%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 11:50:45 AM UTC 2026
% Result : Theorem 0.22s 0.51s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 42 RR)
% Number of literals : 87 ( 86 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_09) ).
cnf(c2,negated_conjecture,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) != '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
'==>'('+'(A,B),C) = '==>'(A,'==>'(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
cnf(c5,plain,
'==>'('+'(a,'==>'(a,b)),c) = '==>'(a,'==>'('==>'(a,b),c)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) = '+'('+'(a,'==>'(a,b)),'==>'(a,'==>'('==>'(a,b),c))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
'+'(A2,'==>'(A2,B2)) = '+'(B2,'==>'(B2,A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
cnf(c8,plain,
'+'(a,'==>'(a,b)) = '+'(b,'==>'(b,a)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
'+'('+'(a,'==>'(a,b)),'==>'(a,'==>'('==>'(a,b),c))) = '+'('+'(b,'==>'(b,a)),'==>'(a,'==>'('==>'(a,b),c))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
'+'('+'(A2,B2),C2) = '+'(A2,'+'(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
cnf(c11,plain,
'+'('+'(b,'==>'(b,a)),'==>'(a,'==>'('==>'(a,b),c))) = '+'(b,'+'('==>'(b,a),'==>'(a,'==>'('==>'(a,b),c)))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
'==>'('+'(X2,'==>'(X2,X3)),X) = '==>'(X2,'==>'('==>'(X2,X3),X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c13,plain,
'==>'(X2,'==>'('==>'(X2,X3),X)) = '==>'('+'(X2,'==>'(X2,X3)),X),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
'+'(X2,'==>'(X2,X)) = '+'(X,'==>'(X,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c15,plain,
'+'(X,'==>'(X,X2)) = '+'(X2,'==>'(X2,X)),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
'==>'('+'(X2,'==>'(X2,X3)),X) = '==>'('+'(X3,'==>'(X3,X2)),X),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
'==>'('+'(X3,'==>'(X3,X2)),X) = '==>'(X3,'==>'('==>'(X3,X2),X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c18,plain,
'==>'('+'(X2,'==>'(X2,X3)),X) = '==>'(X3,'==>'('==>'(X3,X2),X)),
inference(transitivity,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
'==>'(X2,'==>'('==>'(X2,X3),X)) = '==>'(X3,'==>'('==>'(X3,X2),X)),
inference(transitivity,[status(thm)],[c13,c18]) ).
cnf(c20,plain,
'==>'(b,'==>'('==>'(b,a),c)) = '==>'(a,'==>'('==>'(a,b),c)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
'==>'(a,'==>'('==>'(a,b),c)) = '==>'(b,'==>'('==>'(b,a),c)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
'+'('==>'(b,a),'==>'(a,'==>'('==>'(a,b),c))) = '+'('==>'(b,a),'==>'(b,'==>'('==>'(b,a),c))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
'+'(b,'+'('==>'(b,a),'==>'(a,'==>'('==>'(a,b),c)))) = '+'(b,'+'('==>'(b,a),'==>'(b,'==>'('==>'(b,a),c)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
'+'(X,'==>'(X,'==>'(X3,X2))) = '+'('==>'(X3,X2),'==>'('==>'(X3,X2),X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c25,plain,
'+'('==>'(X3,X2),'==>'('==>'(X3,X2),X)) = '+'(X,'==>'(X,'==>'(X3,X2))),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
'==>'('+'(X2,X3),X) = '==>'(X2,'==>'(X3,X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c27,plain,
'==>'(X2,'==>'(X3,X)) = '==>'('+'(X2,X3),X),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
'+'(A2,B2) = '+'(B2,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
cnf(c29,plain,
'+'(X2,X) = '+'(X,X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
'+'(X,X2) = '+'(X2,X),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
'==>'('+'(X2,X3),X) = '==>'('+'(X3,X2),X),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
'==>'('+'(X3,X2),X) = '==>'(X3,'==>'(X2,X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c33,plain,
'==>'('+'(X2,X3),X) = '==>'(X3,'==>'(X2,X)),
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
'==>'(X2,'==>'(X3,X)) = '==>'(X3,'==>'(X2,X)),
inference(transitivity,[status(thm)],[c27,c33]) ).
