%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Tue Sep 29 09:30:46 AM UTC 2026
% Result : Unsatisfiable 6.89s 1.17s
% Output : CNFRefutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of clauses : 108 ( 108 unt; 0 nHn; 55 RR)
% Number of literals : 108 ( 107 equ; 1 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
d(T) != times(x,cos(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
d('+'(T2,U)) = '+'(d(T2),d(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_plus) ).
cnf(c3,plain,
d('+'(times(x,minus(d(cos(x)))),cos(x))) = '+'(d(times(x,minus(d(cos(x))))),d(cos(x))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
'+'(X,Y) = '+'(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).
cnf(c5,plain,
'+'(minus(d(cos(x))),times(x,cos(x))) = '+'(times(x,cos(x)),minus(d(cos(x)))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
'+'(times(x,cos(x)),minus(d(cos(x)))) = '+'(minus(d(cos(x))),times(x,cos(x))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
times(one,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
cnf(c8,plain,
times(one,sin(x)) = sin(x),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
sin(x) = times(one,sin(x)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
minus(sin(x)) = minus(times(one,sin(x))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
d(x) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
one = d(x),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
times(one,sin(x)) = times(d(x),sin(x)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
minus(times(one,sin(x))) = minus(times(d(x),sin(x))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
times(X2,Y2) = times(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_times) ).
cnf(c16,plain,
times(sin(X2),d(X2)) = times(d(X2),sin(X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
times(d(X2),sin(X2)) = times(sin(X2),d(X2)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
minus(times(d(X2),sin(X2))) = minus(times(sin(X2),d(X2))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
d(cos(T2)) = minus(times(sin(T2),d(T2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_cos) ).
cnf(c20,plain,
d(cos(X2)) = minus(times(sin(X2),d(X2))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
minus(times(sin(X2),d(X2))) = d(cos(X2)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
minus(times(d(X2),sin(X2))) = d(cos(X2)),
inference(transitivity,[status(thm)],[c18,c21]) ).
cnf(c23,plain,
minus(times(d(x),sin(x))) = d(cos(x)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
minus(times(one,sin(x))) = d(cos(x)),
inference(transitivity,[status(thm)],[c14,c23]) ).
cnf(c25,plain,
minus(sin(x)) = d(cos(x)),
inference(transitivity,[status(thm)],[c10,c24]) ).
cnf(c26,plain,
d(cos(x)) = minus(sin(x)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
minus(d(cos(x))) = minus(minus(sin(x))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
'+'(X3,minus(X2)) = '+'(minus(X2),X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c29,plain,
'+'(minus(X3),X2) = '+'(X2,minus(X3)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
'+'(X3,'+'(minus(X3),X2)) = '+'(X3,'+'(X2,minus(X3))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
'+'(minus(X3),X2) = '+'(X2,minus(X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c32,plain,
'+'(X2,minus(X3)) = '+'(minus(X3),X2),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
'+'(X3,'+'(X2,minus(X3))) = '+'(X3,'+'(minus(X3),X2)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
'+'(X2,'+'(Y2,Z)) = '+'('+'(X2,Y2),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associtivity_of_plus) ).
cnf(c35,plain,
'+'(X3,'+'(minus(X3),X2)) = '+'('+'(X3,minus(X3)),X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,axiom,
'+'(X2,minus(X2)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c37,plain,
'+'('+'(X3,minus(X3)),X2) = '+'(zero,X2),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
'+'(zero,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c39,plain,
'+'('+'(X3,minus(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
'+'(X3,'+'(minus(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c35,c39]) ).
cnf(c41,plain,
'+'(X3,'+'(X2,minus(X3))) = X2,
inference(transitivity,[status(thm)],[c33,c40]) ).
cnf(c42,plain,
'+'(X3,'+'(minus(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c30,c41]) ).
cnf(c43,plain,
'+'(X2,'+'(minus(X2),minus(minus(X2)))) = minus(minus(X2)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
minus(minus(X2)) = '+'(X2,'+'(minus(X2),minus(minus(X2)))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
'+'(minus(X2),minus(minus(X2))) = zero,
inference(substitution,[status(thm)],[c36]) ).
