%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 11:49:10 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 10
% Syntax : Number of clauses : 122 ( 122 unt; 0 nHn; 20 RR)
% Number of literals : 122 ( 121 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
and_star(x,truth) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
cnf(c2,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
or(falsehood,not(X2)) = or(not(truth),not(X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
not(or(falsehood,not(X2))) = not(or(not(truth),not(X2))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
and_star(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_definition) ).
cnf(c7,plain,
and_star(truth,X2) = not(or(not(truth),not(X2))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
not(or(not(truth),not(X2))) = and_star(truth,X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
and_star(X2,Y2) = and_star(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c10,plain,
and_star(truth,X2) = and_star(X2,truth),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
not(or(not(truth),not(X2))) = and_star(X2,truth),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
not(or(falsehood,not(X2))) = and_star(X2,truth),
inference(transitivity,[status(thm)],[c5,c11]) ).
cnf(c13,plain,
and_star(X2,truth) = not(or(falsehood,not(X2))),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
or(X2,Y2) = or(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
cnf(c15,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(substitution,[status(thm)],[c14]) ).
cnf(c18,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,axiom,
or(X2,Y2) = implies(not(X2),Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_definition) ).
cnf(c20,plain,
or(falsehood,X2) = implies(not(falsehood),X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,axiom,
implies(truth,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
cnf(c22,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
not(falsehood) = implies(truth,not(falsehood)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
or(X2,falsehood) = or(falsehood,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c25,plain,
or(falsehood,X2) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
implies(or(falsehood,X2),X2) = implies(or(X2,falsehood),X2),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c28,plain,
implies(or(X2,falsehood),X2) = implies(or(X2,falsehood),implies(truth,X2)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c30,plain,
or(X2,falsehood) = or(X2,not(truth)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
implies(or(X2,falsehood),implies(truth,X2)) = implies(or(X2,not(truth)),implies(truth,X2)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
or(X2,not(X3)) = implies(not(X2),not(X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c33,plain,
implies(or(X3,not(X2)),implies(X2,X3)) = implies(implies(not(X3),not(X2)),implies(X2,X3)),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
implies(implies(not(X2),not(Y2)),implies(Y2,X2)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
cnf(c35,plain,
implies(implies(not(X3),not(X2)),implies(X2,X3)) = truth,
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
implies(or(X3,not(X2)),implies(X2,X3)) = truth,
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
implies(or(X2,not(truth)),implies(truth,X2)) = truth,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
implies(or(X2,falsehood),implies(truth,X2)) = truth,
inference(transitivity,[status(thm)],[c31,c37]) ).
cnf(c39,plain,
implies(or(X2,falsehood),X2) = truth,
inference(transitivity,[status(thm)],[c28,c38]) ).
cnf(c40,plain,
implies(or(falsehood,X2),X2) = truth,
inference(transitivity,[status(thm)],[c26,c39]) ).
cnf(c41,plain,
implies(or(falsehood,truth),truth) = truth,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
truth = implies(or(falsehood,truth),truth),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
implies(truth,not(falsehood)) = implies(implies(or(falsehood,truth),truth),not(falsehood)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
or(X2,truth) = implies(not(X2),truth),
inference(substitution,[status(thm)],[c19]) ).
cnf(c45,plain,
implies(or(X2,truth),truth) = implies(implies(not(X2),truth),truth),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
implies(implies(X2,Y2),Y2) = implies(implies(Y2,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
cnf(c47,plain,
implies(implies(truth,X2),X2) = implies(implies(X2,truth),truth),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
implies(implies(X2,truth),truth) = implies(implies(truth,X2),X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
implies(implies(truth,X2),X2) = implies(X2,X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c50,plain,
implies(implies(X2,truth),truth) = implies(X2,X2),
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
implies(implies(not(X2),truth),truth) = implies(not(X2),not(X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
or(X2,not(X2)) = implies(not(X2),not(X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c53,plain,
implies(not(X2),not(X2)) = or(X2,not(X2)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
implies(implies(not(X2),truth),truth) = or(X2,not(X2)),
inference(transitivity,[status(thm)],[c51,c53]) ).
cnf(c55,plain,
implies(or(X2,truth),truth) = or(X2,not(X2)),
inference(transitivity,[status(thm)],[c45,c54]) ).
cnf(c56,plain,
implies(or(falsehood,truth),truth) = or(falsehood,not(falsehood)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
implies(implies(or(falsehood,truth),truth),not(falsehood)) = implies(or(falsehood,not(falsehood)),not(falsehood)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
implies(or(falsehood,not(falsehood)),not(falsehood)) = truth,
inference(substitution,[status(thm)],[c40]) ).
cnf(c59,plain,
implies(implies(or(falsehood,truth),truth),not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
implies(truth,not(falsehood)) = truth,
inference(transitivity,[status(thm)],[c43,c59]) ).
cnf(c61,plain,
not(falsehood) = truth,
inference(transitivity,[status(thm)],[c23,c60]) ).
cnf(c62,plain,
implies(not(falsehood),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
implies(not(falsehood),X2) = X2,
inference(transitivity,[status(thm)],[c62,c21]) ).
cnf(c64,plain,
or(falsehood,X2) = X2,
inference(transitivity,[status(thm)],[c20,c63]) ).
cnf(c65,plain,
or(X2,falsehood) = X2,
inference(transitivity,[status(thm)],[c18,c64]) ).