cnf(c35,plain,
'==>'(X3,'==>'(X,X2)) = '==>'(X,'==>'(X3,X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
'==>'(X,'==>'(X3,X2)) = '==>'(X3,'==>'(X,X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
'+'(X,'==>'(X,'==>'(X3,X2))) = '+'(X,'==>'(X3,'==>'(X,X2))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
'+'('==>'(X3,X2),'==>'('==>'(X3,X2),X)) = '+'(X,'==>'(X3,'==>'(X,X2))),
inference(transitivity,[status(thm)],[c25,c37]) ).
cnf(c39,plain,
'+'('==>'(b,c),'==>'('==>'(b,c),'==>'(b,a))) = '+'('==>'(b,a),'==>'(b,'==>'('==>'(b,a),c))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
'+'('==>'(b,a),'==>'(b,'==>'('==>'(b,a),c))) = '+'('==>'(b,c),'==>'('==>'(b,c),'==>'(b,a))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
'+'(b,'+'('==>'(b,a),'==>'(b,'==>'('==>'(b,a),c)))) = '+'(b,'+'('==>'(b,c),'==>'('==>'(b,c),'==>'(b,a)))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
'==>'(b,'==>'('==>'(b,c),a)) = '==>'('==>'(b,c),'==>'(b,a)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c43,plain,
'==>'('==>'(b,c),'==>'(b,a)) = '==>'(b,'==>'('==>'(b,c),a)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
'+'('==>'(b,c),'==>'('==>'(b,c),'==>'(b,a))) = '+'('==>'(b,c),'==>'(b,'==>'('==>'(b,c),a))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
'+'(b,'+'('==>'(b,c),'==>'('==>'(b,c),'==>'(b,a)))) = '+'(b,'+'('==>'(b,c),'==>'(b,'==>'('==>'(b,c),a)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
'+'('+'(X,'==>'(X,X3)),X2) = '+'(X,'+'('==>'(X,X3),X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c47,plain,
'+'(X,'+'('==>'(X,X3),X2)) = '+'('+'(X,'==>'(X,X3)),X2),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
'+'(X2,'==>'(X2,X)) = '+'(X,'==>'(X,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c49,plain,
'+'(X,'==>'(X,X2)) = '+'(X2,'==>'(X2,X)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
'+'('+'(X,'==>'(X,X3)),X2) = '+'('+'(X3,'==>'(X3,X)),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
'+'('+'(X3,'==>'(X3,X)),X2) = '+'(X3,'+'('==>'(X3,X),X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c52,plain,
'+'('==>'(X3,X),X2) = '+'(X2,'==>'(X3,X)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c53,plain,
'+'(X3,'+'('==>'(X3,X),X2)) = '+'(X3,'+'(X2,'==>'(X3,X))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
'+'('+'(X3,'==>'(X3,X)),X2) = '+'(X3,'+'(X2,'==>'(X3,X))),
inference(transitivity,[status(thm)],[c51,c53]) ).
cnf(c55,plain,
'+'('+'(X,'==>'(X,X3)),X2) = '+'(X3,'+'(X2,'==>'(X3,X))),
inference(transitivity,[status(thm)],[c50,c54]) ).
cnf(c56,plain,
'+'(X,'+'('==>'(X,X3),X2)) = '+'(X3,'+'(X2,'==>'(X3,X))),
inference(transitivity,[status(thm)],[c47,c55]) ).
cnf(c57,plain,
'+'(b,'+'('==>'(b,c),'==>'(b,'==>'('==>'(b,c),a)))) = '+'(c,'+'('==>'(b,'==>'('==>'(b,c),a)),'==>'(c,b))),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
'+'('==>'(b,'==>'('==>'(b,c),a)),'==>'(c,b)) = '+'('==>'(c,b),'==>'(b,'==>'('==>'(b,c),a))),
inference(substitution,[status(thm)],[c28]) ).
