%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE090+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 : n011.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 07:44:18 AM UTC 2026
% Result : Theorem 109.29s 20.24s
% Output : CNFRefutation 109.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 13
% Syntax : Number of formulae : 95 ( 91 unt; 0 def)
% Number of atoms : 99 ( 98 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 2 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
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(domain2,axiom,
! [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))),
file('theBenchmark.p',domain2) ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('theBenchmark.p',domain3) ).
fof(goals,conjecture,
! [X0,X1] :
( addition(X0,X1) = X1
=> addition(antidomain(X1),antidomain(X0)) = antidomain(X0) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( addition(X0,X1) = X1
=> addition(antidomain(X1),antidomain(X0)) = antidomain(X0) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_21,plain,
? [X0,X1] :
( antidomain(X0) != addition(antidomain(X1),antidomain(X0))
& addition(X0,X1) = X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( antidomain(sK0) != addition(antidomain(sK1),antidomain(sK0))
& addition(sK0,sK1) = sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_21]) ).
cnf(c_24,negated_conjecture,
antidomain(sK0) != addition(antidomain(sK1),antidomain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_25,negated_conjecture,
addition(antidomain(sK1),antidomain(sK0)) != antidomain(sK0),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_26,negated_conjecture,
addition(sK0,sK1) = sK1,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_33,plain,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_34,plain,
antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_35,plain,
addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))),
inference(copy,[status(thm)],[c_34]) ).
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_41,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_42,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_43,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_47,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_48,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_49,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_50,plain,
addition(antidomain(A),antidomain(antidomain(A))) = one,
inference(paramod,[status(thm)],[c_49,c_33]) ).
cnf(c_52,negated_conjecture,
addition(antidomain(sK0),antidomain(sK1)) != antidomain(sK0),
inference(paramod,[status(thm)],[c_49,c_25]) ).
cnf(c_11254,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_36,c_40]) ).
cnf(c_11255,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,antidomain(B)),B),
inference(paramod,[status(thm)],[c_49,c_11254]) ).
cnf(c_64,plain,
multiplication(addition(A,antidomain(B)),B) = addition(zero,multiplication(A,B)),
inference(copy,[status(thm)],[c_11255]) ).
cnf(c_65,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_37,c_40]) ).
cnf(c_11256,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_37,c_40]) ).
cnf(c_11257,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_49,c_11256]) ).
cnf(c_11258,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_65,c_11257]) ).
cnf(c_66,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_47,c_11258]) ).
cnf(c_11259,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_65,c_64]) ).
cnf(c_67,plain,
multiplication(addition(A,antidomain(B)),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_66,c_11259]) ).
cnf(c_71,plain,
addition(zero,multiplication(A,B)) = multiplication(A,B),
inference(paramod,[status(thm)],[c_66,c_65]) ).
cnf(c_11260,plain,
addition(multiplication(antidomain(A),B),zero) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_36,c_42]) ).
cnf(c_11261,plain,
addition(zero,multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_49,c_11260]) ).
cnf(c_11262,plain,
multiplication(antidomain(A),B) = multiplication(antidomain(A),addition(B,A)),
inference(paramod,[status(thm)],[c_71,c_11261]) ).
cnf(c_75,plain,
multiplication(antidomain(A),addition(B,A)) = multiplication(antidomain(A),B),
inference(copy,[status(thm)],[c_11262]) ).
cnf(c_85,plain,
antidomain(one) = zero,
inference(paramod,[status(thm)],[c_44,c_36]) ).
cnf(c_11263,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_44,c_42]) ).
cnf(c_86,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_11263]) ).
cnf(c_11264,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_46,c_48]) ).
cnf(c_103,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_11264]) ).
cnf(c_107,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_49,c_47]) ).
cnf(c_11265,plain,
addition(one,A) = addition(antidomain(B),addition(antidomain(antidomain(B)),A)),
inference(paramod,[status(thm)],[c_50,c_48]) ).
cnf(c_109,plain,
addition(antidomain(A),addition(antidomain(antidomain(A)),B)) = addition(one,B),
inference(copy,[status(thm)],[c_11265]) ).
cnf(c_11266,plain,
addition(zero,antidomain(antidomain(one))) = one,
inference(paramod,[status(thm)],[c_85,c_50]) ).
cnf(c_11267,plain,
addition(zero,antidomain(zero)) = one,
inference(paramod,[status(thm)],[c_85,c_11266]) ).
cnf(c_126,plain,
antidomain(zero) = one,
inference(paramod,[status(thm)],[c_107,c_11267]) ).
cnf(c_11268,plain,
multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,antidomain(antidomain(B)))) = multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_35,c_67]) ).
cnf(c_11269,plain,
zero = multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))),
inference(paramod,[status(thm)],[c_36,c_11268]) ).
cnf(c_142,plain,
multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero,
inference(copy,[status(thm)],[c_11269]) ).
cnf(c_11270,plain,
addition(antidomain(A),one) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_50,c_103]) ).
cnf(c_11271,plain,
addition(one,antidomain(A)) = addition(antidomain(A),antidomain(antidomain(A))),
inference(paramod,[status(thm)],[c_49,c_11270]) ).
cnf(c_189,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_50,c_11271]) ).
cnf(c_11272,plain,
multiplication(antidomain(sK1),sK1) = multiplication(antidomain(sK1),sK0),
inference(paramod,[status(thm)],[c_26,c_75]) ).
