%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE023+2 : 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 : n005.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 07:44:07 AM UTC 2026
% Result : Theorem 280.88s 38.12s
% Output : CNFRefutation 280.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 16
% Syntax : Number of formulae : 158 ( 115 unt; 0 def)
% Number of atoms : 245 ( 187 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 161 ( 74 ~; 64 |; 14 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 160 ( 3 sgn 40 !; 5 ?)
% 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_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
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(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('theBenchmark.p',right_annihilation) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('theBenchmark.p',test_1) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('theBenchmark.p',test_2) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('theBenchmark.p',test_3) ).
fof(test_deMorgan2,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(multiplication(X0,X1)) = addition(c(X0),c(X1)) ),
file('theBenchmark.p',test_deMorgan2) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X1,X0),multiplication(X0,X2)) = multiplication(X0,X2)
=> addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_22,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_23,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_24,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_25,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_26,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X3] : complement(X3,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK0(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_28,plain,
( ~ complement(B,A)
| test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_29,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_31,plain,
( addition(A,sK0(A)) = one
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_25]) ).
cnf(c_35,plain,
( addition(A,B) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| test(A) ),
inference(resolve,[status(thm)],[c_28,c_24]) ).
cnf(c_37,plain,
( c(A) != B
| ~ test(A)
| multiplication(A,B) = zero ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_38,plain,
( c(B) != A
| ~ test(B)
| addition(A,B) = one ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_39,plain,
( c(B) = A
| ~ test(B)
| addition(A,B) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_40,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_41,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_42,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_43,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_44,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_45,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_47,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_48,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_49,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_50,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_51,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_52,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_55,plain,
( c(multiplication(A,B)) = addition(c(A),c(B))
| ~ test(B)
| ~ test(A) ),
inference(clausify,[status(thm)],[test_deMorgan2]) ).
fof(nnf_19,plain,
? [X0,X1,X2] :
( multiplication(c(X1),X0) != addition(multiplication(X0,c(X2)),multiplication(c(X1),X0))
& multiplication(X0,X2) = addition(multiplication(X1,X0),multiplication(X0,X2))
& test(X2)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(c(sK1),sK3) != addition(multiplication(sK3,c(sK2)),multiplication(c(sK1),sK3))
& multiplication(sK3,sK2) = addition(multiplication(sK1,sK3),multiplication(sK3,sK2))
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK3),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_19]) ).
cnf(c_56,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_57,negated_conjecture,
test(sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_58,negated_conjecture,
multiplication(sK3,sK2) = addition(multiplication(sK1,sK3),multiplication(sK3,sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_13214,negated_conjecture,
multiplication(sK3,sK2) = addition(multiplication(sK3,sK2),multiplication(sK1,sK3)),
inference(paramod,[status(thm)],[c_40,c_58]) ).
cnf(c_59,negated_conjecture,
addition(multiplication(sK3,sK2),multiplication(sK1,sK3)) = multiplication(sK3,sK2),
inference(copy,[status(thm)],[c_13214]) ).
cnf(c_60,negated_conjecture,
multiplication(c(sK1),sK3) != addition(multiplication(sK3,c(sK2)),multiplication(c(sK1),sK3)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_13215,negated_conjecture,
multiplication(c(sK1),sK3) != addition(multiplication(c(sK1),sK3),multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_40,c_60]) ).
cnf(c_61,negated_conjecture,
addition(multiplication(c(sK1),sK3),multiplication(sK3,c(sK2))) != multiplication(c(sK1),sK3),
inference(copy,[status(thm)],[c_13215]) ).
cnf(c_13216,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_69,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_13216]) ).
cnf(c_13217,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_70,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_13217]) ).
cnf(c_13218,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_72,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_40,c_13218]) ).
cnf(c_13219,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_45,c_48]) ).
cnf(c_74,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_13219]) ).
cnf(c_101,plain,
( c(sK1) != A
| addition(A,sK1) = one ),
inference(resolve,[status(thm)],[c_56,c_38]) ).
