%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL015-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 : Tue Sep 29 12:33:06 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of clauses : 144 ( 144 unt; 0 nHn; 29 RR)
% Number of literals : 144 ( 143 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 148 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
composition(top,top) != top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
cnf(c2,axiom,
composition(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c3,plain,
composition(composition(top,top),one) = composition(top,top),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
composition(top,top) = composition(composition(top,top),one),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
composition(A2,composition(B,C)) = composition(composition(A2,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
cnf(c6,plain,
composition(top,composition(top,X)) = composition(composition(top,top),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
composition(composition(top,top),X) = composition(top,composition(top,X)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
join(A2,B2) = join(B2,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c9,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c12,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c14,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
join(A2,join(B2,C2)) = join(join(A2,B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c17,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,axiom,
top = join(A2,complement(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
cnf(c19,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c8]) ).
cnf(c23,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c17,c23]) ).
cnf(c25,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c15,c24]) ).
cnf(c26,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c29,plain,
converse(composition(converse(X2),X)) = composition(converse(X),converse(converse(X2))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c31,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
composition(converse(X),converse(converse(X2))) = composition(converse(X),X2),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
converse(composition(converse(X2),X)) = composition(converse(X),X2),
inference(transitivity,[status(thm)],[c29,c32]) ).
cnf(c34,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c37,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c39,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c35,c39]) ).
cnf(c41,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c40]) ).
cnf(c45,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
composition(X2,composition(one,X)) = composition(composition(X2,one),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c47,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c48,plain,
composition(composition(X2,one),X) = composition(X2,X),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
composition(X2,composition(one,X)) = composition(X2,X),
inference(transitivity,[status(thm)],[c46,c48]) ).
cnf(c50,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c50,c40]) ).
cnf(c52,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c45,c51]) ).
cnf(c53,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = join(complement(X2),composition(converse(X),complement(composition(X,X2)))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c58,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = join(composition(converse(X),complement(composition(X,X2))),complement(X2)),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c60,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c56,c62]) ).
cnf(c64,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c43,c63]) ).
cnf(c65,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c67,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c65,c67]) ).
cnf(c69,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c27,c68]) ).
cnf(c70,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c12,c69]) ).
cnf(c71,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c25]) ).
cnf(c74,plain,
join(complement(zero),top) = join(top,complement(zero)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c75,plain,
join(top,complement(zero)) = join(complement(zero),top),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c77,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
join(top,join(zero,X)) = join(top,join(X,zero)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c8]) ).
cnf(c80,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
join(top,join(X,zero)) = join(top,join(zero,X)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
join(top,join(zero,X)) = join(join(top,zero),X),
inference(substitution,[status(thm)],[c16]) ).
cnf(c83,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c84,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,axiom,
meet(A2,B2) = complement(join(complement(A2),complement(B2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c86,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c89,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c87,c90]) ).
cnf(c92,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c84,c91]) ).
cnf(c93,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
join(top,zero) = join(top,complement(top)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
top = join(top,complement(top)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c96,plain,
join(top,complement(top)) = top,
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
join(top,zero) = top,
inference(transitivity,[status(thm)],[c94,c96]) ).
cnf(c98,plain,
join(join(top,zero),X) = join(top,X),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c8]) ).
cnf(c100,plain,
join(join(top,zero),X) = join(X,top),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
join(top,join(zero,X)) = join(X,top),
inference(transitivity,[status(thm)],[c82,c100]) ).
cnf(c102,plain,
join(top,join(X,zero)) = join(X,top),
inference(transitivity,[status(thm)],[c81,c101]) ).
cnf(c103,plain,
join(top,join(zero,X)) = join(X,top),
inference(transitivity,[status(thm)],[c78,c102]) ).
cnf(c104,plain,
join(top,join(zero,complement(zero))) = join(complement(zero),top),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
join(complement(zero),top) = join(top,join(zero,complement(zero))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c107,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
join(top,join(zero,complement(zero))) = join(top,top),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
join(complement(zero),top) = join(top,top),
inference(transitivity,[status(thm)],[c105,c108]) ).
cnf(c110,plain,
join(top,complement(zero)) = join(top,top),
inference(transitivity,[status(thm)],[c75,c109]) ).
cnf(c111,plain,
join(top,top) = join(top,complement(zero)),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
join(top,complement(zero)) = top,
inference(substitution,[status(thm)],[c70]) ).
cnf(c113,plain,
join(top,top) = top,
inference(transitivity,[status(thm)],[c111,c112]) ).
cnf(c114,plain,
join(X,join(top,complement(X))) = top,
inference(transitivity,[status(thm)],[c73,c113]) ).
cnf(c115,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c72,c114]) ).
cnf(c116,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c10,c115]) ).
cnf(c117,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
composition(top,composition(top,X)) = composition(join(top,one),composition(top,X)),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c8]) ).
cnf(c121,plain,
join(X,one) = join(one,X),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
composition(join(X2,one),X) = composition(join(one,X2),X),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c124,plain,
composition(join(one,X2),X) = join(composition(one,X),composition(X2,X)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c125,plain,
join(composition(one,X),composition(X2,X)) = join(X,composition(X2,X)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c126,plain,
composition(join(one,X2),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
composition(join(X2,one),X) = join(X,composition(X2,X)),
inference(transitivity,[status(thm)],[c122,c126]) ).
cnf(c128,plain,
composition(join(top,one),composition(top,X)) = join(composition(top,X),composition(top,composition(top,X))),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
composition(top,composition(top,X)) = composition(composition(top,top),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c130,plain,
join(composition(top,X),composition(top,composition(top,X))) = join(composition(top,X),composition(composition(top,top),X)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
composition(join(top,composition(top,top)),X) = join(composition(top,X),composition(composition(top,top),X)),
inference(substitution,[status(thm)],[c123]) ).
cnf(c132,plain,
join(composition(top,X),composition(composition(top,top),X)) = composition(join(top,composition(top,top)),X),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
join(top,composition(top,top)) = top,
inference(substitution,[status(thm)],[c116]) ).
cnf(c134,plain,
composition(join(top,composition(top,top)),X) = composition(top,X),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
join(composition(top,X),composition(composition(top,top),X)) = composition(top,X),
inference(transitivity,[status(thm)],[c132,c134]) ).
cnf(c136,plain,
join(composition(top,X),composition(top,composition(top,X))) = composition(top,X),
inference(transitivity,[status(thm)],[c130,c135]) ).
cnf(c137,plain,
composition(join(top,one),composition(top,X)) = composition(top,X),
inference(transitivity,[status(thm)],[c128,c136]) ).
cnf(c138,plain,
composition(top,composition(top,X)) = composition(top,X),
inference(transitivity,[status(thm)],[c119,c137]) ).
cnf(c139,plain,
composition(composition(top,top),X) = composition(top,X),
inference(transitivity,[status(thm)],[c7,c138]) ).
cnf(c140,plain,
composition(composition(top,top),one) = composition(top,one),
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
composition(top,one) = top,
inference(substitution,[status(thm)],[c2]) ).
cnf(c142,plain,
composition(composition(top,top),one) = top,
inference(transitivity,[status(thm)],[c140,c141]) ).
cnf(c143,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c4,c142]) ).
cnf(c144,plain,
$false,
inference(resolution,[status(thm)],[c1,c143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL015-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:48:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation
% See solution above
% 0.20/0.51
% 0.20/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------