%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.25s 0.56s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 4 RR)
% Number of literals : 39 ( 38 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 : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
implies(truth,x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c2,axiom,
implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
cnf(c3,plain,
implies(truth,X2) = xor(truth,and_star(truth,xor(truth,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
and_star(X2,Y2) = and_star(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
cnf(c5,plain,
and_star(X2,truth) = and_star(truth,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
and_star(truth,X2) = and_star(X2,truth),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
and_star(X2,truth) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
and_star(truth,X2) = X2,
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
and_star(truth,xor(truth,X2)) = xor(truth,X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
xor(truth,and_star(truth,xor(truth,X2))) = xor(truth,xor(truth,X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
xor(X2,Y2) = xor(Y2,X2),
file('/export/starexec/sandbox2/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/sandbox2/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,xor(truth,X2)) = not(xor(truth,X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
not(xor(truth,X2)) = not(not(X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c19,plain,
not(not(X2)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c14]) ).
cnf(c20,axiom,
xor(X2,xor(truth,Y2)) = xor(xor(X2,truth),Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
cnf(c21,plain,
xor(X2,xor(truth,X3)) = xor(xor(X2,truth),X3),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
xor(X2,truth) = not(X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c23,plain,
xor(xor(X3,truth),X2) = xor(not(X3),X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
xor(X3,xor(truth,X2)) = xor(not(X3),X2),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
xor(X2,xor(truth,truth)) = xor(not(X2),truth),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
xor(not(X2),truth) = xor(X2,xor(truth,truth)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,axiom,
xor(X2,X2) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
cnf(c28,plain,
xor(truth,truth) = falsehood,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
xor(X2,xor(truth,truth)) = xor(X2,falsehood),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
xor(X2,falsehood) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c31,plain,
xor(X2,xor(truth,truth)) = X2,
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
xor(not(X2),truth) = X2,
inference(transitivity,[status(thm)],[c26,c31]) ).
cnf(c33,plain,
not(not(X2)) = X2,
inference(transitivity,[status(thm)],[c19,c32]) ).
cnf(c34,plain,
not(xor(truth,X2)) = X2,
inference(transitivity,[status(thm)],[c18,c33]) ).
cnf(c35,plain,
xor(truth,xor(truth,X2)) = X2,
inference(transitivity,[status(thm)],[c17,c34]) ).
cnf(c36,plain,
xor(truth,and_star(truth,xor(truth,X2))) = X2,
inference(transitivity,[status(thm)],[c10,c35]) ).
cnf(c37,plain,
implies(truth,X2) = X2,
inference(transitivity,[status(thm)],[c3,c36]) ).
cnf(c38,plain,
implies(truth,x) = x,
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
$false,
inference(resolution,[status(thm)],[c1,c38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n013.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 15:23:51 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.56 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.25/0.56
% 0.25/0.56 % SZS status Unsatisfiable
% 0.25/0.56
% 0.25/0.56 % SZS output start CNFRefutation
% See solution above
% 0.25/0.57
% 0.25/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------