%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:26:33 PM UTC 2026
% Result : Unsatisfiable 18.73s 2.81s
% Output : CNFRefutation 18.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of clauses : 97 ( 97 unt; 0 nHn; 18 RR)
% Number of literals : 97 ( 96 equ; 1 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
times(sum(s(a)),sum(s(a))) != cubes(s(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
sum(s(N)) = '+'(s(N),sum(N)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_s) ).
cnf(c3,plain,
sum(s(a)) = '+'(s(a),sum(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
times(sum(s(a)),sum(s(a))) = times(sum(s(a)),'+'(s(a),sum(a))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
times(X,'+'(Y,Z)) = '+'(times(X,Y),times(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr) ).
cnf(c6,plain,
times(sum(s(a)),'+'(s(a),sum(a))) = '+'(times(sum(s(a)),s(a)),times(sum(s(a)),sum(a))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,axiom,
'+'(X2,Y2) = '+'(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_comm) ).
cnf(c8,plain,
'+'(times(X4,X2),X3) = '+'(X3,times(X4,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
'+'(X3,times(X4,X2)) = '+'(times(X4,X2),X3),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
'+'(times(X4,X5),'+'(X3,times(X4,X2))) = '+'(times(X4,X5),'+'(times(X4,X2),X3)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
'+'(X2,'+'(Y2,Z2)) = '+'('+'(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_assoc) ).
cnf(c12,plain,
'+'(times(X5,X4),'+'(times(X5,X2),X3)) = '+'('+'(times(X5,X4),times(X5,X2)),X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
times(X4,'+'(X3,X2)) = '+'(times(X4,X3),times(X4,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c14,plain,
'+'(times(X4,X3),times(X4,X2)) = times(X4,'+'(X3,X2)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
'+'('+'(times(X5,X4),times(X5,X2)),X3) = '+'(times(X5,'+'(X4,X2)),X3),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
'+'(times(X5,'+'(X4,X2)),X3) = '+'(X3,times(X5,'+'(X4,X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c17,plain,
'+'('+'(times(X5,X4),times(X5,X2)),X3) = '+'(X3,times(X5,'+'(X4,X2))),
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
'+'(times(X5,X4),'+'(times(X5,X2),X3)) = '+'(X3,times(X5,'+'(X4,X2))),
inference(transitivity,[status(thm)],[c12,c17]) ).
cnf(c19,plain,
'+'(times(X5,X4),'+'(X3,times(X5,X2))) = '+'(X3,times(X5,'+'(X4,X2))),
inference(transitivity,[status(thm)],[c10,c18]) ).
cnf(c20,plain,
'+'(times(s(X3),X4),'+'(times(X2,sum(X3)),times(s(X3),X2))) = '+'(times(X2,sum(X3)),times(s(X3),'+'(X4,X2))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
'+'(times(X2,sum(X3)),times(s(X3),'+'(X4,X2))) = '+'(times(s(X3),X4),'+'(times(X2,sum(X3)),times(s(X3),X2))),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
times(X2,Y2) = times(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_comm) ).
cnf(c23,plain,
times(X3,X2) = times(X2,X3),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
times(X2,X3) = times(X3,X2),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
'+'(times(X4,X2),times(X3,X4)) = '+'(times(X4,X2),times(X4,X3)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
times(X4,'+'(X2,X3)) = '+'(times(X4,X2),times(X4,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c27,plain,
'+'(times(X4,X2),times(X4,X3)) = times(X4,'+'(X2,X3)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
'+'(X2,X3) = '+'(X3,X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c29,plain,
times(X4,'+'(X2,X3)) = times(X4,'+'(X3,X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
'+'(times(X4,X2),times(X4,X3)) = times(X4,'+'(X3,X2)),
inference(transitivity,[status(thm)],[c27,c29]) ).
cnf(c31,plain,
'+'(times(X4,X2),times(X3,X4)) = times(X4,'+'(X3,X2)),
inference(transitivity,[status(thm)],[c25,c30]) ).
cnf(c32,plain,
'+'(times(X3,sum(X2)),times(s(X2),X3)) = times(X3,'+'(s(X2),sum(X2))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
sum(s(X2)) = '+'(s(X2),sum(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c34,plain,
'+'(s(X2),sum(X2)) = sum(s(X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
times(X3,'+'(s(X2),sum(X2))) = times(X3,sum(s(X2))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
times(X3,sum(s(X2))) = times(sum(s(X2)),X3),
inference(substitution,[status(thm)],[c22]) ).
