%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL018-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:34:46 PM UTC 2026
% Result : Unsatisfiable 9.30s 1.70s
% Output : CNFRefutation 9.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 17
% Syntax : Number of clauses : 151 ( 151 unt; 0 nHn; 68 RR)
% Number of literals : 151 ( 150 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 114 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
sF0 = composition(sk1,top),
introduced(definition) ).
cnf(t1,axiom,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t18,plain,
composition(sk1,top) = sk1,
inference(orient,[status(thm)],[t1]) ).
cnf(t3898,plain,
sF0 = sk1,
inference(step,[status(thm)],[t13,t18]) ).
cnf(t20,plain,
sk1 = sF0,
inference(orient,[status(thm)],[t3898]) ).
cnf(t14,axiom,
sF1 = complement(sk1),
introduced(definition) ).
cnf(t16,plain,
complement(sk1) = sF1,
inference(orient,[status(thm)],[t14]) ).
cnf(t3899,plain,
complement(sF0) = sF1,
inference(step,[status(thm)],[t16,t20]) ).
cnf(t21,plain,
complement(sF0) = sF1,
inference(rw,[status(thm)],[t3899]) ).
cnf(t23,plain,
complement(sF0) = sF1,
inference(orient,[status(thm)],[t21]) ).
cnf(t15,axiom,
sF2 = composition(complement(sk1),top),
introduced(definition) ).
cnf(t3901,plain,
sF2 = composition(complement(sF0),top),
inference(step,[status(thm)],[t15,t20]) ).
cnf(t3902,plain,
sF2 = composition(sF1,top),
inference(step,[status(thm)],[t3901,t23]) ).
cnf(t28,plain,
composition(sF1,top) = sF2,
inference(orient,[status(thm)],[t3902]) ).
cnf(t2,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t10,axiom,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t104,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t10]) ).
cnf(t6,axiom,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t32,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t6]) ).
cnf(t34,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t32,t19]) ).
cnf(t56,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t34]) ).
cnf(t0,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t17,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t57,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t56,t17]) ).
cnf(t3903,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t57,t19]) ).
cnf(t60,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t3903]) ).
cnf(t61,plain,
one = converse(one),
inference(cp,[status(thm)],[t60,t17]) ).
cnf(t62,plain,
converse(one) = one,
inference(orient,[status(thm)],[t61]) ).
cnf(t3904,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t60,t62]) ).
cnf(t63,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t3904]) ).
cnf(t69,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t63]) ).
cnf(t114,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(cp,[status(thm)],[t104,t69]) ).
cnf(t3671,plain,
composition(join(one,X1),X2) = join(X2,composition(X1,X2)),
inference(orient,[status(thm)],[t114]) ).
cnf(t9,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t44,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t3,axiom,
join(X1,complement(X1)) = top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t25,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t3]) ).
cnf(t45,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(cp,[status(thm)],[t44,t25]) ).
cnf(t325,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(orient,[status(thm)],[t45]) ).
cnf(t11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t4,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t29,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3911,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t11,t29]) ).
cnf(t151,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t3911]) ).
cnf(t162,plain,
complement(X1) = join(complement(X1),composition(one,complement(composition(one,X1)))),
inference(cp,[status(thm)],[t151,t62]) ).
cnf(t3918,plain,
complement(X1) = join(complement(X1),complement(composition(one,X1))),
inference(step,[status(thm)],[t162,t69]) ).
cnf(t3919,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t3918,t69]) ).
cnf(t240,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t3919]) ).
cnf(t341,plain,
top = join(complement(X1),join(complement(X1),complement(complement(X1)))),
inference(cp,[status(thm)],[t325,t240]) ).
cnf(t3938,plain,
top = join(complement(X1),top),
inference(step,[status(thm)],[t341,t25]) ).
cnf(t3939,plain,
top = join(top,complement(X1)),
inference(step,[status(thm)],[t3938,t29]) ).
cnf(t364,plain,
join(top,complement(X1)) = top,
inference(orient,[status(thm)],[t3939]) ).
cnf(t372,plain,
top = join(X1,top),
inference(cp,[status(thm)],[t325,t364]) ).
cnf(t380,plain,
join(X1,top) = top,
inference(orient,[status(thm)],[t372]) ).
cnf(t3678,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(cp,[status(thm)],[t3671,t380]) ).
cnf(t3723,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(orient,[status(thm)],[t3678]) ).
cnf(t7,axiom,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t35,plain,
join(converse(X1),converse(X2)) = converse(join(X1,X2)),
inference(orient,[status(thm)],[t7]) ).
cnf(t36,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(cp,[status(thm)],[t35,t19]) ).
cnf(t90,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(orient,[status(thm)],[t36]) ).
cnf(t391,plain,
join(X1,converse(top)) = converse(top),
inference(cp,[status(thm)],[t90,t380]) ).
cnf(t409,plain,
join(X1,converse(top)) = converse(top),
inference(orient,[status(thm)],[t391]) ).
