%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:01:21 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of clauses : 84 ( 84 unt; 0 nHn; 64 RR)
% Number of literals : 84 ( 83 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c2,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
f(n3,n3) = f(n3,f(n2,n1)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c4,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
cnf(c5,plain,
f(n2,f(n1,X2)) = f(f(n2,n1),f(n2,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
f(n2,n1) = n3,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c7,plain,
f(f(n2,n1),f(n2,X2)) = f(n3,f(n2,X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
f(n2,f(n1,X2)) = f(n3,f(n2,X2)),
inference(transitivity,[status(thm)],[c5,c7]) ).
cnf(c9,plain,
f(n2,f(n1,n1)) = f(n3,f(n2,n1)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
f(n3,f(n2,n1)) = f(n2,f(n1,n1)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
f(n1,n1) = n2,
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
f(n2,f(n1,n1)) = f(n2,n2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
f(n2,f(n1,n1)) = u,
inference(transitivity,[status(thm)],[c13,c15]) ).
cnf(c17,plain,
f(n3,f(n2,n1)) = u,
inference(transitivity,[status(thm)],[c10,c16]) ).
cnf(c18,plain,
f(n3,n3) = u,
inference(transitivity,[status(thm)],[c3,c17]) ).
cnf(c19,plain,
u = f(n3,n3),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
f(f(n3,X2),u) = f(f(n3,X2),f(n3,n3)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
f(n3,f(X2,n3)) = f(f(n3,X2),f(n3,n3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c22,plain,
f(f(n3,X2),f(n3,n3)) = f(n3,f(X2,n3)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
f(f(n3,X2),u) = f(n3,f(X2,n3)),
inference(transitivity,[status(thm)],[c20,c22]) ).
cnf(c24,plain,
f(f(n3,n2),u) = f(n3,f(n2,n3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
f(u,n3) = f(f(n2,n2),n3),
inference(congruence,[status(thm)],[c14]) ).
cnf(c26,plain,
f(f(n2,X2),n3) = f(f(n2,X2),f(n2,n1)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c27,plain,
f(n2,f(X2,n1)) = f(f(n2,X2),f(n2,n1)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c28,plain,
f(f(n2,X2),f(n2,n1)) = f(n2,f(X2,n1)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
f(f(n2,X2),n3) = f(n2,f(X2,n1)),
inference(transitivity,[status(thm)],[c26,c28]) ).
cnf(c30,plain,
f(f(n2,n2),n3) = f(n2,f(n2,n1)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
f(n2,n1) = n3,
inference(symmetry,[status(thm)],[c2]) ).
cnf(c32,plain,
f(n2,f(n2,n1)) = f(n2,n3),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
f(f(n2,n2),n3) = f(n2,n3),
inference(transitivity,[status(thm)],[c30,c32]) ).
cnf(c34,plain,
f(u,n3) = f(n2,n3),
inference(transitivity,[status(thm)],[c25,c33]) ).
cnf(c35,plain,
f(n2,n3) = f(u,n3),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
f(n3,f(n2,n3)) = f(n3,f(u,n3)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
f(f(n3,u),u) = f(n3,f(u,n3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c38,plain,
f(n3,f(u,n3)) = f(f(n3,u),u),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
f(u,u) = f(u,f(n2,n2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c40,plain,
f(u,f(n2,X2)) = f(f(n2,n2),f(n2,X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c41,plain,
f(n2,f(n2,X2)) = f(f(n2,n2),f(n2,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c42,plain,
f(f(n2,n2),f(n2,X2)) = f(n2,f(n2,X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
f(u,f(n2,X2)) = f(n2,f(n2,X2)),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
f(u,f(n2,n2)) = f(n2,f(n2,n2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c14]) ).
cnf(c46,plain,
f(n2,f(n2,n2)) = f(n2,u),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
f(n1,n2) = f(n1,f(n1,n1)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c48,plain,
f(n2,f(n1,X2)) = f(f(n1,n1),f(n1,X2)),
inference(congruence,[status(thm)],[c11]) ).
