%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE012+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 07:44:04 AM UTC 2026
% Result : Theorem 11.85s 1.93s
% Output : CNFRefutation 11.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of formulae : 137 ( 106 unt; 0 def)
% Number of atoms : 193 ( 135 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 43 ~; 39 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 34 !; 4 ?)
% 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(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(goals,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> multiplication(X0,X1) = multiplication(X1,X0) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> multiplication(X0,X1) = multiplication(X1,X0) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_20,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_17,plain,
? [X0,X1] :
( multiplication(X1,X0) != multiplication(X0,X1)
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(sK0,sK1) != multiplication(sK1,sK0)
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_17]) ).
cnf(c_22,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(fof_nnf,[status(thm)],[test_1]) ).
fof(sk_test_1_sk,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( complement(sK2(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK2(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_26,plain,
( complement(sK2(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_27,negated_conjecture,
complement(sK2(sK1),sK1),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_28,negated_conjecture,
complement(sK2(sK0),sK0),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_33,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_34,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_36,negated_conjecture,
( ~ complement(sK1,A)
| c(sK1) = A ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_37,negated_conjecture,
( ~ complement(sK0,A)
| c(sK0) = A ),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_40,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_41,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_42,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_43,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_45,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_46,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_47,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_52,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_53,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_54,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_55,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_56,negated_conjecture,
multiplication(sK0,sK1) != multiplication(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_64,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_65,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_3915,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_39,c_40]) ).
cnf(c_72,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_3915]) ).
cnf(c_3916,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_77,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_3916]) ).
cnf(c_3917,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_78,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_3917]) ).
cnf(c_86,plain,
addition(multiplication(A,B),multiplication(C,multiplication(D,B))) = multiplication(addition(A,multiplication(C,D)),B),
inference(paramod,[status(thm)],[c_43,c_49]) ).
cnf(c_90,plain,
multiplication(sK0,sK2(sK0)) = zero,
inference(resolve,[status(thm)],[c_52,c_28]) ).
cnf(c_91,plain,
multiplication(sK1,sK2(sK1)) = zero,
inference(resolve,[status(thm)],[c_52,c_27]) ).
cnf(c_93,plain,
multiplication(sK2(sK0),sK0) = zero,
inference(resolve,[status(thm)],[c_53,c_28]) ).
cnf(c_94,plain,
multiplication(sK2(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_53,c_27]) ).
cnf(c_96,plain,
addition(sK0,sK2(sK0)) = one,
inference(resolve,[status(thm)],[c_54,c_28]) ).
cnf(c_97,plain,
addition(sK1,sK2(sK1)) = one,
inference(resolve,[status(thm)],[c_54,c_27]) ).
cnf(c_3918,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_64,c_54]) ).
cnf(c_114,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_39,c_3918]) ).
cnf(c_115,plain,
multiplication(sK1,c(sK1)) = zero,
inference(resolve,[status(thm)],[c_64,c_53]) ).
cnf(c_3919,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_65,c_54]) ).
cnf(c_120,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_39,c_3919]) ).
cnf(c_3920,plain,
( addition(sK2(sK0),sK0) != one
| multiplication(sK2(sK0),sK0) != zero
| complement(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_90,c_55]) ).
cnf(c_3921,plain,
( addition(sK2(sK0),sK0) != one
| zero != zero
| complement(sK0,sK2(sK0)) ),
inference(paramod,[status(thm)],[c_93,c_3920]) ).
cnf(c_3922,plain,
( addition(sK0,sK2(sK0)) != one
| zero != zero
| complement(sK0,sK2(sK0)) ),
inference(paramod,[status(thm)],[c_39,c_3921]) ).
cnf(c_3923,plain,
( one != one
| zero != zero
| complement(sK0,sK2(sK0)) ),
inference(paramod,[status(thm)],[c_96,c_3922]) ).
cnf(c_3924,plain,
( one != one
| complement(sK0,sK2(sK0)) ),
inference(copy,[status(thm)],[c_3923]) ).
cnf(c_143,plain,
complement(sK0,sK2(sK0)),
inference(copy,[status(thm)],[c_3924]) ).