cnf(t26,plain,
top = join(sF0,sF1),
inference(cp,[status(thm)],[t25,t23]) ).
cnf(t27,plain,
join(sF0,sF1) = top,
inference(orient,[status(thm)],[t26]) ).
cnf(t47,plain,
join(sF0,join(sF1,X1)) = join(top,X1),
inference(cp,[status(thm)],[t44,t27]) ).
cnf(t123,plain,
join(sF0,join(sF1,X1)) = join(top,X1),
inference(orient,[status(thm)],[t47]) ).
cnf(t126,plain,
join(top,X1) = join(sF0,join(X1,sF1)),
inference(cp,[status(thm)],[t123,t29]) ).
cnf(t196,plain,
join(sF0,join(X1,sF1)) = join(top,X1),
inference(orient,[status(thm)],[t126]) ).
cnf(t197,plain,
join(top,X1) = join(join(X1,sF1),sF0),
inference(cp,[status(thm)],[t196,t29]) ).
cnf(t3929,plain,
join(top,X1) = join(X1,join(sF1,sF0)),
inference(step,[status(thm)],[t197,t44]) ).
cnf(t3930,plain,
join(top,X1) = join(X1,join(sF0,sF1)),
inference(step,[status(thm)],[t3929,t29]) ).
cnf(t3931,plain,
join(top,X1) = join(X1,top),
inference(step,[status(thm)],[t3930,t27]) ).
cnf(t283,plain,
join(top,X1) = join(X1,top),
inference(orient,[status(thm)],[t3931]) ).
cnf(t3949,plain,
join(top,X1) = top,
inference(step,[status(thm)],[t283,t380]) ).
cnf(t385,plain,
join(top,X1) = top,
inference(orient,[status(thm)],[t3949]) ).
cnf(t412,plain,
converse(top) = top,
inference(cp,[status(thm)],[t409,t385]) ).
cnf(t418,plain,
converse(top) = top,
inference(orient,[status(thm)],[t412]) ).
cnf(t422,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(cp,[status(thm)],[t32,t418]) ).
cnf(t468,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(orient,[status(thm)],[t422]) ).
cnf(t470,plain,
composition(top,converse(sF1)) = converse(sF2),
inference(cp,[status(thm)],[t468,t28]) ).
cnf(t501,plain,
composition(top,converse(sF1)) = converse(sF2),
inference(orient,[status(thm)],[t470]) ).
cnf(t3729,plain,
composition(top,converse(sF1)) = join(converse(sF1),converse(sF2)),
inference(cp,[status(thm)],[t3723,t501]) ).
cnf(t4178,plain,
converse(sF2) = join(converse(sF1),converse(sF2)),
inference(step,[status(thm)],[t3729,t501]) ).
cnf(t4179,plain,
converse(sF2) = converse(join(sF1,sF2)),
inference(step,[status(thm)],[t4178,t35]) ).
cnf(t22,plain,
composition(sF0,top) = sk1,
inference(rw,[status(thm)],[t18]) ).
cnf(t3900,plain,
composition(sF0,top) = sF0,
inference(step,[status(thm)],[t22,t20]) ).
cnf(t24,plain,
composition(sF0,top) = sF0,
inference(orient,[status(thm)],[t3900]) ).
cnf(t155,plain,
complement(top) = join(complement(top),composition(converse(sF0),complement(sF0))),
inference(cp,[status(thm)],[t151,t24]) ).
cnf(u0,axiom,
zero = meet(A,complement(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
meet(A,B) = complement(join(complement(A),complement(B))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t3905,plain,
complement(top) = zero,
inference(step,[status(thm)],[t5,t25]) ).
cnf(t67,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t3905]) ).
cnf(t3991,plain,
zero = join(complement(top),composition(converse(sF0),complement(sF0))),
inference(step,[status(thm)],[t155,t67]) ).
cnf(t3992,plain,
zero = join(zero,composition(converse(sF0),complement(sF0))),
inference(step,[status(thm)],[t3991,t67]) ).
cnf(t242,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t240,t67]) ).
cnf(t3922,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t242,t67]) ).
cnf(t3923,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t3922,t67]) ).
cnf(t250,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t3923]) ).
cnf(t251,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t44,t250]) ).
cnf(t561,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t251]) ).
cnf(t12,axiom,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t3916,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t12,t29]) ).
cnf(t209,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(orient,[status(thm)],[t3916]) ).
cnf(t244,plain,
X1 = join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))),
inference(cp,[status(thm)],[t209,t240]) ).
cnf(t3934,plain,
X1 = join(complement(complement(X1)),complement(top)),
inference(step,[status(thm)],[t244,t25]) ).
cnf(t3935,plain,
X1 = join(complement(top),complement(complement(X1))),
inference(step,[status(thm)],[t3934,t29]) ).
cnf(t3936,plain,
X1 = join(zero,complement(complement(X1))),
inference(step,[status(thm)],[t3935,t67]) ).
