%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:36:11 PM UTC 2026
% Result : Unsatisfiable 31.98s 4.54s
% Output : CNFRefutation 31.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of clauses : 88 ( 88 unt; 0 nHn; 33 RR)
% Number of literals : 88 ( 87 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 128 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
ifeq3(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c3,plain,
ifeq3(negate(e),negate(e),a,b) = a,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
a = ifeq3(negate(e),negate(e),a,b),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
ifeq4(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c6,plain,
ifeq4(d,d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = ifeq4(d,d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
d = negate(add(negate(e),negate(add(d,negate(e))))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
ifeq4(d,d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = ifeq4(d,negate(add(negate(e),negate(add(d,negate(e))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
ifeq4(negate(add(X3,negate(X2))),negate(add(X3,negate(X2))),negate(add(X3,negate(add(X2,multiply(k,add(X3,negate(add(X3,negate(X2))))))))),negate(add(X3,negate(X2)))) = negate(add(X3,negate(add(X2,multiply(k,add(X3,negate(add(X3,negate(X2))))))))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c12,plain,
negate(add(X3,negate(add(X2,multiply(k,add(X3,negate(add(X3,negate(X2))))))))) = ifeq4(negate(add(X3,negate(X2))),negate(add(X3,negate(X2))),negate(add(X3,negate(add(X2,multiply(k,add(X3,negate(add(X3,negate(X2))))))))),negate(add(X3,negate(X2)))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
ifeq2(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(c14,plain,
ifeq2(true,true,ifeq4(negate(add(X3,negate(X2))),X4,negate(add(X3,negate(add(X2,multiply(k,add(X3,X4)))))),X4),X4) = ifeq4(negate(add(X3,negate(X2))),X4,negate(add(X3,negate(add(X2,multiply(k,add(X3,X4)))))),X4),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
ifeq4(negate(add(X4,negate(X3))),X2,negate(add(X4,negate(add(X3,multiply(k,add(X4,X2)))))),X2) = ifeq2(true,true,ifeq4(negate(add(X4,negate(X3))),X2,negate(add(X4,negate(add(X3,multiply(k,add(X4,X2)))))),X2),X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,axiom,
positive_integer(k) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c17,plain,
true = positive_integer(k),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq2(true,true,ifeq4(negate(add(X4,negate(X3))),X2,negate(add(X4,negate(add(X3,multiply(k,add(X4,X2)))))),X2),X2) = ifeq2(positive_integer(k),true,ifeq4(negate(add(X4,negate(X3))),X2,negate(add(X4,negate(add(X3,multiply(k,add(X4,X2)))))),X2),X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,axiom,
ifeq2(positive_integer(Vk),true,ifeq4(negate(add(X,negate(Y))),Z,negate(add(X,negate(add(Y,multiply(Vk,add(X,Z)))))),Z),Z) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_4) ).
cnf(c20,plain,
ifeq2(positive_integer(k),true,ifeq4(negate(add(X4,negate(X3))),X2,negate(add(X4,negate(add(X3,multiply(k,add(X4,X2)))))),X2),X2) = X2,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq2(true,true,ifeq4(negate(add(X4,negate(X3))),X2,negate(add(X4,negate(add(X3,multiply(k,add(X4,X2)))))),X2),X2) = X2,
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
ifeq4(negate(add(X4,negate(X3))),X2,negate(add(X4,negate(add(X3,multiply(k,add(X4,X2)))))),X2) = X2,
inference(transitivity,[status(thm)],[c15,c21]) ).
cnf(c23,plain,
ifeq4(negate(add(X3,negate(X2))),negate(add(X3,negate(X2))),negate(add(X3,negate(add(X2,multiply(k,add(X3,negate(add(X3,negate(X2))))))))),negate(add(X3,negate(X2)))) = negate(add(X3,negate(X2))),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
negate(add(X3,negate(add(X2,multiply(k,add(X3,negate(add(X3,negate(X2))))))))) = negate(add(X3,negate(X2))),
inference(transitivity,[status(thm)],[c12,c23]) ).
