%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL135-1 : TPTP v9.3.1. Released v1.0.0.
% 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 11:49:07 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.50s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 3 RR)
% Number of literals : 42 ( 41 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
implies(x,implies(y,x)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
cnf(c2,axiom,
implies(truth,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
implies(X2,implies(X3,X2)) = implies(implies(truth,X2),implies(X3,X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = implies(implies(truth,X3),implies(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
implies(implies(truth,X3),implies(X2,X3)) = implies(truth,implies(implies(truth,X3),implies(X2,X3))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c8,plain,
implies(X2,X2) = implies(implies(truth,X2),X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
implies(truth,implies(implies(truth,X2),X2)) = implies(implies(truth,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
implies(implies(truth,X2),X2) = implies(truth,implies(implies(truth,X2),X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c12,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),implies(truth,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
implies(X3,implies(implies(X3,X2),X2)) = implies(X3,implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c15,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
cnf(c17,plain,
implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
implies(X3,implies(implies(X3,X2),X2)) = truth,
inference(transitivity,[status(thm)],[c13,c18]) ).
cnf(c20,plain,
implies(truth,implies(implies(truth,X2),X2)) = truth,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
implies(implies(truth,X2),X2) = truth,
inference(transitivity,[status(thm)],[c10,c20]) ).
cnf(c22,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c8,c21]) ).
cnf(c23,plain,
truth = implies(X2,X2),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
implies(X2,truth) = implies(X2,implies(X2,X2)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c26,plain,
implies(implies(truth,X2),X2) = implies(implies(X2,truth),truth),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
implies(implies(X2,truth),truth) = implies(implies(truth,X2),X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
implies(implies(truth,X2),X2) = implies(X2,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c29,plain,
implies(implies(X2,truth),truth) = implies(X2,X2),
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
implies(X2,X2) = implies(implies(X2,truth),truth),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
implies(X2,implies(X2,X2)) = implies(X2,implies(implies(X2,truth),truth)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
implies(X2,implies(implies(X2,truth),truth)) = truth,
inference(substitution,[status(thm)],[c19]) ).
cnf(c33,plain,
implies(X2,implies(X2,X2)) = truth,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c24,c33]) ).
cnf(c35,plain,
truth = implies(X2,truth),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
implies(implies(X2,truth),implies(implies(truth,X3),implies(X2,X3))) = truth,
inference(substitution,[status(thm)],[c16]) ).
cnf(c38,plain,
implies(truth,implies(implies(truth,X3),implies(X2,X3))) = truth,
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
implies(implies(truth,X3),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c6,c38]) ).
cnf(c40,plain,
implies(X3,implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c4,c39]) ).
cnf(c41,plain,
implies(x,implies(y,x)) = truth,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
$false,
inference(resolution,[status(thm)],[c1,c41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL135-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n015.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 15:27:15 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.50 Command-line arguments: --no-flatten-goal
% 0.23/0.50
% 0.23/0.50 % SZS status Unsatisfiable
% 0.23/0.50
% 0.23/0.50 % SZS output start CNFRefutation
% See solution above
% 0.23/0.52
% 0.23/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------