cnf(c_102,plain,
( c(sK1) != A
| multiplication(sK1,A) = zero ),
inference(resolve,[status(thm)],[c_56,c_37]) ).
cnf(c_107,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_56,c_31]) ).
cnf(c_115,plain,
( c(sK2) != A
| multiplication(sK2,A) = zero ),
inference(resolve,[status(thm)],[c_57,c_37]) ).
cnf(c_120,plain,
addition(sK2,sK0(sK2)) = one,
inference(resolve,[status(thm)],[c_57,c_31]) ).
cnf(c_13220,plain,
( multiplication(one,zero) != zero
| multiplication(zero,one) != zero
| test(zero) ),
inference(resolve,[status(thm)],[c_69,c_35]) ).
cnf(c_13221,plain,
( multiplication(one,zero) != zero
| zero != zero
| test(zero) ),
inference(paramod,[status(thm)],[c_45,c_13220]) ).
cnf(c_13222,plain,
( zero != zero
| zero != zero
| test(zero) ),
inference(paramod,[status(thm)],[c_51,c_13221]) ).
cnf(c_13223,plain,
( zero != zero
| test(zero) ),
inference(copy,[status(thm)],[c_13222]) ).
cnf(c_143,plain,
test(zero),
inference(copy,[status(thm)],[c_13223]) ).
cnf(c_13224,plain,
( c(multiplication(zero,A)) = addition(c(zero),c(A))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_143,c_55]) ).
cnf(c_13225,plain,
( c(zero) = addition(c(zero),c(A))
| ~ test(A) ),
inference(paramod,[status(thm)],[c_52,c_13224]) ).
cnf(c_147,plain,
( addition(c(zero),c(A)) = c(zero)
| ~ test(A) ),
inference(copy,[status(thm)],[c_13225]) ).
cnf(c_13226,plain,
( c(zero) = A
| addition(A,zero) != one
| multiplication(zero,A) != zero
| multiplication(A,zero) != zero ),
inference(resolve,[status(thm)],[c_143,c_39]) ).
cnf(c_13227,plain,
( c(zero) = A
| addition(A,zero) != one
| multiplication(zero,A) != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_51,c_13226]) ).
cnf(c_13228,plain,
( c(zero) = A
| addition(A,zero) != one
| zero != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_52,c_13227]) ).
cnf(c_13229,plain,
( c(zero) = A
| A != one
| zero != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_42,c_13228]) ).
cnf(c_13230,plain,
( c(zero) = A
| one != A
| zero != zero
| zero != zero ),
inference(copy,[status(thm)],[c_13229]) ).
cnf(c_13231,plain,
( c(zero) = A
| one != A
| zero != zero ),
inference(copy,[status(thm)],[c_13230]) ).
cnf(c_150,plain,
( c(zero) = A
| one != A ),
inference(copy,[status(thm)],[c_13231]) ).
cnf(c_13232,plain,
addition(zero,sK0(zero)) = one,
inference(resolve,[status(thm)],[c_143,c_31]) ).
cnf(c_153,plain,
sK0(zero) = one,
inference(paramod,[status(thm)],[c_69,c_13232]) ).
cnf(c_13233,plain,
one = sK0(zero),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_13234,plain,
c(zero) = sK0(zero),
inference(resolve,[status(thm)],[c_150,c_13233]) ).
cnf(c_204,plain,
c(zero) = one,
inference(paramod,[status(thm)],[c_153,c_13234]) ).
cnf(c_13235,plain,
( addition(one,c(A)) = c(zero)
| ~ test(A) ),
inference(paramod,[status(thm)],[c_204,c_147]) ).
cnf(c_206,plain,
( addition(one,c(A)) = one
| ~ test(A) ),
inference(paramod,[status(thm)],[c_204,c_13235]) ).
cnf(c_13236,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_13237,plain,
addition(addition(zero,c(sK1)),sK1) = one,
inference(resolve,[status(thm)],[c_101,c_13236]) ).
cnf(c_13238,plain,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_69,c_13237]) ).