cnf(c_3925,plain,
addition(zero,multiplication(sK0,A)) = multiplication(sK0,addition(sK2(sK0),A)),
inference(paramod,[status(thm)],[c_90,c_47]) ).
cnf(c_3926,plain,
multiplication(sK0,A) = multiplication(sK0,addition(sK2(sK0),A)),
inference(paramod,[status(thm)],[c_77,c_3925]) ).
cnf(c_145,plain,
multiplication(sK0,addition(sK2(sK0),A)) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_3926]) ).
cnf(c_3927,plain,
addition(multiplication(sK0,A),zero) = multiplication(sK0,addition(A,sK2(sK0))),
inference(paramod,[status(thm)],[c_90,c_47]) ).
cnf(c_3928,plain,
addition(zero,multiplication(sK0,A)) = multiplication(sK0,addition(A,sK2(sK0))),
inference(paramod,[status(thm)],[c_39,c_3927]) ).
cnf(c_3929,plain,
multiplication(sK0,A) = multiplication(sK0,addition(A,sK2(sK0))),
inference(paramod,[status(thm)],[c_77,c_3928]) ).
cnf(c_146,plain,
multiplication(sK0,addition(A,sK2(sK0))) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_3929]) ).
cnf(c_3930,negated_conjecture,
c(sK0) = sK2(sK0),
inference(resolve,[status(thm)],[c_143,c_37]) ).
cnf(c_152,negated_conjecture,
sK2(sK0) = c(sK0),
inference(copy,[status(thm)],[c_3930]) ).
cnf(c_156,plain,
multiplication(sK0,addition(A,c(sK0))) = multiplication(sK0,A),
inference(paramod,[status(thm)],[c_152,c_146]) ).
cnf(c_157,plain,
multiplication(sK0,addition(c(sK0),A)) = multiplication(sK0,A),
inference(paramod,[status(thm)],[c_152,c_145]) ).
cnf(c_3931,plain,
( addition(sK2(sK1),sK1) != one
| multiplication(sK2(sK1),sK1) != zero
| complement(sK1,sK2(sK1)) ),
inference(resolve,[status(thm)],[c_91,c_55]) ).
cnf(c_3932,plain,
( addition(sK2(sK1),sK1) != one
| zero != zero
| complement(sK1,sK2(sK1)) ),
inference(paramod,[status(thm)],[c_94,c_3931]) ).
cnf(c_3933,plain,
( addition(sK1,sK2(sK1)) != one
| zero != zero
| complement(sK1,sK2(sK1)) ),
inference(paramod,[status(thm)],[c_39,c_3932]) ).
cnf(c_3934,plain,
( one != one
| zero != zero
| complement(sK1,sK2(sK1)) ),
inference(paramod,[status(thm)],[c_97,c_3933]) ).
cnf(c_3935,plain,
( one != one
| complement(sK1,sK2(sK1)) ),
inference(copy,[status(thm)],[c_3934]) ).
cnf(c_167,plain,
complement(sK1,sK2(sK1)),
inference(copy,[status(thm)],[c_3935]) ).
cnf(c_3936,plain,
addition(multiplication(sK1,A),zero) = multiplication(sK1,addition(A,sK2(sK1))),
inference(paramod,[status(thm)],[c_91,c_47]) ).
cnf(c_3937,plain,
addition(zero,multiplication(sK1,A)) = multiplication(sK1,addition(A,sK2(sK1))),
inference(paramod,[status(thm)],[c_39,c_3936]) ).
cnf(c_3938,plain,
multiplication(sK1,A) = multiplication(sK1,addition(A,sK2(sK1))),
inference(paramod,[status(thm)],[c_77,c_3937]) ).
cnf(c_170,plain,
multiplication(sK1,addition(A,sK2(sK1))) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_3938]) ).
cnf(c_3939,negated_conjecture,
c(sK1) = sK2(sK1),
inference(resolve,[status(thm)],[c_167,c_36]) ).
cnf(c_176,negated_conjecture,
sK2(sK1) = c(sK1),
inference(copy,[status(thm)],[c_3939]) ).
