%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/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 01:45:34 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 21 RR)
% Number of literals : 45 ( 44 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 28 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
eq2(mul_idem(X),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
mul_idem(X2) = eq(x22(X2,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
cnf(c3,plain,
mul_idem(s(s(z))) = eq(x22(s(s(z)),s(s(z))),s(s(z))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
x22(s(N),Y) = x2(Y,x22(N,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
cnf(c5,plain,
x22(s(z),X2) = x2(X2,x22(z,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,axiom,
x22(z,Y2) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(c7,plain,
x22(z,X2) = z,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
x2(X2,x22(z,X2)) = x2(X2,z),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
x22(s(z),X2) = x2(X2,z),
inference(transitivity,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
x2(X2,z) = x22(s(z),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
x2(X2,x2(X2,z)) = x2(X2,x22(s(z),X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
x22(s(s(z)),X2) = x2(X2,x22(s(z),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c13,plain,
x2(X2,x22(s(z),X2)) = x22(s(s(z)),X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
x2(X2,x2(X2,z)) = x22(s(s(z)),X2),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
x2(s(s(z)),x2(s(s(z)),z)) = x22(s(s(z)),s(s(z))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
x22(s(s(z)),s(s(z))) = x2(s(s(z)),x2(s(s(z)),z)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,axiom,
x2(s(N2),Y2) = s(x2(N2,Y2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
cnf(c18,plain,
x2(s(s(z)),X2) = s(x2(s(z),X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
x2(s(z),X2) = s(x2(z,X2)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c20,axiom,
x2(z,Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(c21,plain,
x2(z,X2) = X2,
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
s(x2(z,X2)) = s(X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
x2(s(z),X2) = s(X2),
inference(transitivity,[status(thm)],[c19,c22]) ).
cnf(c24,plain,
s(x2(s(z),X2)) = s(s(X2)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
x2(s(s(z)),X2) = s(s(X2)),
inference(transitivity,[status(thm)],[c18,c24]) ).
cnf(c26,plain,
x2(s(s(z)),z) = s(s(z)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
x2(s(s(z)),x2(s(s(z)),z)) = x2(s(s(z)),s(s(z))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
x2(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(substitution,[status(thm)],[c25]) ).
cnf(c29,plain,
x2(s(s(z)),x2(s(s(z)),z)) = s(s(s(s(z)))),
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
x22(s(s(z)),s(s(z))) = s(s(s(s(z)))),
inference(transitivity,[status(thm)],[c16,c29]) ).
cnf(c31,plain,
eq(x22(s(s(z)),s(s(z))),s(s(z))) = eq(s(s(s(s(z)))),s(s(z))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
eq(s(X2),s(Y2)) = eq(X2,Y2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
cnf(c33,plain,
eq(s(s(s(s(z)))),s(s(z))) = eq(s(s(s(z))),s(z)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
eq(s(s(s(z))),s(z)) = eq(s(s(z)),z),
inference(substitution,[status(thm)],[c32]) ).
cnf(c35,axiom,
eq(s(X2),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
cnf(c36,plain,
eq(s(s(z)),z) = bfalse,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
eq(s(s(s(z))),s(z)) = bfalse,
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
eq(s(s(s(s(z)))),s(s(z))) = bfalse,
inference(transitivity,[status(thm)],[c33,c37]) ).
cnf(c39,plain,
eq(x22(s(s(z)),s(s(z))),s(s(z))) = bfalse,
inference(transitivity,[status(thm)],[c31,c38]) ).
cnf(c40,plain,
mul_idem(s(s(z))) = bfalse,
inference(transitivity,[status(thm)],[c3,c39]) ).
cnf(c41,plain,
eq2(mul_idem(s(s(z))),bfalse) = eq2(bfalse,bfalse),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,axiom,
eq2(X2,X2) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(c43,plain,
eq2(bfalse,bfalse) = btrue,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
eq2(mul_idem(s(s(z))),bfalse) = btrue,
inference(transitivity,[status(thm)],[c41,c43]) ).
cnf(c45,plain,
$false,
inference(resolution,[status(thm)],[c1,c44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 15:13:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.27 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.27
% 0.22/0.27 % SZS status Unsatisfiable
% 0.22/0.27
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.28
% 0.22/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------