cnf(c59,plain,
'+'(c,'+'('==>'(b,'==>'('==>'(b,c),a)),'==>'(c,b))) = '+'(c,'+'('==>'(c,b),'==>'(b,'==>'('==>'(b,c),a)))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
'==>'(c,'==>'('==>'(c,b),a)) = '==>'(b,'==>'('==>'(b,c),a)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c61,plain,
'==>'(b,'==>'('==>'(b,c),a)) = '==>'(c,'==>'('==>'(c,b),a)),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
'+'('==>'(c,b),'==>'(b,'==>'('==>'(b,c),a))) = '+'('==>'(c,b),'==>'(c,'==>'('==>'(c,b),a))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
'+'(c,'+'('==>'(c,b),'==>'(b,'==>'('==>'(b,c),a)))) = '+'(c,'+'('==>'(c,b),'==>'(c,'==>'('==>'(c,b),a)))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
'+'('+'(X2,X),'==>'(X2,'==>'(X,X3))) = '+'(X2,'+'(X,'==>'(X2,'==>'(X,X3)))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c65,plain,
'+'(X2,'+'(X,'==>'(X2,'==>'(X,X3)))) = '+'('+'(X2,X),'==>'(X2,'==>'(X,X3))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
'==>'('+'(X2,X),X3) = '==>'(X2,'==>'(X,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c67,plain,
'==>'(X2,'==>'(X,X3)) = '==>'('+'(X2,X),X3),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
'+'('+'(X2,X),'==>'(X2,'==>'(X,X3))) = '+'('+'(X2,X),'==>'('+'(X2,X),X3)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
'+'('+'(X2,X),'==>'('+'(X2,X),X3)) = '+'(X3,'==>'(X3,'+'(X2,X))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c70,plain,
'+'('+'(X2,X),'==>'(X2,'==>'(X,X3))) = '+'(X3,'==>'(X3,'+'(X2,X))),
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
'+'(X2,'+'(X,'==>'(X2,'==>'(X,X3)))) = '+'(X3,'==>'(X3,'+'(X2,X))),
inference(transitivity,[status(thm)],[c65,c70]) ).
cnf(c72,plain,
'+'(c,'+'('==>'(c,b),'==>'(c,'==>'('==>'(c,b),a)))) = '+'(a,'==>'(a,'+'(c,'==>'(c,b)))),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
'+'(b,'==>'(b,c)) = '+'(c,'==>'(c,b)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c74,plain,
'+'(c,'==>'(c,b)) = '+'(b,'==>'(b,c)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
'==>'(a,'+'(c,'==>'(c,b))) = '==>'(a,'+'(b,'==>'(b,c))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
'+'(a,'==>'(a,'+'(c,'==>'(c,b)))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
'+'(c,'+'('==>'(c,b),'==>'(c,'==>'('==>'(c,b),a)))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c72,c76]) ).
cnf(c78,plain,
'+'(c,'+'('==>'(c,b),'==>'(b,'==>'('==>'(b,c),a)))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c63,c77]) ).
cnf(c79,plain,
'+'(c,'+'('==>'(b,'==>'('==>'(b,c),a)),'==>'(c,b))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c59,c78]) ).
cnf(c80,plain,
'+'(b,'+'('==>'(b,c),'==>'(b,'==>'('==>'(b,c),a)))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c57,c79]) ).
cnf(c81,plain,
'+'(b,'+'('==>'(b,c),'==>'('==>'(b,c),'==>'(b,a)))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c45,c80]) ).
cnf(c82,plain,
'+'(b,'+'('==>'(b,a),'==>'(b,'==>'('==>'(b,a),c)))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c41,c81]) ).
cnf(c83,plain,
'+'(b,'+'('==>'(b,a),'==>'(a,'==>'('==>'(a,b),c)))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c23,c82]) ).
cnf(c84,plain,
'+'('+'(b,'==>'(b,a)),'==>'(a,'==>'('==>'(a,b),c))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c11,c83]) ).
cnf(c85,plain,
'+'('+'(a,'==>'(a,b)),'==>'(a,'==>'('==>'(a,b),c))) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c9,c84]) ).
cnf(c86,plain,
'+'('+'(a,'==>'(a,b)),'==>'('+'(a,'==>'(a,b)),c)) = '+'(a,'==>'(a,'+'(b,'==>'(b,c)))),
inference(transitivity,[status(thm)],[c6,c85]) ).
cnf(c87,plain,
$false,
inference(resolution,[status(thm)],[c3,c86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 17:05:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 Command-line arguments: --no-flatten-goal
% 0.22/0.51
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51
% 0.22/0.51 % SZS output start CNFRefutation
% See solution above
% 0.22/0.55
% 0.22/0.55 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------