%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE089+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 : n008.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 07:44:17 AM UTC 2026
% Result : Theorem 0.17s 15.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 32 unt; 0 def)
% Number of atoms : 40 ( 39 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 : 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 : 45 ( 1 sgn 13 !; 2 ?)
% 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(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(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('theBenchmark.p',domain4) ).
fof(goals,conjecture,
! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_21,plain,
? [X0,X1] :
( antidomain(X1) = addition(domain(X0),antidomain(X1))
& multiplication(domain(X0),X1) != zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( antidomain(sK0) = addition(domain(sK1),antidomain(sK0))
& multiplication(domain(sK1),sK0) != zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_21]) ).
cnf(c_24,negated_conjecture,
antidomain(sK0) = addition(domain(sK1),antidomain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_25,negated_conjecture,
addition(domain(sK1),antidomain(sK0)) = antidomain(sK0),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_26,negated_conjecture,
multiplication(domain(sK1),sK0) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,plain,
domain(A) = antidomain(antidomain(A)),
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_36,plain,
multiplication(antidomain(A),A) = zero,
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_37,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_39,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_40,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_47,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_49,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_50,negated_conjecture,
multiplication(antidomain(antidomain(sK1)),sK0) != zero,
inference(paramod,[status(thm)],[c_32,c_26]) ).
cnf(c_164,negated_conjecture,
addition(antidomain(antidomain(sK1)),antidomain(sK0)) = antidomain(sK0),
inference(paramod,[status(thm)],[c_32,c_25]) ).
cnf(c_51,negated_conjecture,
addition(antidomain(sK0),antidomain(antidomain(sK1))) = antidomain(sK0),
inference(paramod,[status(thm)],[c_49,c_164]) ).
cnf(c_165,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(antidomain(B),A),B),
inference(paramod,[status(thm)],[c_36,c_40]) ).
cnf(c_64,plain,
multiplication(addition(antidomain(A),B),A) = addition(zero,multiplication(B,A)),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_66,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_37,c_40]) ).
cnf(c_166,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_37,c_40]) ).
cnf(c_167,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_49,c_166]) ).
cnf(c_168,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_66,c_167]) ).
cnf(c_67,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_47,c_168]) ).
cnf(c_169,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(addition(zero,B),A),
inference(paramod,[status(thm)],[c_66,c_64]) ).
cnf(c_69,plain,
multiplication(addition(antidomain(A),B),A) = multiplication(B,A),
inference(paramod,[status(thm)],[c_67,c_169]) ).
cnf(c_170,plain,
multiplication(antidomain(sK0),sK0) = multiplication(antidomain(antidomain(sK1)),sK0),
inference(paramod,[status(thm)],[c_51,c_69]) ).
cnf(c_171,plain,
zero = multiplication(antidomain(antidomain(sK1)),sK0),
inference(paramod,[status(thm)],[c_36,c_170]) ).
cnf(c_162,plain,
multiplication(antidomain(antidomain(sK1)),sK0) = zero,
inference(copy,[status(thm)],[c_171]) ).
cnf(c_163,plain,
$false,
inference(resolve,[status(thm)],[c_162,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE089+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/15.44 % Computer : n008.cluster.edu
% 0.17/15.44 % Model : x86_64 x86_64
% 0.17/15.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.44 % Memory : 8046.5625MB
% 0.17/15.44 % OS : Linux 6.8.0-71-generic
% 0.17/15.44 % CPULimit : 300
% 0.17/15.44 % WCLimit : 300
% 0.17/15.44 % DateTime : Fri Sep 25 19:21:40 UTC 2026
% 0.17/15.44 % CPUTime :
% 0.17/15.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/15.45 % Process 1672570 was started by sandbox2 on n008,
% 0.17/15.45 % Fri Sep 25 19:21:40 2026
% 0.17/15.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/15.46
% 0.17/15.46 % From the command line: assign(max_seconds, 300).
% 0.17/15.49
% 0.17/15.49 % SZS status Theorem for theBenchmark
% 0.17/15.49
% 0.17/15.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/15.49 % Length of proof is 25.
% 0.17/15.49 % Level of proof is 7.
% 0.17/15.49 % Maximum clause weight is 13.000.
% 0.17/15.49 % Given clauses 32.
% 0.17/15.49
% 0.17/15.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------