%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ROB002-1 : TPTP v9.3.1. Released v1.0.0.
% 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 12:36:09 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 3 RR)
% Number of literals : 25 ( 24 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_huntingtons_axiom) ).
cnf(c2,hypothesis,
negate(negate(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',double_negation) ).
cnf(c3,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)],[c2]) ).
cnf(c4,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)],[c3]) ).
cnf(c5,axiom,
add(X2,Y) = add(Y,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c6,plain,
add(X2,negate(X3)) = add(negate(X3),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(negate(X3),X2) = add(X2,negate(X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
negate(add(negate(X3),X2)) = negate(add(X2,negate(X3))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,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)],[c8]) ).
cnf(c10,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)],[c9]) ).
cnf(c11,plain,
add(X2,X3) = add(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c12,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
negate(add(X3,X2)) = negate(add(X2,X3)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,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)],[c13]) ).
cnf(c15,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)],[c14]) ).
cnf(c16,axiom,
negate(add(negate(add(X2,Y2)),negate(add(X2,negate(Y2))))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',robbins_axiom) ).
cnf(c17,plain,
negate(add(negate(add(X2,X3)),negate(add(X2,negate(X3))))) = X2,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
negate(add(negate(add(X3,X2)),negate(add(X2,negate(X3))))) = X2,
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
negate(add(negate(add(X3,X2)),negate(add(negate(X3),X2)))) = X2,
inference(transitivity,[status(thm)],[c10,c18]) ).
cnf(c20,plain,
negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2))))) = negate(X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
negate(negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))))) = negate(negate(X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
negate(negate(add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))))) = X2,
inference(transitivity,[status(thm)],[c21,c2]) ).
cnf(c23,plain,
add(negate(add(X3,negate(X2))),negate(add(negate(X3),negate(X2)))) = X2,
inference(transitivity,[status(thm)],[c4,c22]) ).
cnf(c24,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
$false,
inference(resolution,[status(thm)],[c1,c24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 23:28:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.45 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
% 0.12/0.45
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.46
% 0.12/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------