cnf(c_207,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_40,c_13238]) ).
cnf(c_13239,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_13240,plain,
multiplication(sK1,addition(zero,c(sK1))) = zero,
inference(resolve,[status(thm)],[c_102,c_13239]) ).
cnf(c_208,plain,
multiplication(sK1,c(sK1)) = zero,
inference(paramod,[status(thm)],[c_69,c_13240]) ).
cnf(c_13241,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_13242,plain,
multiplication(sK2,addition(zero,c(sK2))) = zero,
inference(resolve,[status(thm)],[c_115,c_13241]) ).
cnf(c_211,plain,
multiplication(sK2,c(sK2)) = zero,
inference(paramod,[status(thm)],[c_69,c_13242]) ).
cnf(c_13243,plain,
addition(one,A) = addition(sK1,addition(c(sK1),A)),
inference(paramod,[status(thm)],[c_207,c_41]) ).
cnf(c_251,plain,
addition(sK1,addition(c(sK1),A)) = addition(one,A),
inference(copy,[status(thm)],[c_13243]) ).
cnf(c_13244,plain,
addition(zero,multiplication(sK1,A)) = multiplication(sK1,addition(c(sK1),A)),
inference(paramod,[status(thm)],[c_208,c_48]) ).
cnf(c_13245,plain,
multiplication(sK1,A) = multiplication(sK1,addition(c(sK1),A)),
inference(paramod,[status(thm)],[c_69,c_13244]) ).
cnf(c_253,plain,
multiplication(sK1,addition(c(sK1),A)) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_13245]) ).
cnf(c_332,plain,
addition(one,c(sK2)) = one,
inference(resolve,[status(thm)],[c_206,c_57]) ).
cnf(c_13246,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_107,c_70]) ).
cnf(c_13247,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_40,c_13246]) ).
cnf(c_359,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_107,c_13247]) ).
cnf(c_13248,plain,
addition(sK2,one) = addition(sK2,sK0(sK2)),
inference(paramod,[status(thm)],[c_120,c_70]) ).
cnf(c_13249,plain,
addition(one,sK2) = addition(sK2,sK0(sK2)),
inference(paramod,[status(thm)],[c_40,c_13248]) ).
cnf(c_360,plain,
addition(one,sK2) = one,
inference(paramod,[status(thm)],[c_120,c_13249]) ).
cnf(c_13250,plain,
addition(one,A) = addition(one,addition(sK1,A)),
inference(paramod,[status(thm)],[c_359,c_41]) ).
cnf(c_361,plain,
addition(one,addition(sK1,A)) = addition(one,A),
inference(copy,[status(thm)],[c_13250]) ).
cnf(c_13251,plain,
addition(A,addition(B,addition(C,A))) = addition(addition(B,C),A),
inference(paramod,[status(thm)],[c_41,c_72]) ).
cnf(c_382,plain,
addition(A,addition(B,addition(C,A))) = addition(B,addition(C,A)),
inference(paramod,[status(thm)],[c_41,c_13251]) ).
cnf(c_391,plain,
addition(one,addition(A,sK1)) = addition(one,A),
inference(paramod,[status(thm)],[c_40,c_361]) ).
cnf(c_13252,plain,
addition(sK1,addition(c(sK1),addition(A,sK1))) = addition(one,A),
inference(paramod,[status(thm)],[c_391,c_251]) ).
cnf(c_1727,plain,
addition(c(sK1),addition(A,sK1)) = addition(one,A),
inference(paramod,[status(thm)],[c_382,c_13252]) ).
cnf(c_1750,plain,
multiplication(sK1,addition(one,A)) = multiplication(sK1,addition(A,sK1)),
inference(paramod,[status(thm)],[c_1727,c_253]) ).
cnf(c_13253,plain,
multiplication(sK1,one) = multiplication(sK1,addition(zero,sK1)),
inference(paramod,[status(thm)],[c_42,c_1750]) ).
