%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE056+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 : n015.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 0.09s 0.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 3 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('theBenchmark.p',domain1) ).
fof(goals,conjecture,
! [X0] :
( domain(X0) = zero
=> X0 = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( domain(X0) = zero
=> X0 = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0] :
( X0 != zero
& domain(X0) = zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( sK0 != zero
& domain(sK0) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
sK0 != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
domain(sK0) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_22,negated_conjecture,
zero = domain(sK0),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_28,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_29,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_30,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_55,plain,
multiplication(domain(sK0),A) = zero,
inference(paramod,[status(thm)],[c_22,c_30]) ).
cnf(c_31,plain,
multiplication(domain(sK0),A) = domain(sK0),
inference(paramod,[status(thm)],[c_22,c_55]) ).
cnf(c_42,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_43,plain,
addition(A,domain(sK0)) = A,
inference(paramod,[status(thm)],[c_22,c_42]) ).
cnf(c_56,negated_conjecture,
sK0 != domain(sK0),
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_46,negated_conjecture,
domain(sK0) != sK0,
inference(copy,[status(thm)],[c_56]) ).
cnf(c_57,plain,
addition(sK0,domain(sK0)) = multiplication(domain(sK0),sK0),
inference(paramod,[status(thm)],[c_31,c_29]) ).
cnf(c_58,plain,
sK0 = multiplication(domain(sK0),sK0),
inference(paramod,[status(thm)],[c_43,c_57]) ).
cnf(c_59,plain,
sK0 = domain(sK0),
inference(paramod,[status(thm)],[c_31,c_58]) ).
cnf(c_53,plain,
domain(sK0) = sK0,
inference(copy,[status(thm)],[c_59]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE056+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43 % Computer : n015.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8046.5625MB
% 0.09/0.43 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Fri Sep 25 19:21:58 UTC 2026
% 0.09/0.44 % CPUTime :
% 0.09/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.44 % Process 2039489 was started by sandbox on n015,
% 0.09/0.44 % Fri Sep 25 19:21:58 2026
% 0.09/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.44
% 0.09/0.44 % From the command line: assign(max_seconds, 300).
% 0.09/0.47
% 0.09/0.47 % SZS status Theorem for theBenchmark
% 0.09/0.47
% 0.09/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.47 % Length of proof is 16.
% 0.09/0.47 % Level of proof is 5.
% 0.09/0.47 % Maximum clause weight is 11.000.
% 0.09/0.47 % Given clauses 6.
% 0.09/0.47
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------