cnf(c25,plain,
negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = negate(add(d,negate(e))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
negate(add(d,negate(e))) = negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
add(negate(e),negate(add(d,negate(e)))) = add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e)))))))))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
ifeq4(d,negate(add(negate(e),negate(add(d,negate(e))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = ifeq4(d,negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq4(d,d,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),d) = negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c31,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = ifeq4(d,d,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),d),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,axiom,
add(X2,Y2) = add(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c33,plain,
add(negate(add(d,negate(e))),X2) = add(X2,negate(add(d,negate(e)))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
add(X2,negate(add(d,negate(e)))) = add(negate(add(d,negate(e))),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(k,add(X2,negate(add(d,negate(e))))) = multiply(k,add(negate(add(d,negate(e))),X2)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
add(e,multiply(k,add(X2,negate(add(d,negate(e)))))) = add(e,multiply(k,add(negate(add(d,negate(e))),X2))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
negate(add(e,multiply(k,add(X2,negate(add(d,negate(e))))))) = negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(X2,negate(add(d,negate(e)))))))) = add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2))))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(X2,negate(add(d,negate(e))))))))) = negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2)))))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
ifeq4(d,X2,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(X2,negate(add(d,negate(e))))))))),X2) = ifeq4(d,X2,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2)))))),X2),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
d = negate(add(negate(e),negate(add(d,negate(e))))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c42,plain,
ifeq4(d,X2,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2)))))),X2) = ifeq4(negate(add(negate(e),negate(add(d,negate(e))))),X2,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2)))))),X2),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
add(X2,negate(X3)) = add(negate(X3),X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c44,plain,
add(negate(X3),X2) = add(X2,negate(X3)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
negate(add(negate(X3),X2)) = negate(add(X2,negate(X3))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq4(negate(add(negate(X4),X3)),X2,negate(add(X3,negate(add(X4,multiply(k,add(X3,X2)))))),X2) = ifeq4(negate(add(X3,negate(X4))),X2,negate(add(X3,negate(add(X4,multiply(k,add(X3,X2)))))),X2),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
ifeq4(negate(add(X3,negate(X4))),X2,negate(add(X3,negate(add(X4,multiply(k,add(X3,X2)))))),X2) = X2,
inference(substitution,[status(thm)],[c22]) ).
cnf(c48,plain,
ifeq4(negate(add(negate(X4),X3)),X2,negate(add(X3,negate(add(X4,multiply(k,add(X3,X2)))))),X2) = X2,
inference(transitivity,[status(thm)],[c46,c47]) ).
cnf(c49,plain,
ifeq4(negate(add(negate(e),negate(add(d,negate(e))))),X2,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2)))))),X2) = X2,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq4(d,X2,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(negate(add(d,negate(e))),X2)))))),X2) = X2,
inference(transitivity,[status(thm)],[c42,c49]) ).
cnf(c51,plain,
ifeq4(d,X2,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(X2,negate(add(d,negate(e))))))))),X2) = X2,
inference(transitivity,[status(thm)],[c40,c50]) ).
cnf(c52,plain,
ifeq4(d,d,negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),d) = d,
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))) = d,
inference(transitivity,[status(thm)],[c31,c52]) ).
