%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE058+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('theBenchmark.p',domain1) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one,
file('theBenchmark.p',domain3) ).
fof(goals,conjecture,
domain(one) = one,
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
domain(one) != one,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,negated_conjecture,
domain(one) != one,
inference(clausify,[status(thm)],[goals_neg]) ).
cnf(c_23,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_25,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_26,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_34,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_40,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_39,c_23]) ).
cnf(c_61,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(paramod,[status(thm)],[c_34,c_26]) ).
cnf(c_62,plain,
one = multiplication(domain(one),one),
inference(paramod,[status(thm)],[c_40,c_61]) ).
cnf(c_63,plain,
one = domain(one),
inference(paramod,[status(thm)],[c_34,c_62]) ).
cnf(c_59,plain,
domain(one) = one,
inference(copy,[status(thm)],[c_63]) ).
cnf(c_60,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE058+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 : Fri Sep 25 19:18:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 990133 was started by sandbox2 on n013,
% 0.14/0.37 % Fri Sep 25 19:18:36 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 14.
% 0.14/0.39 % Level of proof is 4.
% 0.14/0.39 % Maximum clause weight is 11.000.
% 0.14/0.39 % Given clauses 11.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------