%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ROB003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:36:09 PM UTC 2026
% Result : Unsatisfiable 0.66s 0.51s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of clauses : 124 ( 124 unt; 0 nHn; 12 RR)
% Number of literals : 124 ( 123 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 162 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c3,plain,
add(add(X4,X2),X3) = add(X3,add(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(X3,add(X4,X2)) = add(add(X4,X2),X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(add(X2,Y2),Z) = add(X2,add(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(c6,plain,
add(add(X4,X2),X3) = add(X4,add(X2,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
add(X4,add(X2,X3)) = add(X4,add(X3,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
add(add(X4,X2),X3) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
add(X3,add(X4,X2)) = add(X4,add(X3,X2)),
inference(transitivity,[status(thm)],[c4,c9]) ).
cnf(c11,plain,
add(X3,add(X2,negate(c))) = add(X2,add(X3,negate(c))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
negate(add(X3,add(X2,negate(c)))) = negate(add(X2,add(X3,negate(c)))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
add(negate(c),negate(add(X3,add(X2,negate(c))))) = add(negate(c),negate(add(X2,add(X3,negate(c))))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
negate(add(negate(c),negate(add(X3,add(X2,negate(c)))))) = negate(add(negate(c),negate(add(X2,add(X3,negate(c)))))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
add(add(X2,X3),negate(c)) = add(X2,add(X3,negate(c))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c16,plain,
add(X2,add(X3,negate(c))) = add(add(X2,X3),negate(c)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
negate(add(X2,add(X3,negate(c)))) = negate(add(add(X2,X3),negate(c))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
add(negate(c),negate(add(X2,add(X3,negate(c))))) = add(negate(c),negate(add(add(X2,X3),negate(c)))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
negate(add(negate(c),negate(add(X2,add(X3,negate(c)))))) = negate(add(negate(c),negate(add(add(X2,X3),negate(c))))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
add(X2,c) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c21,plain,
c = add(X2,c),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
negate(c) = negate(add(X2,c)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
add(negate(c),negate(add(X2,negate(c)))) = add(negate(add(X2,c)),negate(add(X2,negate(c)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
negate(add(negate(c),negate(add(X2,negate(c))))) = negate(add(negate(add(X2,c)),negate(add(X2,negate(c))))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
negate(add(negate(add(X2,Y2)),negate(add(X2,negate(Y2))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
cnf(c26,plain,
negate(add(negate(add(X2,c)),negate(add(X2,negate(c))))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
negate(add(negate(c),negate(add(X2,negate(c))))) = X2,
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
negate(add(negate(c),negate(add(add(X2,X3),negate(c))))) = add(X2,X3),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
negate(add(negate(c),negate(add(add(X2,X3),negate(c))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
negate(add(negate(c),negate(add(X2,add(X3,negate(c)))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c19,c30]) ).
cnf(c32,plain,
negate(add(negate(c),negate(add(X3,add(X2,negate(c)))))) = add(X3,X2),
inference(transitivity,[status(thm)],[c14,c31]) ).
cnf(c33,plain,
negate(add(negate(c),negate(add(X2,add(negate(c),negate(c)))))) = add(X2,negate(c)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
add(X2,negate(c)) = negate(add(negate(c),negate(add(X2,add(negate(c),negate(c)))))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
add(X2,negate(c)) = add(negate(c),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
add(negate(c),X2) = add(X2,negate(c)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
negate(add(negate(c),X2)) = negate(add(X2,negate(c))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
add(negate(c),negate(add(negate(c),X2))) = add(negate(c),negate(add(X2,negate(c)))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
negate(add(negate(c),negate(add(negate(c),X2)))) = negate(add(negate(c),negate(add(X2,negate(c))))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
negate(add(negate(c),negate(add(negate(c),X2)))) = X2,
inference(transitivity,[status(thm)],[c39,c27]) ).
