%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ROB030-1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 07:43:29 AM UTC 2025
% Result : Unsatisfiable 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 12 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 4 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
negate(add(A,B)) != negate(B),
file('theBenchmark.p',prove_absorption_within_negation) ).
fof(e,plain,
! [A,B] :
( true != false
& eq(A,A) = true
& eq(negate(add(A,B)),negate(B)) = false ),
inference(encode_existential,[status(esa)],[g0]) ).
cnf(g1,plain,
true != false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c1,plain,
eq(X,X) = true,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c2,axiom,
add(c,d) = d,
file('theBenchmark.p',absorbtion) ).
cnf(c3,axiom,
add(X,Y) = add(Y,X),
file('ROB001-0.ax',commutativity_of_add) ).
cnf(c4,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('ROB001-0.ax',associativity_of_add) ).
cnf(c6,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c7,plain,
add(c,add(X,d)) = add(X,d),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c8,plain,
eq(negate(add(X,Y)),negate(Y)) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c9,plain,
true = false,
inference(equational,[status(thm)],[c1,c7,c8]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c9]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ROB030-1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 16:40:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.17/0.47 % SZS status Unsatisfiable
% 0.17/0.47 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------