%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : REL023-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:34:50 PM UTC 2026
% Result : Unsatisfiable 9.96s 1.86s
% Output : CNFRefutation 9.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 17
% Syntax : Number of clauses : 101 ( 101 unt; 0 nHn; 44 RR)
% Number of literals : 101 ( 100 equ; 9 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t9,axiom,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t187,plain,
join(composition(X1,X2),composition(X3,X2)) = composition(join(X1,X3),X2),
inference(orient,[status(thm)],[t9]) ).
cnf(t15,axiom,
sF0 = complement(sk1),
introduced(definition) ).
cnf(t27,plain,
complement(sk1) = sF0,
inference(orient,[status(thm)],[t15]) ).
cnf(t16,axiom,
sF1 = converse(sk2),
introduced(definition) ).
cnf(t28,plain,
converse(sk2) = sF1,
inference(orient,[status(thm)],[t16]) ).
cnf(t17,axiom,
sF2 = complement(converse(sk2)),
introduced(definition) ).
cnf(t13984,plain,
sF2 = complement(sF1),
inference(step,[status(thm)],[t17,t28]) ).
cnf(t35,plain,
complement(sF1) = sF2,
inference(orient,[status(thm)],[t13984]) ).
cnf(t18,axiom,
sF3 = join(complement(sk1),complement(converse(sk2))),
introduced(definition) ).
cnf(t14036,plain,
sF3 = join(sF0,complement(converse(sk2))),
inference(step,[status(thm)],[t18,t27]) ).
cnf(t14037,plain,
sF3 = join(sF0,complement(sF1)),
inference(step,[status(thm)],[t14036,t28]) ).
cnf(t14038,plain,
sF3 = join(sF0,sF2),
inference(step,[status(thm)],[t14037,t35]) ).
cnf(t562,plain,
join(sF0,sF2) = sF3,
inference(orient,[status(thm)],[t14038]) ).
cnf(t19,axiom,
sF4 = complement(join(complement(sk1),complement(converse(sk2)))),
introduced(definition) ).
cnf(t14054,plain,
sF4 = complement(join(sF0,complement(converse(sk2)))),
inference(step,[status(thm)],[t19,t27]) ).
cnf(t14055,plain,
sF4 = complement(join(sF0,complement(sF1))),
inference(step,[status(thm)],[t14054,t28]) ).
cnf(t14056,plain,
sF4 = complement(join(sF0,sF2)),
inference(step,[status(thm)],[t14055,t35]) ).
cnf(t14057,plain,
sF4 = complement(sF3),
inference(step,[status(thm)],[t14056,t562]) ).
cnf(t593,plain,
complement(sF3) = sF4,
inference(orient,[status(thm)],[t14057]) ).
cnf(t8,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t139,plain,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t10,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t3,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t42,plain,
join(X1,X2) = join(X2,X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t14005,plain,
join(complement(X2),composition(converse(X1),complement(composition(X1,X2)))) = complement(X2),
inference(step,[status(thm)],[t10,t42]) ).
cnf(t229,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(orient,[status(thm)],[t14005]) ).
cnf(t5,axiom,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t53,plain,
composition(converse(X1),converse(X2)) = converse(composition(X2,X1)),
inference(orient,[status(thm)],[t5]) ).
cnf(t1,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t32,plain,
converse(converse(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t57,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(cp,[status(thm)],[t53,t32]) ).
cnf(t170,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(orient,[status(thm)],[t57]) ).
cnf(t0,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t31,plain,
composition(X1,one) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t171,plain,
composition(converse(one),X1) = converse(converse(X1)),
inference(cp,[status(thm)],[t170,t31]) ).
cnf(t14000,plain,
composition(converse(one),X1) = X1,
inference(step,[status(thm)],[t171,t32]) ).
cnf(t178,plain,
composition(converse(one),X1) = X1,
inference(orient,[status(thm)],[t14000]) ).
