%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE059+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 : Sun Sep 27 07:44:13 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 8 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('theBenchmark.p',domain5) ).
fof(goals,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> addition(domain(X0),domain(X1)) = domain(X1) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0,X1] :
( domain(X1) != addition(domain(X0),domain(X1))
& addition(X0,X1) = X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( domain(sK0) != addition(domain(sK1),domain(sK0))
& addition(sK1,sK0) = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
domain(sK0) != addition(domain(sK1),domain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
addition(domain(sK1),domain(sK0)) != domain(sK0),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
addition(sK1,sK0) = sK0,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,plain,
domain(addition(A,B)) = addition(domain(A),domain(B)),
inference(clausify,[status(thm)],[domain5]) ).
cnf(c_45,plain,
domain(sK0) = addition(domain(sK1),domain(sK0)),
inference(paramod,[status(thm)],[c_22,c_23]) ).
cnf(c_43,plain,
addition(domain(sK1),domain(sK0)) = domain(sK0),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_44,plain,
$false,
inference(resolve,[status(thm)],[c_43,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE059+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n007.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Fri Sep 25 19:16:53 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 1652791 was started by sandbox on n007,
% 0.13/0.39 % Fri Sep 25 19:16:53 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.40
% 0.13/0.40 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.41 % Length of proof is 8.
% 0.13/0.41 % Level of proof is 3.
% 0.13/0.41 % Maximum clause weight is 10.000.
% 0.13/0.41 % Given clauses 3.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------