%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 11:49:11 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of clauses : 81 ( 81 unt; 0 nHn; 15 RR)
% Number of literals : 81 ( 80 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c2,axiom,
xor(X2,falsehood) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = xor(X2,falsehood),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
and_star(X3,X2) = and_star(X3,xor(X2,falsehood)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
not(and_star(X3,X2)) = not(and_star(X3,xor(X2,falsehood))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
falsehood = not(truth),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
xor(X2,falsehood) = xor(X2,not(truth)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
and_star(X3,xor(X2,falsehood)) = and_star(X3,xor(X2,not(truth))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
not(and_star(X3,xor(X2,falsehood))) = not(and_star(X3,xor(X2,not(truth)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
xor(X,Y) = xor(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
cnf(c12,plain,
xor(X2,truth) = xor(truth,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
xor(truth,X2) = xor(X2,truth),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
not(X2) = xor(X2,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
xor(truth,X2) = not(X2),
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = not(and_star(X3,xor(X2,not(truth)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
not(and_star(X3,xor(X2,not(truth)))) = xor(truth,and_star(X3,xor(X2,not(truth)))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
xor(not(X2),X3) = xor(X3,not(X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c20,plain,
xor(X3,not(X2)) = xor(not(X2),X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
xor(X2,xor(truth,Y2)) = xor(xor(X2,truth),Y2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
cnf(c22,plain,
xor(X3,xor(truth,X2)) = xor(xor(X3,truth),X2),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c24,plain,
xor(xor(X3,truth),X2) = xor(not(X3),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
xor(X3,xor(truth,X2)) = xor(not(X3),X2),
inference(transitivity,[status(thm)],[c22,c24]) ).
cnf(c26,plain,
xor(X2,xor(truth,X3)) = xor(not(X2),X3),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
xor(not(X2),X3) = xor(X2,xor(truth,X3)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
xor(truth,X2) = xor(X2,truth),
inference(substitution,[status(thm)],[c11]) ).
cnf(c29,plain,
xor(X2,xor(truth,X3)) = xor(X2,xor(X3,truth)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c31,plain,
xor(X2,xor(X3,truth)) = xor(X2,not(X3)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
xor(X2,xor(truth,X3)) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
xor(not(X2),X3) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
xor(X3,not(X2)) = xor(X2,not(X3)),
inference(transitivity,[status(thm)],[c20,c33]) ).
cnf(c35,plain,
xor(truth,not(X2)) = xor(X2,not(truth)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
xor(X2,not(truth)) = xor(truth,not(X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
and_star(X3,xor(X2,not(truth))) = and_star(X3,xor(truth,not(X2))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = xor(truth,and_star(X3,xor(truth,not(X2)))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
implies(X2,Y2) = xor(truth,and_star(X2,xor(truth,Y2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
cnf(c40,plain,
implies(X3,not(X2)) = xor(truth,and_star(X3,xor(truth,not(X2)))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
xor(truth,and_star(X3,xor(truth,not(X2)))) = implies(X3,not(X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
xor(truth,and_star(X3,xor(X2,not(truth)))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c38,c41]) ).
cnf(c43,plain,
not(and_star(X3,xor(X2,not(truth)))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c18,c42]) ).
cnf(c44,plain,
not(and_star(X3,xor(X2,falsehood))) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c10,c43]) ).
cnf(c45,plain,
not(and_star(X3,X2)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c5,c44]) ).
cnf(c46,plain,
not(and_star(X2,X3)) = implies(X2,not(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
implies(X2,not(X3)) = not(and_star(X2,X3)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,axiom,
and_star(X2,Y2) = and_star(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c49,plain,
and_star(X3,X2) = and_star(X2,X3),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
and_star(X2,X3) = and_star(X3,X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
not(and_star(X2,X3)) = not(and_star(X3,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
not(and_star(X2,X3)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c51,c45]) ).
cnf(c53,plain,
implies(X2,not(X3)) = implies(X3,not(X2)),
inference(transitivity,[status(thm)],[c47,c52]) ).
cnf(c54,plain,
implies(y,not(not(x))) = implies(not(x),not(y)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
implies(not(x),not(y)) = implies(y,not(not(x))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
implies(implies(not(x),not(y)),implies(y,x)) = implies(implies(y,not(not(x))),implies(y,x)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
not(not(X2)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c58,plain,
xor(X2,xor(truth,truth)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c25]) ).
cnf(c59,plain,
xor(not(X2),truth) = xor(X2,xor(truth,truth)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,axiom,
xor(X2,X2) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
cnf(c61,plain,
xor(truth,truth) = falsehood,
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
xor(X2,xor(truth,truth)) = xor(X2,falsehood),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
xor(X2,xor(truth,truth)) = X2,
inference(transitivity,[status(thm)],[c62,c2]) ).
cnf(c64,plain,
xor(not(X2),truth) = X2,
inference(transitivity,[status(thm)],[c59,c63]) ).
cnf(c65,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c57,c64]) ).
cnf(c66,plain,
not(not(x)) = x,
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
implies(y,not(not(x))) = implies(y,x),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
implies(implies(y,not(not(x))),implies(y,x)) = implies(implies(y,x),implies(y,x)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
implies(X2,X2) = xor(truth,and_star(X2,xor(truth,X2))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c70,plain,
and_star(xor(truth,X2),X2) = and_star(X2,xor(truth,X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c71,plain,
and_star(X2,xor(truth,X2)) = and_star(xor(truth,X2),X2),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,axiom,
and_star(xor(truth,X2),X2) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c73,plain,
and_star(X2,xor(truth,X2)) = falsehood,
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
xor(truth,and_star(X2,xor(truth,X2))) = xor(truth,falsehood),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
xor(truth,falsehood) = truth,
inference(substitution,[status(thm)],[c2]) ).
cnf(c76,plain,
xor(truth,and_star(X2,xor(truth,X2))) = truth,
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
implies(X2,X2) = truth,
inference(transitivity,[status(thm)],[c69,c76]) ).
cnf(c78,plain,
implies(implies(y,x),implies(y,x)) = truth,
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
implies(implies(y,not(not(x))),implies(y,x)) = truth,
inference(transitivity,[status(thm)],[c68,c78]) ).
cnf(c80,plain,
implies(implies(not(x),not(y)),implies(y,x)) = truth,
inference(transitivity,[status(thm)],[c56,c79]) ).
cnf(c81,plain,
$false,
inference(resolution,[status(thm)],[c1,c80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.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 15:24:29 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 Command-line arguments: --no-flatten-goal
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
% 0.19/0.49
% 0.19/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------