%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ROB009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:36:10 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 23 RR)
% Number of literals : 33 ( 32 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_result) ).
cnf(c2,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
cnf(c3,plain,
negate(add(negate(add(b,add(a,c))),negate(add(b,negate(add(a,c)))))) = b,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
b = negate(add(negate(add(b,add(a,c))),negate(add(b,negate(add(a,c)))))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
negate(add(a,negate(add(b,c)))) = negate(add(b,negate(add(a,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
negate(add(b,negate(add(a,c)))) = negate(add(a,negate(add(b,c)))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
add(negate(add(b,add(a,c))),negate(add(b,negate(add(a,c))))) = add(negate(add(b,add(a,c))),negate(add(a,negate(add(b,c))))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
negate(add(negate(add(b,add(a,c))),negate(add(b,negate(add(a,c)))))) = negate(add(negate(add(b,add(a,c))),negate(add(a,negate(add(b,c)))))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
add(X2,Y2) = add(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c10,plain,
add(negate(add(b,add(a,c))),negate(add(a,negate(add(b,c))))) = add(negate(add(a,negate(add(b,c)))),negate(add(b,add(a,c)))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
negate(add(negate(add(b,add(a,c))),negate(add(a,negate(add(b,c)))))) = negate(add(negate(add(a,negate(add(b,c)))),negate(add(b,add(a,c))))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
add(add(X3,X2),X4) = add(X4,add(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c13,plain,
add(X4,add(X3,X2)) = add(add(X3,X2),X4),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
add(add(X2,Y2),Z) = add(X2,add(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(c15,plain,
add(add(X3,X2),X4) = add(X3,add(X2,X4)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c17,plain,
add(X3,add(X2,X4)) = add(X3,add(X4,X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
add(add(X3,X2),X4) = add(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
add(X4,add(X3,X2)) = add(X3,add(X4,X2)),
inference(transitivity,[status(thm)],[c13,c18]) ).
cnf(c20,plain,
add(b,add(a,c)) = add(a,add(b,c)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
negate(add(b,add(a,c))) = negate(add(a,add(b,c))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
add(negate(add(a,negate(add(b,c)))),negate(add(b,add(a,c)))) = add(negate(add(a,negate(add(b,c)))),negate(add(a,add(b,c)))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
negate(add(negate(add(a,negate(add(b,c)))),negate(add(b,add(a,c))))) = negate(add(negate(add(a,negate(add(b,c)))),negate(add(a,add(b,c))))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
add(negate(add(a,negate(add(b,c)))),negate(add(a,add(b,c)))) = add(negate(add(a,add(b,c))),negate(add(a,negate(add(b,c))))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c25,plain,
negate(add(negate(add(a,negate(add(b,c)))),negate(add(a,add(b,c))))) = negate(add(negate(add(a,add(b,c))),negate(add(a,negate(add(b,c)))))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
negate(add(negate(add(a,add(b,c))),negate(add(a,negate(add(b,c)))))) = a,
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
negate(add(negate(add(a,negate(add(b,c)))),negate(add(a,add(b,c))))) = a,
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
negate(add(negate(add(a,negate(add(b,c)))),negate(add(b,add(a,c))))) = a,
inference(transitivity,[status(thm)],[c23,c27]) ).
cnf(c29,plain,
negate(add(negate(add(b,add(a,c))),negate(add(a,negate(add(b,c)))))) = a,
inference(transitivity,[status(thm)],[c11,c28]) ).
cnf(c30,plain,
negate(add(negate(add(b,add(a,c))),negate(add(b,negate(add(a,c)))))) = a,
inference(transitivity,[status(thm)],[c8,c29]) ).
cnf(c31,plain,
b = a,
inference(transitivity,[status(thm)],[c4,c30]) ).
cnf(c32,plain,
a = b,
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
$false,
inference(resolution,[status(thm)],[c1,c32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 23:31:19 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 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
% 0.17/0.46
% 0.17/0.46 % SZS status Unsatisfiable
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation
% See solution above
% 0.17/0.48
% 0.17/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------