cnf(t315,plain,
join(zero,complement(complement(X1))) = X1,
inference(orient,[status(thm)],[t3936]) ).
cnf(t563,plain,
join(zero,complement(complement(X1))) = join(zero,X1),
inference(cp,[status(thm)],[t561,t315]) ).
cnf(t3960,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t563,t315]) ).
cnf(t568,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t3960]) ).
cnf(t3993,plain,
zero = composition(converse(sF0),complement(sF0)),
inference(step,[status(thm)],[t3992,t568]) ).
cnf(t3994,plain,
zero = composition(converse(sF0),sF1),
inference(step,[status(thm)],[t3993,t23]) ).
cnf(t992,plain,
composition(converse(sF0),sF1) = zero,
inference(orient,[status(thm)],[t3994]) ).
cnf(t994,plain,
composition(converse(sF1),sF0) = converse(zero),
inference(cp,[status(thm)],[t56,t992]) ).
cnf(t37,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(cp,[status(thm)],[t35,t19]) ).
cnf(t98,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(orient,[status(thm)],[t37]) ).
cnf(t578,plain,
join(converse(zero),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t98,t568]) ).
cnf(t3973,plain,
join(converse(zero),X1) = X1,
inference(step,[status(thm)],[t578,t19]) ).
cnf(t676,plain,
join(converse(zero),X1) = X1,
inference(orient,[status(thm)],[t3973]) ).
cnf(t575,plain,
X1 = join(X1,zero),
inference(cp,[status(thm)],[t568,t29]) ).
cnf(t632,plain,
join(X1,zero) = X1,
inference(orient,[status(thm)],[t575]) ).
cnf(t679,plain,
zero = converse(zero),
inference(cp,[status(thm)],[t676,t632]) ).
cnf(t684,plain,
converse(zero) = zero,
inference(orient,[status(thm)],[t679]) ).
cnf(t3995,plain,
composition(converse(sF1),sF0) = zero,
inference(step,[status(thm)],[t994,t684]) ).
cnf(t1001,plain,
composition(converse(sF1),sF0) = zero,
inference(orient,[status(thm)],[t3995]) ).
cnf(t1005,plain,
complement(sF0) = join(complement(sF0),composition(converse(converse(sF1)),complement(zero))),
inference(cp,[status(thm)],[t151,t1001]) ).
cnf(t3996,plain,
sF1 = join(complement(sF0),composition(converse(converse(sF1)),complement(zero))),
inference(step,[status(thm)],[t1005,t23]) ).
cnf(t3997,plain,
sF1 = join(sF1,composition(converse(converse(sF1)),complement(zero))),
inference(step,[status(thm)],[t3996,t23]) ).
cnf(t3998,plain,
sF1 = join(sF1,composition(sF1,complement(zero))),
inference(step,[status(thm)],[t3997,t19]) ).
cnf(t574,plain,
complement(zero) = top,
inference(cp,[status(thm)],[t568,t25]) ).
cnf(t592,plain,
complement(zero) = top,
inference(orient,[status(thm)],[t574]) ).
cnf(t3999,plain,
sF1 = join(sF1,composition(sF1,top)),
inference(step,[status(thm)],[t3998,t592]) ).
cnf(t4000,plain,
sF1 = join(sF1,sF2),
inference(step,[status(thm)],[t3999,t28]) ).
cnf(t1007,plain,
join(sF1,sF2) = sF1,
inference(orient,[status(thm)],[t4000]) ).
cnf(t4180,plain,
converse(sF2) = converse(sF1),
inference(step,[status(thm)],[t4179,t1007]) ).
cnf(t3766,plain,
converse(sF2) = converse(sF1),
inference(orient,[status(thm)],[t4180]) ).
cnf(t3796,plain,
sF2 = converse(converse(sF1)),
inference(cp,[status(thm)],[t19,t3766]) ).
cnf(t4194,plain,
sF2 = sF1,
inference(step,[status(thm)],[t3796,t19]) ).
cnf(t3825,plain,
sF2 = sF1,
inference(orient,[status(thm)],[t4194]) ).
cnf(t4195,plain,
composition(sF1,top) = sF1,
inference(step,[status(thm)],[t28,t3825]) ).
cnf(t3826,plain,
composition(sF1,top) = sF1,
inference(orient,[status(thm)],[t4195]) ).
cnf(goal_0,negated_conjecture,
composition(complement(sk1),top) != complement(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
composition(complement(sF0),top) != complement(sk1),
inference(rw,[status(thm)],[goal_0,t20]) ).
cnf(g0_1,plain,
composition(sF1,top) != complement(sk1),
inference(rw,[status(thm)],[g0_0,t23]) ).
cnf(g0_2,plain,
sF1 != complement(sk1),
inference(rw,[status(thm)],[g0_1,t3826]) ).
cnf(g0_3,plain,
sF1 != complement(sF0),
inference(rw,[status(thm)],[g0_2,t20]) ).
cnf(g0_4,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_3,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL018-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 07:15:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.30/1.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.30/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------