cnf(c46,plain,
'+'(X2,'+'(minus(X2),minus(minus(X2)))) = '+'(X2,zero),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
'+'(zero,X2) = '+'(X2,zero),
inference(substitution,[status(thm)],[c4]) ).
cnf(c48,plain,
'+'(X2,zero) = '+'(zero,X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
'+'(X2,zero) = X2,
inference(transitivity,[status(thm)],[c48,c38]) ).
cnf(c50,plain,
'+'(X2,'+'(minus(X2),minus(minus(X2)))) = X2,
inference(transitivity,[status(thm)],[c46,c49]) ).
cnf(c51,plain,
minus(minus(X2)) = X2,
inference(transitivity,[status(thm)],[c44,c50]) ).
cnf(c52,plain,
minus(minus(sin(x))) = sin(x),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
minus(d(cos(x))) = sin(x),
inference(transitivity,[status(thm)],[c27,c52]) ).
cnf(c54,plain,
'+'(minus(d(cos(x))),times(x,cos(x))) = '+'(sin(x),times(x,cos(x))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
times(cos(X2),d(X2)) = times(d(X2),cos(X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c56,plain,
times(d(X2),cos(X2)) = times(cos(X2),d(X2)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,axiom,
d(sin(T2)) = times(cos(T2),d(T2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_sin) ).
cnf(c58,plain,
d(sin(X2)) = times(cos(X2),d(X2)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
times(cos(X2),d(X2)) = d(sin(X2)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
times(d(X2),cos(X2)) = d(sin(X2)),
inference(transitivity,[status(thm)],[c56,c59]) ).
cnf(c61,plain,
times(d(x),cos(x)) = d(sin(x)),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
d(sin(x)) = times(d(x),cos(x)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
times(d(x),cos(x)) = times(one,cos(x)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c64,plain,
times(one,cos(x)) = cos(x),
inference(substitution,[status(thm)],[c7]) ).
cnf(c65,plain,
times(d(x),cos(x)) = cos(x),
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
d(sin(x)) = cos(x),
inference(transitivity,[status(thm)],[c62,c65]) ).
cnf(c67,plain,
cos(x) = d(sin(x)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
times(x,cos(x)) = times(x,d(sin(x))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
'+'(sin(x),times(x,cos(x))) = '+'(sin(x),times(x,d(sin(x)))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
times(one,X2) = times(X2,one),
inference(substitution,[status(thm)],[c15]) ).
cnf(c71,plain,
times(X2,one) = times(one,X2),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
times(X2,one) = X2,
inference(transitivity,[status(thm)],[c71,c7]) ).
cnf(c73,plain,
X2 = times(X2,one),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
'+'(X2,times(x,d(X2))) = '+'(times(X2,one),times(x,d(X2))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
one = d(x),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c76,plain,
times(X2,one) = times(X2,d(x)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
'+'(times(X2,one),times(x,d(X2))) = '+'(times(X2,d(x)),times(x,d(X2))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,axiom,
d(times(T2,U2)) = '+'(times(T2,d(U2)),times(U2,d(T2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_times) ).
cnf(c79,plain,
d(times(X2,x)) = '+'(times(X2,d(x)),times(x,d(X2))),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
'+'(times(X2,d(x)),times(x,d(X2))) = d(times(X2,x)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
'+'(times(X2,one),times(x,d(X2))) = d(times(X2,x)),
inference(transitivity,[status(thm)],[c77,c80]) ).
cnf(c82,plain,
'+'(X2,times(x,d(X2))) = d(times(X2,x)),
inference(transitivity,[status(thm)],[c74,c81]) ).
