%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE083+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 : 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 07:44:16 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 37 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 1 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('theBenchmark.p',domain1) ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('theBenchmark.p',domain3) ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('theBenchmark.p',domain4) ).
fof(goals,conjecture,
! [X0] : X0 = multiplication(domain(X0),X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : X0 = multiplication(domain(X0),X0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_21,plain,
? [X0] : multiplication(domain(X0),X0) != X0,
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
multiplication(domain(sK0),sK0) != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_21]) ).
cnf(c_24,negated_conjecture,
multiplication(domain(sK0),sK0) != sK0,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_30,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_31,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_34,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_35,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_37,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_38,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_41,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_45,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_47,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_48,negated_conjecture,
multiplication(antidomain(antidomain(sK0)),sK0) != sK0,
inference(paramod,[status(thm)],[c_30,c_24]) ).
cnf(c_49,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_47,c_31]) ).
cnf(c_159,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_34,c_38]) ).
cnf(c_61,plain,
multiplication(addition(antidomain(A),B),A) = addition(zero,multiplication(B,A)),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_63,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_35,c_38]) ).
cnf(c_160,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_35,c_38]) ).
cnf(c_161,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_47,c_160]) ).
cnf(c_162,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_63,c_161]) ).
cnf(c_64,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_45,c_162]) ).
cnf(c_163,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(addition(zero,B),A),
inference(paramod,[status(thm)],[c_63,c_61]) ).
cnf(c_66,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(paramod,[status(thm)],[c_64,c_163]) ).
cnf(c_164,plain,
multiplication(one,A) = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_49,c_66]) ).
cnf(c_165,plain,
A = multiplication(antidomain(antidomain(A)),A),
inference(paramod,[status(thm)],[c_41,c_164]) ).
cnf(c_157,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(copy,[status(thm)],[c_165]) ).
cnf(c_158,plain,
$false,
inference(resolve,[status(thm)],[c_157,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE083+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 19:23:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2043995 was started by sandbox2 on n015,
% 0.09/0.36 % Fri Sep 25 19:23:12 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 27.
% 0.09/0.40 % Level of proof is 7.
% 0.09/0.40 % Maximum clause weight is 13.000.
% 0.09/0.40 % Given clauses 31.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------