cnf(c_13254,plain,
sK1 = multiplication(sK1,addition(zero,sK1)),
inference(paramod,[status(thm)],[c_45,c_13253]) ).
cnf(c_13255,plain,
sK1 = multiplication(sK1,sK1),
inference(paramod,[status(thm)],[c_69,c_13254]) ).
cnf(c_1756,plain,
multiplication(sK1,sK1) = sK1,
inference(copy,[status(thm)],[c_13255]) ).
cnf(c_13256,plain,
multiplication(sK1,A) = multiplication(sK1,multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_1756,c_44]) ).
cnf(c_1772,plain,
multiplication(sK1,multiplication(sK1,A)) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_13256]) ).
cnf(c_13257,plain,
addition(multiplication(sK1,A),multiplication(sK1,B)) = multiplication(sK1,addition(multiplication(sK1,A),B)),
inference(paramod,[status(thm)],[c_1772,c_48]) ).
cnf(c_13258,plain,
multiplication(sK1,addition(A,B)) = multiplication(sK1,addition(multiplication(sK1,A),B)),
inference(paramod,[status(thm)],[c_48,c_13257]) ).
cnf(c_1775,plain,
multiplication(sK1,addition(multiplication(sK1,A),B)) = multiplication(sK1,addition(A,B)),
inference(copy,[status(thm)],[c_13258]) ).
cnf(c_13259,plain,
multiplication(sK1,addition(multiplication(sK1,multiplication(sK3,sK2)),multiplication(sK1,sK3))) = multiplication(sK1,multiplication(sK3,sK2)),
inference(paramod,[status(thm)],[c_59,c_1775]) ).
cnf(c_13260,plain,
multiplication(sK1,addition(multiplication(sK1,sK3),multiplication(sK1,multiplication(sK3,sK2)))) = multiplication(sK1,multiplication(sK3,sK2)),
inference(paramod,[status(thm)],[c_40,c_13259]) ).
cnf(c_13261,plain,
multiplication(sK1,multiplication(sK1,addition(sK3,multiplication(sK3,sK2)))) = multiplication(sK1,multiplication(sK3,sK2)),
inference(paramod,[status(thm)],[c_48,c_13260]) ).
cnf(c_13262,plain,
multiplication(sK1,multiplication(sK1,multiplication(sK3,addition(one,sK2)))) = multiplication(sK1,multiplication(sK3,sK2)),
inference(paramod,[status(thm)],[c_74,c_13261]) ).
cnf(c_13263,plain,
multiplication(sK1,multiplication(sK1,multiplication(sK3,one))) = multiplication(sK1,multiplication(sK3,sK2)),
inference(paramod,[status(thm)],[c_360,c_13262]) ).
cnf(c_13264,plain,
multiplication(sK1,multiplication(sK1,sK3)) = multiplication(sK1,multiplication(sK3,sK2)),
inference(paramod,[status(thm)],[c_45,c_13263]) ).
cnf(c_13265,plain,
multiplication(sK1,sK3) = multiplication(sK1,multiplication(sK3,sK2)),
inference(paramod,[status(thm)],[c_1772,c_13264]) ).
cnf(c_4940,plain,
multiplication(sK1,multiplication(sK3,sK2)) = multiplication(sK1,sK3),
inference(copy,[status(thm)],[c_13265]) ).
cnf(c_13266,plain,
multiplication(multiplication(sK1,sK3),A) = multiplication(sK1,multiplication(multiplication(sK3,sK2),A)),
inference(paramod,[status(thm)],[c_4940,c_44]) ).
cnf(c_13267,plain,
multiplication(sK1,multiplication(sK3,A)) = multiplication(sK1,multiplication(multiplication(sK3,sK2),A)),
inference(paramod,[status(thm)],[c_44,c_13266]) ).
cnf(c_13268,plain,
multiplication(sK1,multiplication(sK3,A)) = multiplication(sK1,multiplication(sK3,multiplication(sK2,A))),
inference(paramod,[status(thm)],[c_44,c_13267]) ).