cnf(c83,plain,
'+'(sin(x),times(x,d(sin(x)))) = d(times(sin(x),x)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
sin(x) = minus(d(cos(x))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c85,plain,
times(sin(x),x) = times(minus(d(cos(x))),x),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
d(times(sin(x),x)) = d(times(minus(d(cos(x))),x)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
times(minus(d(cos(x))),x) = times(x,minus(d(cos(x)))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c88,plain,
d(times(minus(d(cos(x))),x)) = d(times(x,minus(d(cos(x))))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
d(times(sin(x),x)) = d(times(x,minus(d(cos(x))))),
inference(transitivity,[status(thm)],[c86,c88]) ).
cnf(c90,plain,
'+'(sin(x),times(x,d(sin(x)))) = d(times(x,minus(d(cos(x))))),
inference(transitivity,[status(thm)],[c83,c89]) ).
cnf(c91,plain,
'+'(sin(x),times(x,cos(x))) = d(times(x,minus(d(cos(x))))),
inference(transitivity,[status(thm)],[c69,c90]) ).
cnf(c92,plain,
'+'(minus(d(cos(x))),times(x,cos(x))) = d(times(x,minus(d(cos(x))))),
inference(transitivity,[status(thm)],[c54,c91]) ).
cnf(c93,plain,
'+'(times(x,cos(x)),minus(d(cos(x)))) = d(times(x,minus(d(cos(x))))),
inference(transitivity,[status(thm)],[c6,c92]) ).
cnf(c94,plain,
d(times(x,minus(d(cos(x))))) = '+'(times(x,cos(x)),minus(d(cos(x)))),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
'+'(d(times(x,minus(d(cos(x))))),d(cos(x))) = '+'('+'(times(x,cos(x)),minus(d(cos(x)))),d(cos(x))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
'+'(times(x,cos(x)),'+'(minus(d(cos(x))),d(cos(x)))) = '+'('+'(times(x,cos(x)),minus(d(cos(x)))),d(cos(x))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c97,plain,
'+'('+'(times(x,cos(x)),minus(d(cos(x)))),d(cos(x))) = '+'(times(x,cos(x)),'+'(minus(d(cos(x))),d(cos(x)))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
'+'(minus(d(cos(x))),d(cos(x))) = '+'(d(cos(x)),minus(d(cos(x)))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c99,plain,
'+'(times(x,cos(x)),'+'(minus(d(cos(x))),d(cos(x)))) = '+'(times(x,cos(x)),'+'(d(cos(x)),minus(d(cos(x))))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
'+'(d(cos(x)),minus(d(cos(x)))) = zero,
inference(substitution,[status(thm)],[c36]) ).
cnf(c101,plain,
'+'(times(x,cos(x)),'+'(d(cos(x)),minus(d(cos(x))))) = '+'(times(x,cos(x)),zero),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
'+'(times(x,cos(x)),zero) = times(x,cos(x)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c103,plain,
'+'(times(x,cos(x)),'+'(d(cos(x)),minus(d(cos(x))))) = times(x,cos(x)),
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
'+'(times(x,cos(x)),'+'(minus(d(cos(x))),d(cos(x)))) = times(x,cos(x)),
inference(transitivity,[status(thm)],[c99,c103]) ).
cnf(c105,plain,
'+'('+'(times(x,cos(x)),minus(d(cos(x)))),d(cos(x))) = times(x,cos(x)),
inference(transitivity,[status(thm)],[c97,c104]) ).
cnf(c106,plain,
'+'(d(times(x,minus(d(cos(x))))),d(cos(x))) = times(x,cos(x)),
inference(transitivity,[status(thm)],[c95,c105]) ).
cnf(c107,plain,
d('+'(times(x,minus(d(cos(x)))),cos(x))) = times(x,cos(x)),
inference(transitivity,[status(thm)],[c3,c106]) ).
cnf(c108,plain,
$false,
inference(resolution,[status(thm)],[c1,c107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA133-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.22 % Computer : n009.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Mon Sep 28 20:38:44 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.89/1.17 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
% 6.89/1.17
% 6.89/1.17 % SZS status Unsatisfiable
% 6.89/1.17
% 6.89/1.19 % SZS output start CNFRefutation
% See solution above
% 7.17/1.25
% 7.17/1.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------