cnf(c_11273,plain,
zero = multiplication(antidomain(sK1),sK0),
inference(paramod,[status(thm)],[c_36,c_11272]) ).
cnf(c_257,plain,
multiplication(antidomain(sK1),sK0) = zero,
inference(copy,[status(thm)],[c_11273]) ).
cnf(c_11274,plain,
multiplication(antidomain(zero),multiplication(antidomain(sK1),antidomain(antidomain(sK0)))) = zero,
inference(paramod,[status(thm)],[c_257,c_142]) ).
cnf(c_11275,plain,
multiplication(one,multiplication(antidomain(sK1),antidomain(antidomain(sK0)))) = zero,
inference(paramod,[status(thm)],[c_126,c_11274]) ).
cnf(c_1426,plain,
multiplication(antidomain(sK1),antidomain(antidomain(sK0))) = zero,
inference(paramod,[status(thm)],[c_43,c_11275]) ).
cnf(c_11276,plain,
addition(zero,multiplication(A,antidomain(antidomain(sK0)))) = multiplication(addition(antidomain(sK1),A),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_1426,c_40]) ).
cnf(c_11277,plain,
multiplication(A,antidomain(antidomain(sK0))) = multiplication(addition(antidomain(sK1),A),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_107,c_11276]) ).
cnf(c_1545,plain,
multiplication(addition(antidomain(sK1),A),antidomain(antidomain(sK0))) = multiplication(A,antidomain(antidomain(sK0))),
inference(copy,[status(thm)],[c_11277]) ).
cnf(c_11278,plain,
multiplication(one,antidomain(antidomain(sK0))) = multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_50,c_1545]) ).
cnf(c_11279,plain,
antidomain(antidomain(sK0)) = multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_43,c_11278]) ).
cnf(c_10765,plain,
multiplication(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))) = antidomain(antidomain(sK0)),
inference(copy,[status(thm)],[c_11279]) ).
cnf(c_11280,plain,
multiplication(antidomain(antidomain(sK1)),addition(one,antidomain(antidomain(sK0)))) = addition(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_10765,c_86]) ).
cnf(c_11281,plain,
multiplication(antidomain(antidomain(sK1)),one) = addition(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_189,c_11280]) ).
cnf(c_11282,plain,
antidomain(antidomain(sK1)) = addition(antidomain(antidomain(sK1)),antidomain(antidomain(sK0))),
inference(paramod,[status(thm)],[c_44,c_11281]) ).
cnf(c_11283,plain,
antidomain(antidomain(sK1)) = addition(antidomain(antidomain(sK0)),antidomain(antidomain(sK1))),
inference(paramod,[status(thm)],[c_49,c_11282]) ).
cnf(c_10795,plain,
addition(antidomain(antidomain(sK0)),antidomain(antidomain(sK1))) = antidomain(antidomain(sK1)),
inference(copy,[status(thm)],[c_11283]) ).
cnf(c_11284,plain,
addition(antidomain(sK0),antidomain(antidomain(sK1))) = addition(one,antidomain(antidomain(sK1))),
inference(paramod,[status(thm)],[c_10795,c_109]) ).
cnf(c_10824,plain,
addition(antidomain(sK0),antidomain(antidomain(sK1))) = one,
inference(paramod,[status(thm)],[c_189,c_11284]) ).
cnf(c_11285,plain,
multiplication(one,antidomain(sK1)) = multiplication(antidomain(sK0),antidomain(sK1)),
inference(paramod,[status(thm)],[c_10824,c_67]) ).
cnf(c_11286,plain,
antidomain(sK1) = multiplication(antidomain(sK0),antidomain(sK1)),
inference(paramod,[status(thm)],[c_43,c_11285]) ).
cnf(c_11225,plain,
multiplication(antidomain(sK0),antidomain(sK1)) = antidomain(sK1),
inference(copy,[status(thm)],[c_11286]) ).
cnf(c_11287,plain,
multiplication(antidomain(sK0),addition(one,antidomain(sK1))) = addition(antidomain(sK0),antidomain(sK1)),
inference(paramod,[status(thm)],[c_11225,c_86]) ).
cnf(c_11288,plain,
multiplication(antidomain(sK0),one) = addition(antidomain(sK0),antidomain(sK1)),
inference(paramod,[status(thm)],[c_189,c_11287]) ).
cnf(c_11289,plain,
antidomain(sK0) = addition(antidomain(sK0),antidomain(sK1)),
inference(paramod,[status(thm)],[c_44,c_11288]) ).
cnf(c_11290,plain,
addition(antidomain(sK0),antidomain(sK1)) = antidomain(sK0),
inference(copy,[status(thm)],[c_11289]) ).
cnf(c_11253,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_52,c_11290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE090+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n011.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Fri Sep 25 19:20:50 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 2668955 was started by sandbox2 on n011,
% 0.18/5.45 % Fri Sep 25 19:20:50 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 109.29/20.24
% 109.29/20.24 % SZS status Theorem for theBenchmark
% 109.29/20.24
% 109.29/20.24 % Proof 1 at 5.24 (+ 1.42) seconds.
% 109.29/20.24 % Length of proof is 55.
% 109.29/20.24 % Level of proof is 14.
% 109.29/20.24 % Maximum clause weight is 48.000.
% 109.29/20.24 % Given clauses 377.
% 109.29/20.24
% 109.29/20.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------