cnf(c66,plain,
or(falsehood,X2) = X2,
inference(transitivity,[status(thm)],[c16,c65]) ).
cnf(c67,plain,
or(falsehood,not(X2)) = not(X2),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
not(or(falsehood,not(X2))) = not(not(X2)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
and_star(X2,truth) = not(not(X2)),
inference(transitivity,[status(thm)],[c13,c68]) ).
cnf(c70,plain,
and_star(x,truth) = not(not(x)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
X2 = or(X2,falsehood),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c72,plain,
implies(X2,falsehood) = implies(or(X2,falsehood),falsehood),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
or(X2,falsehood) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c19]) ).
cnf(c74,plain,
implies(or(X2,falsehood),falsehood) = implies(implies(not(X2),falsehood),falsehood),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
implies(implies(falsehood,X2),X2) = implies(implies(X2,falsehood),falsehood),
inference(substitution,[status(thm)],[c46]) ).
cnf(c76,plain,
implies(implies(X2,falsehood),falsehood) = implies(implies(falsehood,X2),X2),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c78,plain,
implies(falsehood,X2) = implies(not(truth),X2),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
or(truth,X2) = implies(not(truth),X2),
inference(substitution,[status(thm)],[c19]) ).
cnf(c80,plain,
implies(not(truth),X2) = or(truth,X2),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
or(truth,X2) = or(X2,truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c82,plain,
implies(not(truth),X2) = or(X2,truth),
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
implies(falsehood,X2) = or(X2,truth),
inference(transitivity,[status(thm)],[c78,c82]) ).
cnf(c84,plain,
implies(implies(falsehood,X2),X2) = implies(or(X2,truth),X2),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
implies(implies(X2,falsehood),falsehood) = implies(or(X2,truth),X2),
inference(transitivity,[status(thm)],[c76,c84]) ).
cnf(c86,plain,
or(X2,truth) = implies(not(X2),truth),
inference(substitution,[status(thm)],[c19]) ).
cnf(c87,plain,
X2 = or(X2,falsehood),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c88,plain,
implies(X2,X2) = implies(or(X2,falsehood),X2),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c88,c39]) ).
cnf(c90,plain,
truth = implies(X2,X2),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
implies(X2,truth) = implies(X2,implies(X2,X2)),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
implies(X2,X2) = implies(implies(X2,truth),truth),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c93,plain,
implies(X2,implies(X2,X2)) = implies(X2,implies(implies(X2,truth),truth)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c95,plain,
implies(implies(X3,X2),X2) = implies(implies(X3,X2),implies(truth,X2)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
implies(X3,implies(implies(X3,X2),X2)) = implies(X3,implies(implies(X3,X2),implies(truth,X2))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
X2 = implies(truth,X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c98,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)],[c97]) ).
cnf(c99,axiom,
implies(implies(X2,Y2),implies(implies(Y2,Z),implies(X2,Z))) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
cnf(c100,plain,
implies(implies(truth,X3),implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
implies(X3,implies(implies(X3,X2),implies(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c98,c100]) ).
cnf(c102,plain,
implies(X3,implies(implies(X3,X2),X2)) = truth,
inference(transitivity,[status(thm)],[c96,c101]) ).
cnf(c103,plain,
implies(X2,implies(implies(X2,truth),truth)) = truth,
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
implies(X2,implies(X2,X2)) = truth,
inference(transitivity,[status(thm)],[c93,c103]) ).
cnf(c105,plain,
implies(X2,truth) = truth,
inference(transitivity,[status(thm)],[c91,c104]) ).
cnf(c106,plain,
implies(not(X2),truth) = truth,
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
or(X2,truth) = truth,
inference(transitivity,[status(thm)],[c86,c106]) ).
cnf(c108,plain,
implies(or(X2,truth),X2) = implies(truth,X2),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
implies(or(X2,truth),X2) = X2,
inference(transitivity,[status(thm)],[c108,c21]) ).
cnf(c110,plain,
implies(implies(X2,falsehood),falsehood) = X2,
inference(transitivity,[status(thm)],[c85,c109]) ).
cnf(c111,plain,
implies(implies(not(X2),falsehood),falsehood) = not(X2),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
implies(or(X2,falsehood),falsehood) = not(X2),
inference(transitivity,[status(thm)],[c74,c111]) ).
cnf(c113,plain,
implies(X2,falsehood) = not(X2),
inference(transitivity,[status(thm)],[c72,c112]) ).
cnf(c114,plain,
implies(not(X2),falsehood) = not(not(X2)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
not(not(X2)) = implies(not(X2),falsehood),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
or(X2,falsehood) = implies(not(X2),falsehood),
inference(substitution,[status(thm)],[c19]) ).
cnf(c117,plain,
implies(not(X2),falsehood) = or(X2,falsehood),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
implies(not(X2),falsehood) = X2,
inference(transitivity,[status(thm)],[c117,c65]) ).
cnf(c119,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c115,c118]) ).
cnf(c120,plain,
not(not(x)) = x,
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
and_star(x,truth) = x,
inference(transitivity,[status(thm)],[c70,c120]) ).
cnf(c122,plain,
$false,
inference(resolution,[status(thm)],[c1,c121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 15:26:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 Command-line arguments: --no-flatten-goal
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48
% 0.19/0.49 % SZS output start CNFRefutation
% See solution above
% 0.19/0.53
% 0.19/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------