cnf(c49,plain,
f(n1,f(n1,X2)) = f(f(n1,n1),f(n1,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c50,plain,
f(f(n1,n1),f(n1,X2)) = f(n1,f(n1,X2)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
f(n2,f(n1,X2)) = f(n1,f(n1,X2)),
inference(transitivity,[status(thm)],[c48,c50]) ).
cnf(c52,plain,
f(n2,f(n1,n1)) = f(n1,f(n1,n1)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
f(n1,f(n1,n1)) = f(n2,f(n1,n1)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
f(n1,n1) = n2,
inference(symmetry,[status(thm)],[c11]) ).
cnf(c55,plain,
f(n2,f(n1,n1)) = f(n2,n2),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c14]) ).
cnf(c57,plain,
f(n2,f(n1,n1)) = u,
inference(transitivity,[status(thm)],[c55,c56]) ).
cnf(c58,plain,
f(n1,f(n1,n1)) = u,
inference(transitivity,[status(thm)],[c53,c57]) ).
cnf(c59,plain,
f(n1,n2) = u,
inference(transitivity,[status(thm)],[c47,c58]) ).
cnf(c60,plain,
u = f(n1,n2),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c61,plain,
f(n2,u) = f(n2,f(n1,n2)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
f(n2,f(n1,n2)) = f(n1,f(n1,n2)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c63,plain,
f(n1,f(n1,n2)) = f(n1,u),
inference(congruence,[status(thm)],[c59]) ).
cnf(c64,plain,
f(n2,f(n1,n2)) = f(n1,u),
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
f(n2,u) = f(n1,u),
inference(transitivity,[status(thm)],[c61,c64]) ).
cnf(c66,plain,
f(n1,u) = f(n2,u),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
u = f(n1,n2),
inference(symmetry,[status(thm)],[c59]) ).
cnf(c68,plain,
f(n2,u) = f(n2,f(n1,n2)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
f(n2,f(n1,n2)) = f(n3,f(n2,n2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c70,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[c14]) ).
cnf(c71,plain,
f(n3,f(n2,n2)) = f(n3,u),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
f(n2,f(n1,n2)) = f(n3,u),
inference(transitivity,[status(thm)],[c69,c71]) ).
cnf(c73,plain,
f(n2,u) = f(n3,u),
inference(transitivity,[status(thm)],[c68,c72]) ).
cnf(c74,plain,
f(n1,u) = f(n3,u),
inference(transitivity,[status(thm)],[c66,c73]) ).
cnf(c75,plain,
f(n2,u) = f(n3,u),
inference(transitivity,[status(thm)],[c65,c74]) ).
cnf(c76,plain,
f(n2,f(n2,n2)) = f(n3,u),
inference(transitivity,[status(thm)],[c46,c75]) ).
cnf(c77,plain,
f(u,f(n2,n2)) = f(n3,u),
inference(transitivity,[status(thm)],[c44,c76]) ).
cnf(c78,plain,
f(u,u) = f(n3,u),
inference(transitivity,[status(thm)],[c39,c77]) ).
cnf(c79,plain,
f(n3,u) = f(u,u),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
f(f(n3,u),u) = f(f(u,u),u),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
f(n3,f(u,n3)) = f(f(u,u),u),
inference(transitivity,[status(thm)],[c38,c80]) ).
cnf(c82,plain,
f(n3,f(n2,n3)) = f(f(u,u),u),
inference(transitivity,[status(thm)],[c36,c81]) ).
cnf(c83,plain,
f(f(n3,n2),u) = f(f(u,u),u),
inference(transitivity,[status(thm)],[c24,c82]) ).
cnf(c84,plain,
$false,
inference(resolution,[status(thm)],[c1,c83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 17:05:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 Command-line arguments: --no-flatten-goal
% 0.17/0.46
% 0.17/0.46 % SZS status Unsatisfiable
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation
% See solution above
% 0.17/0.48
% 0.17/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------