cnf(t181,plain,
one = converse(one),
inference(cp,[status(thm)],[t178,t31]) ).
cnf(t182,plain,
converse(one) = one,
inference(orient,[status(thm)],[t181]) ).
cnf(t252,plain,
complement(X1) = join(complement(X1),composition(one,complement(composition(one,X1)))),
inference(cp,[status(thm)],[t229,t182]) ).
cnf(t14003,plain,
composition(one,X1) = X1,
inference(step,[status(thm)],[t178,t182]) ).
cnf(t183,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[t14003]) ).
cnf(t194,plain,
composition(one,X1) = X1,
inference(orient,[status(thm)],[t183]) ).
cnf(t14019,plain,
complement(X1) = join(complement(X1),complement(composition(one,X1))),
inference(step,[status(thm)],[t252,t194]) ).
cnf(t14020,plain,
complement(X1) = join(complement(X1),complement(X1)),
inference(step,[status(thm)],[t14019,t194]) ).
cnf(t454,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(orient,[status(thm)],[t14020]) ).
cnf(t11,axiom,
join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t14008,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(step,[status(thm)],[t11,t42]) ).
cnf(t284,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(orient,[status(thm)],[t14008]) ).
cnf(t461,plain,
X1 = join(complement(complement(X1)),complement(join(complement(X1),complement(complement(X1))))),
inference(cp,[status(thm)],[t284,t454]) ).
cnf(t2,axiom,
join(X1,complement(X1)) = top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t36,plain,
join(X1,complement(X1)) = top,
inference(orient,[status(thm)],[t2]) ).
cnf(t14121,plain,
X1 = join(complement(complement(X1)),complement(top)),
inference(step,[status(thm)],[t461,t36]) ).
cnf(t14122,plain,
X1 = join(complement(top),complement(complement(X1))),
inference(step,[status(thm)],[t14121,t42]) ).
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(t4,plain,
complement(join(complement(X1),complement(complement(X1)))) = zero,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t13988,plain,
complement(top) = zero,
inference(step,[status(thm)],[t4,t36]) ).
cnf(t60,plain,
complement(top) = zero,
inference(orient,[status(thm)],[t13988]) ).
cnf(t14123,plain,
X1 = join(zero,complement(complement(X1))),
inference(step,[status(thm)],[t14122,t60]) ).
cnf(t773,plain,
join(zero,complement(complement(X1))) = X1,
inference(orient,[status(thm)],[t14123]) ).
cnf(t459,plain,
complement(top) = join(zero,complement(top)),
inference(cp,[status(thm)],[t454,t60]) ).
cnf(t14029,plain,
zero = join(zero,complement(top)),
inference(step,[status(thm)],[t459,t60]) ).
cnf(t14030,plain,
zero = join(zero,zero),
inference(step,[status(thm)],[t14029,t60]) ).
cnf(t542,plain,
join(zero,zero) = zero,
inference(orient,[status(thm)],[t14030]) ).
cnf(t543,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(cp,[status(thm)],[t139,t542]) ).
cnf(t858,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(orient,[status(thm)],[t543]) ).
cnf(t861,plain,
join(zero,complement(complement(X1))) = join(zero,X1),
inference(cp,[status(thm)],[t858,t773]) ).
cnf(t14126,plain,
X1 = join(zero,X1),
inference(step,[status(thm)],[t861,t773]) ).
cnf(t862,plain,
join(zero,X1) = X1,
inference(orient,[status(thm)],[t14126]) ).
cnf(t14131,plain,
complement(complement(X1)) = X1,
inference(step,[status(thm)],[t773,t862]) ).
cnf(t867,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[t14131]) ).
cnf(t1005,plain,
complement(complement(X1)) = X1,
inference(orient,[status(thm)],[t867]) ).
cnf(t1013,plain,
complement(complement(X1)) = join(X1,complement(complement(X1))),
inference(cp,[status(thm)],[t454,t1005]) ).