cnf(c41,plain,
negate(add(negate(c),negate(add(negate(c),add(negate(c),negate(c)))))) = add(negate(c),negate(c)),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
add(negate(c),negate(c)) = negate(add(negate(c),negate(add(negate(c),add(negate(c),negate(c)))))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
add(X2,add(negate(c),negate(c))) = add(negate(c),add(X2,negate(c))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c44,plain,
negate(add(X2,add(negate(c),negate(c)))) = negate(add(negate(c),add(X2,negate(c)))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
add(X2,negate(add(X2,add(negate(c),negate(c))))) = add(X2,negate(add(negate(c),add(X2,negate(c))))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
negate(add(X2,negate(add(X2,add(negate(c),negate(c)))))) = negate(add(X2,negate(add(negate(c),add(X2,negate(c)))))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
add(negate(add(negate(c),add(X2,negate(c)))),X2) = add(X2,negate(add(negate(c),add(X2,negate(c))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c48,plain,
add(X2,negate(add(negate(c),add(X2,negate(c))))) = add(negate(add(negate(c),add(X2,negate(c)))),X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
negate(add(X2,negate(add(negate(c),add(X2,negate(c)))))) = negate(add(negate(add(negate(c),add(X2,negate(c)))),X2)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
X2 = negate(add(negate(c),negate(add(X2,negate(c))))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c51,plain,
add(negate(add(negate(c),add(X2,negate(c)))),X2) = add(negate(add(negate(c),add(X2,negate(c)))),negate(add(negate(c),negate(add(X2,negate(c)))))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
negate(add(negate(add(negate(c),add(X2,negate(c)))),X2)) = negate(add(negate(add(negate(c),add(X2,negate(c)))),negate(add(negate(c),negate(add(X2,negate(c))))))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
negate(add(negate(add(negate(c),add(X2,negate(c)))),negate(add(negate(c),negate(add(X2,negate(c))))))) = negate(c),
inference(substitution,[status(thm)],[c25]) ).
cnf(c54,plain,
negate(add(negate(add(negate(c),add(X2,negate(c)))),X2)) = negate(c),
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
negate(add(X2,negate(add(negate(c),add(X2,negate(c)))))) = negate(c),
inference(transitivity,[status(thm)],[c49,c54]) ).
cnf(c56,plain,
negate(add(X2,negate(add(X2,add(negate(c),negate(c)))))) = negate(c),
inference(transitivity,[status(thm)],[c46,c55]) ).
cnf(c57,plain,
negate(add(negate(c),negate(add(negate(c),add(negate(c),negate(c)))))) = negate(c),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
add(negate(c),negate(c)) = negate(c),
inference(transitivity,[status(thm)],[c42,c57]) ).
cnf(c59,plain,
add(X2,add(negate(c),negate(c))) = add(X2,negate(c)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
negate(add(X2,add(negate(c),negate(c)))) = negate(add(X2,negate(c))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
add(negate(c),negate(add(X2,add(negate(c),negate(c))))) = add(negate(c),negate(add(X2,negate(c)))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
negate(add(negate(c),negate(add(X2,add(negate(c),negate(c)))))) = negate(add(negate(c),negate(add(X2,negate(c))))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
negate(add(negate(c),negate(add(X2,add(negate(c),negate(c)))))) = X2,
inference(transitivity,[status(thm)],[c62,c27]) ).
cnf(c64,plain,
add(X2,negate(c)) = X2,
inference(transitivity,[status(thm)],[c34,c63]) ).
cnf(c65,plain,
add(negate(X2),negate(c)) = negate(X2),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
negate(X2) = add(negate(X2),negate(c)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
negate(negate(X2)) = negate(add(negate(X2),negate(c))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
c = add(X2,c),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c69,plain,
negate(c) = negate(add(X2,c)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
add(negate(X2),negate(c)) = add(negate(X2),negate(add(X2,c))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
negate(add(negate(X2),negate(c))) = negate(add(negate(X2),negate(add(X2,c)))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
negate(c) = add(negate(c),negate(c)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c73,plain,
negate(negate(c)) = negate(add(negate(c),negate(c))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
add(X2,c) = add(c,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
add(c,X2) = add(X2,c),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
add(c,X2) = c,
inference(transitivity,[status(thm)],[c75,c20]) ).
cnf(c77,plain,
add(c,negate(X2)) = c,
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
c = add(c,negate(X2)),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
negate(c) = negate(add(c,negate(X2))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
add(negate(c),negate(c)) = add(negate(c),negate(add(c,negate(X2)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
negate(add(negate(c),negate(c))) = negate(add(negate(c),negate(add(c,negate(X2))))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
c = add(c,X2),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c83,plain,
negate(c) = negate(add(c,X2)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
add(negate(c),negate(add(c,negate(X2)))) = add(negate(add(c,X2)),negate(add(c,negate(X2)))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
negate(add(negate(c),negate(add(c,negate(X2))))) = negate(add(negate(add(c,X2)),negate(add(c,negate(X2))))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
negate(add(negate(add(c,X2)),negate(add(c,negate(X2))))) = c,
inference(substitution,[status(thm)],[c25]) ).
