%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.22s 0.61s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 18 RR)
% Number of literals : 55 ( 54 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 : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
'+'(X,Y) = '+'(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_comm) ).
cnf(c3,plain,
'+'(sum(X3),X2) = '+'(X2,sum(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
'+'(X2,sum(X3)) = '+'(sum(X3),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
'+'(s(X3),'+'(X2,sum(X3))) = '+'(s(X3),'+'(sum(X3),X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
'+'(X2,'+'(Y2,Z)) = '+'('+'(X2,Y2),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_assoc) ).
cnf(c7,plain,
'+'(s(X3),'+'(sum(X3),X2)) = '+'('+'(s(X3),sum(X3)),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,axiom,
sum(s(N)) = '+'(s(N),sum(N)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_s) ).
cnf(c9,plain,
sum(s(X2)) = '+'(s(X2),sum(X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
'+'(s(X2),sum(X2)) = sum(s(X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
'+'('+'(s(X3),sum(X3)),X2) = '+'(sum(s(X3)),X2),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
'+'(sum(s(X3)),X2) = '+'(X2,sum(s(X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
'+'('+'(s(X3),sum(X3)),X2) = '+'(X2,sum(s(X3))),
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
'+'(s(X3),'+'(sum(X3),X2)) = '+'(X2,sum(s(X3))),
inference(transitivity,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
'+'(s(X3),'+'(X2,sum(X3))) = '+'(X2,sum(s(X3))),
inference(transitivity,[status(thm)],[c5,c14]) ).
cnf(c16,plain,
'+'(s(a),'+'(sum(s(a)),sum(a))) = '+'(sum(s(a)),sum(s(a))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
'+'(sum(s(a)),sum(s(a))) = '+'(s(a),'+'(sum(s(a)),sum(a))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
'+'(sum(a),sum(s(a))) = '+'(sum(s(a)),sum(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
'+'(sum(s(a)),sum(a)) = '+'(sum(a),sum(s(a))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
sum(s(a)) = '+'(s(a),sum(a)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c21,plain,
'+'(sum(a),sum(s(a))) = '+'(sum(a),'+'(s(a),sum(a))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
'+'(sum(a),X2) = '+'(X2,sum(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
'+'(X2,sum(a)) = '+'(sum(a),X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
'+'(sum(a),'+'(X2,sum(a))) = '+'(sum(a),'+'(sum(a),X2)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
'+'(sum(a),'+'(sum(a),X2)) = '+'('+'(sum(a),sum(a)),X2),
inference(substitution,[status(thm)],[c6]) ).
cnf(c26,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
'+'('+'(sum(a),sum(a)),X2) = '+'(times(a,s(a)),X2),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
'+'(times(a,s(a)),X2) = '+'(X2,times(a,s(a))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
'+'('+'(sum(a),sum(a)),X2) = '+'(X2,times(a,s(a))),
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
'+'(sum(a),'+'(sum(a),X2)) = '+'(X2,times(a,s(a))),
inference(transitivity,[status(thm)],[c25,c29]) ).
cnf(c31,plain,
'+'(sum(a),'+'(X2,sum(a))) = '+'(X2,times(a,s(a))),
inference(transitivity,[status(thm)],[c24,c30]) ).
cnf(c32,plain,
'+'(sum(a),'+'(s(a),sum(a))) = '+'(s(a),times(a,s(a))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,axiom,
times(X2,Y2) = times(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_comm) ).
cnf(c34,plain,
times(X3,X2) = times(X2,X3),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
times(X2,X3) = times(X3,X2),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
'+'(X3,times(X2,X3)) = '+'(X3,times(X3,X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
times(X2,X3) = times(X3,X2),
inference(substitution,[status(thm)],[c33]) ).
cnf(c38,plain,
times(X3,X2) = times(X2,X3),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
'+'(X3,times(X3,X2)) = '+'(X3,times(X2,X3)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
times(s(X2),Y2) = '+'(Y2,times(X2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_s) ).
cnf(c41,plain,
times(s(X2),X3) = '+'(X3,times(X2,X3)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
'+'(X3,times(X2,X3)) = times(s(X2),X3),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
times(s(X2),X3) = times(X3,s(X2)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c44,plain,
'+'(X3,times(X2,X3)) = times(X3,s(X2)),
inference(transitivity,[status(thm)],[c42,c43]) ).
cnf(c45,plain,
'+'(X3,times(X3,X2)) = times(X3,s(X2)),
inference(transitivity,[status(thm)],[c39,c44]) ).
cnf(c46,plain,
'+'(X3,times(X2,X3)) = times(X3,s(X2)),
inference(transitivity,[status(thm)],[c36,c45]) ).
cnf(c47,plain,
'+'(s(a),times(a,s(a))) = times(s(a),s(a)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
'+'(sum(a),'+'(s(a),sum(a))) = times(s(a),s(a)),
inference(transitivity,[status(thm)],[c32,c47]) ).
cnf(c49,plain,
'+'(sum(a),sum(s(a))) = times(s(a),s(a)),
inference(transitivity,[status(thm)],[c21,c48]) ).
cnf(c50,plain,
'+'(sum(s(a)),sum(a)) = times(s(a),s(a)),
inference(transitivity,[status(thm)],[c19,c49]) ).
cnf(c51,plain,
'+'(s(a),'+'(sum(s(a)),sum(a))) = '+'(s(a),times(s(a),s(a))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
'+'(s(a),times(s(a),s(a))) = times(s(a),s(s(a))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c53,plain,
'+'(s(a),'+'(sum(s(a)),sum(a))) = times(s(a),s(s(a))),
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
'+'(sum(s(a)),sum(s(a))) = times(s(a),s(s(a))),
inference(transitivity,[status(thm)],[c17,c53]) ).
cnf(c55,plain,
$false,
inference(resolution,[status(thm)],[c1,c54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 22:09:15 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.61 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.22/0.61
% 0.22/0.61 % SZS status Unsatisfiable
% 0.22/0.61
% 0.22/0.61 % SZS output start CNFRefutation
% See solution above
% 0.92/0.65
% 0.92/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------