cnf(c_4952,plain,
multiplication(sK1,multiplication(sK3,multiplication(sK2,A))) = multiplication(sK1,multiplication(sK3,A)),
inference(copy,[status(thm)],[c_13268]) ).
cnf(c_13269,plain,
multiplication(sK1,multiplication(sK3,zero)) = multiplication(sK1,multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_211,c_4952]) ).
cnf(c_13270,plain,
multiplication(sK1,zero) = multiplication(sK1,multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_51,c_13269]) ).
cnf(c_13271,plain,
zero = multiplication(sK1,multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_51,c_13270]) ).
cnf(c_5577,plain,
multiplication(sK1,multiplication(sK3,c(sK2))) = zero,
inference(copy,[status(thm)],[c_13271]) ).
cnf(c_13272,plain,
addition(zero,multiplication(A,multiplication(sK3,c(sK2)))) = multiplication(addition(sK1,A),multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_5577,c_50]) ).
cnf(c_13273,plain,
multiplication(A,multiplication(sK3,c(sK2))) = multiplication(addition(sK1,A),multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_69,c_13272]) ).
cnf(c_5595,plain,
multiplication(addition(sK1,A),multiplication(sK3,c(sK2))) = multiplication(A,multiplication(sK3,c(sK2))),
inference(copy,[status(thm)],[c_13273]) ).
cnf(c_13274,plain,
multiplication(one,multiplication(sK3,c(sK2))) = multiplication(c(sK1),multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_207,c_5595]) ).
cnf(c_13275,plain,
multiplication(sK3,c(sK2)) = multiplication(c(sK1),multiplication(sK3,c(sK2))),
inference(paramod,[status(thm)],[c_46,c_13274]) ).
cnf(c_13182,plain,
multiplication(c(sK1),multiplication(sK3,c(sK2))) = multiplication(sK3,c(sK2)),
inference(copy,[status(thm)],[c_13275]) ).
cnf(c_13208,plain,
addition(multiplication(c(sK1),A),multiplication(sK3,c(sK2))) = multiplication(c(sK1),addition(A,multiplication(sK3,c(sK2)))),
inference(paramod,[status(thm)],[c_13182,c_48]) ).
cnf(c_13276,negated_conjecture,
multiplication(c(sK1),addition(sK3,multiplication(sK3,c(sK2)))) != multiplication(c(sK1),sK3),
inference(paramod,[status(thm)],[c_13208,c_61]) ).
cnf(c_13277,negated_conjecture,
multiplication(c(sK1),multiplication(sK3,addition(one,c(sK2)))) != multiplication(c(sK1),sK3),
inference(paramod,[status(thm)],[c_74,c_13276]) ).
cnf(c_13278,negated_conjecture,
multiplication(c(sK1),multiplication(sK3,one)) != multiplication(c(sK1),sK3),
inference(paramod,[status(thm)],[c_332,c_13277]) ).
cnf(c_13279,negated_conjecture,
multiplication(c(sK1),sK3) != multiplication(c(sK1),sK3),
inference(paramod,[status(thm)],[c_45,c_13278]) ).
cnf(c_13213,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_13279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:14:33 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 4123823 was started by sandbox2 on n005,
% 0.14/0.36 % Fri Sep 25 19:14:33 2026
% 0.14/0.36 % 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).
% 280.88/38.12
% 280.88/38.12 % given #500 (W,wt=33): 413 addition(A,multiplication(A,addition(c3,B))) = multiplication(A,addition(one,B)). [para(365(a,1),48(a,2,2)),rewrite([45(2)])].
% 280.88/38.12
% 280.88/38.12 % SZS status Theorem for theBenchmark
% 280.88/38.12
% 280.88/38.12 % Proof 1 at 4.27 (+ 1.20) seconds.
% 280.88/38.12 % Length of proof is 86.
% 280.88/38.12 % Level of proof is 18.
% 280.88/38.12 % Maximum clause weight is 44.000.
% 280.88/38.12 % Given clauses 978.
% 280.88/38.12
% 280.88/38.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------