cnf(t14160,plain,
X1 = join(X1,complement(complement(X1))),
inference(step,[status(thm)],[t1013,t1005]) ).
cnf(t14161,plain,
X1 = join(X1,X1),
inference(step,[status(thm)],[t14160,t1005]) ).
cnf(t1095,plain,
join(X1,X1) = X1,
inference(orient,[status(thm)],[t14161]) ).
cnf(t1111,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(cp,[status(thm)],[t139,t1095]) ).
cnf(t2271,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(orient,[status(thm)],[t1111]) ).
cnf(t285,plain,
sk1 = join(complement(join(sF0,X1)),complement(join(complement(sk1),complement(X1)))),
inference(cp,[status(thm)],[t284,t27]) ).
cnf(t14616,plain,
sk1 = join(complement(join(sF0,X1)),complement(join(sF0,complement(X1)))),
inference(step,[status(thm)],[t285,t27]) ).
cnf(t12707,plain,
join(complement(join(sF0,X1)),complement(join(sF0,complement(X1)))) = sk1,
inference(orient,[status(thm)],[t14616]) ).
cnf(t12710,plain,
sk1 = join(complement(join(sF0,sF1)),complement(join(sF0,sF2))),
inference(cp,[status(thm)],[t12707,t35]) ).
cnf(t14663,plain,
sk1 = join(complement(join(sF0,sF1)),complement(sF3)),
inference(step,[status(thm)],[t12710,t562]) ).
cnf(t14664,plain,
sk1 = join(complement(sF3),complement(join(sF0,sF1))),
inference(step,[status(thm)],[t14663,t42]) ).
cnf(t14665,plain,
sk1 = join(sF4,complement(join(sF0,sF1))),
inference(step,[status(thm)],[t14664,t593]) ).
cnf(t13953,plain,
join(sF4,complement(join(sF0,sF1))) = sk1,
inference(orient,[status(thm)],[t14665]) ).
cnf(t13960,plain,
join(sF4,complement(join(sF0,sF1))) = join(sF4,sk1),
inference(cp,[status(thm)],[t2271,t13953]) ).
cnf(t14666,plain,
sk1 = join(sF4,sk1),
inference(step,[status(thm)],[t13960,t13953]) ).
cnf(t13971,plain,
join(sF4,sk1) = sk1,
inference(orient,[status(thm)],[t14666]) ).
cnf(u4,negated_conjecture,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(sk1,meet(sk2,sk3))) != composition(sk1,meet(sk2,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(goal_0,negated_conjecture,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(sk1,complement(join(complement(sk2),complement(sk3))))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(definition_unfolding,[status(thm)],[u4,d0]) ).
cnf(g0_0,plain,
composition(join(complement(join(complement(sk1),complement(converse(sk2)))),sk1),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(rw,[status(thm)],[goal_0,t187]) ).
cnf(g0_1,plain,
composition(join(complement(join(sF0,complement(converse(sk2)))),sk1),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(rw,[status(thm)],[g0_0,t27]) ).
cnf(g0_2,plain,
composition(join(complement(join(sF0,complement(sF1))),sk1),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(rw,[status(thm)],[g0_1,t28]) ).
cnf(g0_3,plain,
composition(join(complement(join(sF0,sF2)),sk1),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(rw,[status(thm)],[g0_2,t35]) ).
cnf(g0_4,plain,
composition(join(complement(sF3),sk1),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(rw,[status(thm)],[g0_3,t562]) ).
cnf(g0_5,plain,
composition(join(sF4,sk1),complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(rw,[status(thm)],[g0_4,t593]) ).
cnf(g0_6,plain,
composition(sk1,complement(join(complement(sk2),complement(sk3)))) != composition(sk1,complement(join(complement(sk2),complement(sk3)))),
inference(rw,[status(thm)],[g0_5,t13971]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 07:18:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.96/1.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.96/1.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------