cnf(c37,plain,
times(X3,'+'(s(X2),sum(X2))) = times(sum(s(X2)),X3),
inference(transitivity,[status(thm)],[c35,c36]) ).
cnf(c38,plain,
'+'(times(X3,sum(X2)),times(s(X2),X3)) = times(sum(s(X2)),X3),
inference(transitivity,[status(thm)],[c32,c37]) ).
cnf(c39,plain,
'+'(times(X2,sum(X3)),times(s(X3),X2)) = times(sum(s(X3)),X2),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
'+'(times(s(X3),X4),'+'(times(X2,sum(X3)),times(s(X3),X2))) = '+'(times(s(X3),X4),times(sum(s(X3)),X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
times(s(X2),X3) = times(X3,s(X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c42,plain,
'+'(times(s(X3),X4),times(sum(s(X3)),X2)) = '+'(times(X4,s(X3)),times(sum(s(X3)),X2)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
'+'(times(s(X3),X4),'+'(times(X2,sum(X3)),times(s(X3),X2))) = '+'(times(X4,s(X3)),times(sum(s(X3)),X2)),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
'+'(times(X2,sum(X3)),times(s(X3),'+'(X4,X2))) = '+'(times(X4,s(X3)),times(sum(s(X3)),X2)),
inference(transitivity,[status(thm)],[c21,c43]) ).
cnf(c45,plain,
'+'(times(sum(a),sum(a)),times(s(a),'+'(sum(s(a)),sum(a)))) = '+'(times(sum(s(a)),s(a)),times(sum(s(a)),sum(a))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
'+'(times(sum(s(a)),s(a)),times(sum(s(a)),sum(a))) = '+'(times(sum(a),sum(a)),times(s(a),'+'(sum(s(a)),sum(a)))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
'+'(sum(X2),sum(s(X2))) = '+'(sum(s(X2)),sum(X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c48,plain,
'+'(sum(s(X2)),sum(X2)) = '+'(sum(X2),sum(s(X2))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
'+'(sum(X3),X2) = '+'(X2,sum(X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c50,plain,
'+'(X2,sum(X3)) = '+'(sum(X3),X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
'+'(s(X3),'+'(X2,sum(X3))) = '+'(s(X3),'+'(sum(X3),X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
'+'(s(X3),'+'(sum(X3),X2)) = '+'('+'(s(X3),sum(X3)),X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c53,plain,
sum(s(X2)) = '+'(s(X2),sum(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c54,plain,
'+'(s(X2),sum(X2)) = sum(s(X2)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
'+'('+'(s(X3),sum(X3)),X2) = '+'(sum(s(X3)),X2),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
'+'(sum(s(X3)),X2) = '+'(X2,sum(s(X3))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c57,plain,
'+'('+'(s(X3),sum(X3)),X2) = '+'(X2,sum(s(X3))),
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
'+'(s(X3),'+'(sum(X3),X2)) = '+'(X2,sum(s(X3))),
inference(transitivity,[status(thm)],[c52,c57]) ).
cnf(c59,plain,
'+'(s(X3),'+'(X2,sum(X3))) = '+'(X2,sum(s(X3))),
inference(transitivity,[status(thm)],[c51,c58]) ).
cnf(c60,plain,
'+'(s(X2),'+'(sum(X2),sum(X2))) = '+'(sum(X2),sum(s(X2))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
'+'(sum(X2),sum(s(X2))) = '+'(s(X2),'+'(sum(X2),sum(X2))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,axiom,
'+'(sum(N2),sum(N2)) = times(N2,s(N2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_sum) ).
cnf(c63,plain,
'+'(sum(X2),sum(X2)) = times(X2,s(X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
times(X2,s(X2)) = times(s(X2),X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c65,plain,
'+'(sum(X2),sum(X2)) = times(s(X2),X2),
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
'+'(s(X2),'+'(sum(X2),sum(X2))) = '+'(s(X2),times(s(X2),X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
times(X2,X3) = times(X3,X2),
inference(substitution,[status(thm)],[c22]) ).
cnf(c68,plain,
times(X3,X2) = times(X2,X3),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
'+'(X3,times(X3,X2)) = '+'(X3,times(X2,X3)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,axiom,
times(s(X2),Y2) = '+'(Y2,times(X2,Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_s) ).
