%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX206-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 18 RR)
% Number of literals : 26 ( 25 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
eq2(plus_not_idem(X),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
eq2(btrue,bfalse) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
bfalse = eq2(btrue,bfalse),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
impl(eq(x2(X2,X2),X2),bfalse) = impl(eq(x2(X2,X2),X2),eq2(btrue,bfalse)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
plus_not_idem(X2) = impl(eq(x2(X2,X2),X2),eq2(btrue,bfalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
impl(eq(x2(X2,X2),X2),eq2(btrue,bfalse)) = plus_not_idem(X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
impl(eq(x2(X2,X2),X2),bfalse) = plus_not_idem(X2),
inference(transitivity,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
impl(eq(x2(z,z),z),bfalse) = plus_not_idem(z),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
plus_not_idem(z) = impl(eq(x2(z,z),z),bfalse),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
x2(z,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
cnf(c11,plain,
x2(z,z) = z,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
eq(x2(z,z),z) = eq(z,z),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
impl(eq(x2(z,z),z),bfalse) = impl(eq(z,z),bfalse),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
eq(X2,X2) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
cnf(c15,plain,
eq(z,z) = btrue,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
impl(eq(z,z),bfalse) = impl(btrue,bfalse),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,axiom,
impl(btrue,Q) = Q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
cnf(c18,plain,
impl(btrue,bfalse) = bfalse,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
impl(eq(z,z),bfalse) = bfalse,
inference(transitivity,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
impl(eq(x2(z,z),z),bfalse) = bfalse,
inference(transitivity,[status(thm)],[c13,c19]) ).
cnf(c21,plain,
plus_not_idem(z) = bfalse,
inference(transitivity,[status(thm)],[c9,c20]) ).
cnf(c22,plain,
eq2(plus_not_idem(z),bfalse) = eq2(bfalse,bfalse),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
eq2(X2,X2) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
cnf(c24,plain,
eq2(bfalse,bfalse) = btrue,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
eq2(plus_not_idem(z),bfalse) = btrue,
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
$false,
inference(resolution,[status(thm)],[c1,c25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX206-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:12:08 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 Command-line arguments: --no-flatten-goal
% 0.08/0.25
% 0.08/0.25 % SZS status Unsatisfiable
% 0.08/0.25
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27
% 0.08/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------