%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : ROB009-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.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 07:43:27 AM UTC 2025
% Result : Unsatisfiable 0.55s 0.73s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 6 RR)
% Number of literals : 14 ( 13 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != b,
file('theBenchmark.p',prove_result) ).
cnf(c1,axiom,
add(X,Y) = add(Y,X),
file('ROB001-0.ax',commutativity_of_add) ).
cnf(c2,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)),
file('ROB001-0.ax',associativity_of_add) ).
cnf(c3,plain,
add(X,add(Y,Z)) = add(Y,add(X,Z)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(c4,axiom,
negate(add(a,negate(add(b,c)))) = negate(add(b,negate(add(a,c)))),
file('theBenchmark.p',condition) ).
cnf(c5,plain,
negate(add(a,negate(add(c,b)))) = negate(add(negate(add(c,a)),b)),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('ROB001-0.ax',robbins_axiom) ).
cnf(c7,plain,
negate(add(negate(add(X,Y)),negate(add(Y,negate(X))))) = Y,
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c8,plain,
negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X,
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c22,plain,
negate(add(negate(add(X,add(Y,Z))),negate(add(negate(add(X,Z)),Y)))) = Y,
inference(equational,[status(thm)],[c3,c8]) ).
cnf(c23,plain,
negate(add(negate(add(X,add(Y,Z))),negate(add(Z,negate(add(X,Y)))))) = Z,
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c24,plain,
b = a,
inference(equational,[status(thm)],[c5,c22,c23]) ).
cnf(g1,plain,
a = b,
inference(equational,[status(thm)],[c24]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ROB009-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.31 % Computer : n012.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon Jul 14 16:39:04 EDT 2025
% 0.12/0.31 % CPUTime :
% 0.55/0.73 % SZS status Unsatisfiable
% 0.55/0.73 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------