A,cons2(B,nil2))),btrue),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_365,c_2679]) ).
cnf(c_2654,plain,
eq2(eq2(andb(rec(A,cons2(B,nil2)),btrue),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_71,c_2680]) ).
cnf(c_2681,plain,
eq2(eq2(andb(rec(eps,nil2),btrue),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_297,c_2654]) ).
cnf(c_2682,plain,
eq2(eq2(andb(btrue,btrue),bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_140,c_2681]) ).
cnf(c_2683,plain,
eq2(eq2(btrue,bfalse),bfalse) != btrue,
inference(paramod,[status(thm)],[c_77,c_2682]) ).
cnf(c_2684,plain,
eq2(bfalse,bfalse) != btrue,
inference(paramod,[status(thm)],[c_128,c_2683]) ).
cnf(c_2685,plain,
btrue != btrue,
inference(paramod,[status(thm)],[c_131,c_2684]) ).
cnf(c_2656,plain,
$false,
inference(copy,[status(thm)],[c_2685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX239-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n014.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 17:01:38 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3674921 was started by sandbox on n014,
% 0.10/5.38 % Sat Sep 26 17:01:38 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.13/6.02
% 0.13/6.02 % SZS status Unsatisfiable for theBenchmark
% 0.13/6.02
% 0.13/6.02 % Proof 1 at 0.51 (+ 0.11) seconds.
% 0.13/6.02 % Length of proof is 50.
% 0.13/6.02 % Level of proof is 7.
% 0.13/6.02 % Maximum clause weight is 49.000.
% 0.13/6.02 % Given clauses 378.
% 0.13/6.02
% 0.13/6.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------