cnf(c87,plain,
negate(add(negate(c),negate(add(c,negate(X2))))) = c,
inference(transitivity,[status(thm)],[c85,c86]) ).
cnf(c88,plain,
negate(add(negate(c),negate(c))) = c,
inference(transitivity,[status(thm)],[c81,c87]) ).
cnf(c89,plain,
negate(negate(c)) = c,
inference(transitivity,[status(thm)],[c73,c88]) ).
cnf(c90,plain,
c = negate(negate(c)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
add(X2,c) = add(X2,negate(negate(c))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
negate(add(X2,c)) = negate(add(X2,negate(negate(c)))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
add(negate(X2),negate(add(X2,c))) = add(negate(X2),negate(add(X2,negate(negate(c))))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
negate(add(negate(X2),negate(add(X2,c)))) = negate(add(negate(X2),negate(add(X2,negate(negate(c)))))),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
X2 = add(X2,negate(c)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c96,plain,
negate(X2) = negate(add(X2,negate(c))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
add(negate(X2),negate(add(X2,negate(negate(c))))) = add(negate(add(X2,negate(c))),negate(add(X2,negate(negate(c))))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
negate(add(negate(X2),negate(add(X2,negate(negate(c)))))) = negate(add(negate(add(X2,negate(c))),negate(add(X2,negate(negate(c)))))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
negate(add(negate(add(X2,negate(c))),negate(add(X2,negate(negate(c)))))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c100,plain,
negate(add(negate(X2),negate(add(X2,negate(negate(c)))))) = X2,
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
negate(add(negate(X2),negate(add(X2,c)))) = X2,
inference(transitivity,[status(thm)],[c94,c100]) ).
cnf(c102,plain,
negate(add(negate(X2),negate(c))) = X2,
inference(transitivity,[status(thm)],[c71,c101]) ).
cnf(c103,plain,
negate(negate(X2)) = X2,
inference(transitivity,[status(thm)],[c67,c102]) ).
cnf(c104,plain,
negate(negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))))) = add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))) = negate(negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))))),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
add(X2,negate(X3)) = add(negate(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c107,plain,
add(negate(X3),X2) = add(X2,negate(X3)),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
negate(add(negate(X3),X2)) = negate(add(X2,negate(X3))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
add(negate(add(X3,X2)),negate(add(negate(X3),X2))) = add(negate(add(X3,X2)),negate(add(X2,negate(X3)))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
negate(add(negate(add(X3,X2)),negate(add(negate(X3),X2)))) = negate(add(negate(add(X3,X2)),negate(add(X2,negate(X3))))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c112,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
negate(add(X3,X2)) = negate(add(X2,X3)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
add(negate(add(X3,X2)),negate(add(X2,negate(X3)))) = add(negate(add(X2,X3)),negate(add(X2,negate(X3)))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
negate(add(negate(add(X3,X2)),negate(add(X2,negate(X3))))) = negate(add(negate(add(X2,X3)),negate(add(X2,negate(X3))))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
negate(add(negate(add(X2,X3)),negate(add(X2,negate(X3))))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c117,plain,
negate(add(negate(add(X3,X2)),negate(add(X2,negate(X3))))) = X2,
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
negate(add(negate(add(X3,X2)),negate(add(negate(X3),X2)))) = X2,
inference(transitivity,[status(thm)],[c110,c117]) ).
cnf(c119,plain,
negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2))))) = negate(X2),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
negate(negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))))) = negate(negate(X2)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
negate(negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))))) = X2,
inference(transitivity,[status(thm)],[c120,c103]) ).
cnf(c122,plain,
add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))) = X2,
inference(transitivity,[status(thm)],[c105,c121]) ).
cnf(c123,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
$false,
inference(resolution,[status(thm)],[c1,c123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 23:25:06 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.51 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
% 0.66/0.51
% 0.66/0.51 % SZS status Unsatisfiable
% 0.66/0.51
% 0.66/0.51 % SZS output start CNFRefutation
% See solution above
% 0.66/0.56
% 0.66/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------