cnf(c71,plain,
times(s(X2),X3) = '+'(X3,times(X2,X3)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
'+'(X3,times(X2,X3)) = times(s(X2),X3),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
times(s(X2),X3) = times(X3,s(X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c74,plain,
'+'(X3,times(X2,X3)) = times(X3,s(X2)),
inference(transitivity,[status(thm)],[c72,c73]) ).
cnf(c75,plain,
'+'(X3,times(X3,X2)) = times(X3,s(X2)),
inference(transitivity,[status(thm)],[c69,c74]) ).
cnf(c76,plain,
'+'(s(X2),times(s(X2),X2)) = times(s(X2),s(X2)),
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
'+'(s(X2),'+'(sum(X2),sum(X2))) = times(s(X2),s(X2)),
inference(transitivity,[status(thm)],[c66,c76]) ).
cnf(c78,plain,
'+'(sum(X2),sum(s(X2))) = times(s(X2),s(X2)),
inference(transitivity,[status(thm)],[c61,c77]) ).
cnf(c79,plain,
'+'(sum(s(X2)),sum(X2)) = times(s(X2),s(X2)),
inference(transitivity,[status(thm)],[c48,c78]) ).
cnf(c80,plain,
'+'(sum(s(a)),sum(a)) = times(s(a),s(a)),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
times(s(a),'+'(sum(s(a)),sum(a))) = times(s(a),times(s(a),s(a))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
'+'(times(sum(a),sum(a)),times(s(a),'+'(sum(s(a)),sum(a)))) = '+'(times(sum(a),sum(a)),times(s(a),times(s(a),s(a)))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,axiom,
times(sum(a),sum(a)) = cubes(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c84,plain,
'+'(times(sum(a),sum(a)),times(s(a),times(s(a),s(a)))) = '+'(cubes(a),times(s(a),times(s(a),s(a)))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
'+'(times(s(X2),times(s(X2),s(X2))),cubes(X2)) = '+'(cubes(X2),times(s(X2),times(s(X2),s(X2)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c86,plain,
'+'(cubes(X2),times(s(X2),times(s(X2),s(X2)))) = '+'(times(s(X2),times(s(X2),s(X2))),cubes(X2)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,axiom,
cubes(s(N2)) = '+'(times(s(N2),times(s(N2),s(N2))),cubes(N2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cubes_s) ).
cnf(c88,plain,
cubes(s(X2)) = '+'(times(s(X2),times(s(X2),s(X2))),cubes(X2)),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
'+'(times(s(X2),times(s(X2),s(X2))),cubes(X2)) = cubes(s(X2)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
'+'(cubes(X2),times(s(X2),times(s(X2),s(X2)))) = cubes(s(X2)),
inference(transitivity,[status(thm)],[c86,c89]) ).
cnf(c91,plain,
'+'(cubes(a),times(s(a),times(s(a),s(a)))) = cubes(s(a)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
'+'(times(sum(a),sum(a)),times(s(a),times(s(a),s(a)))) = cubes(s(a)),
inference(transitivity,[status(thm)],[c84,c91]) ).
cnf(c93,plain,
'+'(times(sum(a),sum(a)),times(s(a),'+'(sum(s(a)),sum(a)))) = cubes(s(a)),
inference(transitivity,[status(thm)],[c82,c92]) ).
cnf(c94,plain,
'+'(times(sum(s(a)),s(a)),times(sum(s(a)),sum(a))) = cubes(s(a)),
inference(transitivity,[status(thm)],[c46,c93]) ).
cnf(c95,plain,
times(sum(s(a)),'+'(s(a),sum(a))) = cubes(s(a)),
inference(transitivity,[status(thm)],[c6,c94]) ).
cnf(c96,plain,
times(sum(s(a)),sum(s(a))) = cubes(s(a)),
inference(transitivity,[status(thm)],[c4,c95]) ).
cnf(c97,plain,
$false,
inference(resolution,[status(thm)],[c1,c96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:11:47 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.73/2.81 Command-line arguments: --flatten --complete-subsets
% 18.73/2.81
% 18.73/2.81 % SZS status Unsatisfiable
% 18.73/2.81
% 18.73/2.81 % SZS output start CNFRefutation
% See solution above
% 18.73/2.86
% 18.73/2.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------