cnf(c54,plain,
d = negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
ifeq4(d,negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = ifeq4(negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c57,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
negate(add(X3,X2)) = negate(add(X2,X3)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
add(X3,negate(add(X4,X2))) = add(X3,negate(add(X2,X4))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
negate(add(X3,negate(add(X4,X2)))) = negate(add(X3,negate(add(X2,X4)))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
ifeq4(negate(add(negate(add(X4,X3)),X2)),negate(add(X3,negate(add(X4,X2)))),X2,X3) = ifeq4(negate(add(negate(add(X4,X3)),X2)),negate(add(X3,negate(add(X2,X4)))),X2,X3),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c63,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
negate(add(X3,X2)) = negate(add(X2,X3)),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
add(negate(add(X4,X3)),X2) = add(negate(add(X3,X4)),X2),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
negate(add(negate(add(X4,X3)),X2)) = negate(add(negate(add(X3,X4)),X2)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
ifeq4(negate(add(negate(add(X4,X3)),X2)),negate(add(X3,negate(add(X2,X4)))),X2,X3) = ifeq4(negate(add(negate(add(X3,X4)),X2)),negate(add(X3,negate(add(X2,X4)))),X2,X3),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
add(X2,negate(add(X4,X3))) = add(negate(add(X4,X3)),X2),
inference(substitution,[status(thm)],[c32]) ).
cnf(c69,plain,
add(negate(add(X4,X3)),X2) = add(X2,negate(add(X4,X3))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
negate(add(negate(add(X4,X3)),X2)) = negate(add(X2,negate(add(X4,X3)))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
ifeq4(negate(add(negate(add(X4,X3)),X2)),negate(add(X4,negate(add(X2,X3)))),X2,X4) = ifeq4(negate(add(X2,negate(add(X4,X3)))),negate(add(X4,negate(add(X2,X3)))),X2,X4),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,axiom,
ifeq4(negate(add(X2,negate(add(Y2,Z2)))),negate(add(Y2,negate(add(X2,Z2)))),X2,Y2) = Y2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2) ).
cnf(c73,plain,
ifeq4(negate(add(X2,negate(add(X4,X3)))),negate(add(X4,negate(add(X2,X3)))),X2,X4) = X4,
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
ifeq4(negate(add(negate(add(X4,X3)),X2)),negate(add(X4,negate(add(X2,X3)))),X2,X4) = X4,
inference(transitivity,[status(thm)],[c71,c73]) ).
cnf(c75,plain,
ifeq4(negate(add(negate(add(X3,X4)),X2)),negate(add(X3,negate(add(X2,X4)))),X2,X3) = X3,
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq4(negate(add(negate(add(X4,X3)),X2)),negate(add(X3,negate(add(X2,X4)))),X2,X3) = X3,
inference(transitivity,[status(thm)],[c67,c75]) ).
cnf(c77,plain,
ifeq4(negate(add(negate(add(X4,X3)),X2)),negate(add(X3,negate(add(X4,X2)))),X2,X3) = X3,
inference(transitivity,[status(thm)],[c61,c76]) ).
cnf(c78,plain,
ifeq4(negate(add(negate(add(d,negate(e))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))),negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
ifeq4(d,negate(add(negate(e),negate(add(d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(transitivity,[status(thm)],[c55,c78]) ).
cnf(c80,plain,
ifeq4(d,negate(add(negate(e),negate(add(d,negate(e))))),negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(transitivity,[status(thm)],[c29,c79]) ).
cnf(c81,plain,
ifeq4(d,d,negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e)) = negate(e),
inference(transitivity,[status(thm)],[c10,c80]) ).
cnf(c82,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = negate(e),
inference(transitivity,[status(thm)],[c7,c81]) ).
cnf(c83,plain,
negate(e) = negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
ifeq3(negate(e),negate(e),a,b) = ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,axiom,
ifeq3(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e),a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c86,plain,
ifeq3(negate(e),negate(e),a,b) = b,
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
a = b,
inference(transitivity,[status(thm)],[c4,c86]) ).
cnf(c88,plain,
$false,
inference(resolution,[status(thm)],[c1,c87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n017.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 23:22:05 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.98/4.54 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
% 31.98/4.54
% 31.98/4.54 % SZS status Unsatisfiable
% 31.98/4.54
% 31.98/4.55 % SZS output start CNFRefutation
% See solution above
% 31.98/4.59
% 31.98/4.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------