cnf(c_180,plain,
multiplication(sK1,addition(A,c(sK1))) = multiplication(sK1,A),
inference(paramod,[status(thm)],[c_176,c_170]) ).
cnf(c_3940,plain,
addition(A,multiplication(B,addition(C,D))) = addition(multiplication(B,C),addition(A,multiplication(B,D))),
inference(paramod,[status(thm)],[c_47,c_72]) ).
cnf(c_187,plain,
addition(multiplication(A,B),addition(C,multiplication(A,D))) = addition(C,multiplication(A,addition(B,D))),
inference(copy,[status(thm)],[c_3940]) ).
cnf(c_3941,plain,
addition(sK1,one) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_114,c_78]) ).
cnf(c_3942,plain,
addition(one,sK1) = addition(sK1,c(sK1)),
inference(paramod,[status(thm)],[c_39,c_3941]) ).
cnf(c_207,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_114,c_3942]) ).
cnf(c_3943,plain,
addition(sK0,one) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_120,c_78]) ).
cnf(c_3944,plain,
addition(one,sK0) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_39,c_3943]) ).
cnf(c_208,plain,
addition(one,sK0) = one,
inference(paramod,[status(thm)],[c_120,c_3944]) ).
cnf(c_3945,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_207,c_49]) ).
cnf(c_3946,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_45,c_3945]) ).
cnf(c_213,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_45,c_3946]) ).
cnf(c_3947,plain,
addition(multiplication(one,A),multiplication(sK0,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_208,c_49]) ).
cnf(c_3948,plain,
addition(A,multiplication(sK0,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_45,c_3947]) ).
cnf(c_219,plain,
addition(A,multiplication(sK0,A)) = A,
inference(paramod,[status(thm)],[c_45,c_3948]) ).
cnf(c_3949,plain,
addition(multiplication(sK1,A),B) = addition(B,multiplication(sK1,addition(A,B))),
inference(paramod,[status(thm)],[c_213,c_187]) ).
cnf(c_976,plain,
addition(A,multiplication(sK1,addition(B,A))) = addition(multiplication(sK1,B),A),
inference(copy,[status(thm)],[c_3949]) ).
cnf(c_3950,plain,
addition(multiplication(sK0,A),B) = addition(B,multiplication(sK0,addition(A,B))),
inference(paramod,[status(thm)],[c_219,c_187]) ).
cnf(c_977,plain,
addition(A,multiplication(sK0,addition(B,A))) = addition(multiplication(sK0,B),A),
inference(copy,[status(thm)],[c_3950]) ).
cnf(c_3951,plain,
addition(c(sK0),multiplication(sK1,one)) = addition(multiplication(sK1,sK0),c(sK0)),
inference(paramod,[status(thm)],[c_120,c_976]) ).
cnf(c_3952,plain,
addition(c(sK0),sK1) = addition(multiplication(sK1,sK0),c(sK0)),
inference(paramod,[status(thm)],[c_44,c_3951]) ).
cnf(c_3953,plain,
addition(sK1,c(sK0)) = addition(multiplication(sK1,sK0),c(sK0)),
inference(paramod,[status(thm)],[c_39,c_3952]) ).
cnf(c_3954,plain,
addition(sK1,c(sK0)) = addition(c(sK0),multiplication(sK1,sK0)),
inference(paramod,[status(thm)],[c_39,c_3953]) ).
cnf(c_3667,plain,
addition(c(sK0),multiplication(sK1,sK0)) = addition(sK1,c(sK0)),
inference(copy,[status(thm)],[c_3954]) ).
cnf(c_3955,plain,
multiplication(sK0,addition(sK1,c(sK0))) = multiplication(sK0,multiplication(sK1,sK0)),
inference(paramod,[status(thm)],[c_3667,c_157]) ).
cnf(c_3956,plain,
multiplication(sK0,sK1) = multiplication(sK0,multiplication(sK1,sK0)),
inference(paramod,[status(thm)],[c_156,c_3955]) ).
cnf(c_3834,plain,
multiplication(sK0,multiplication(sK1,sK0)) = multiplication(sK0,sK1),
inference(copy,[status(thm)],[c_3956]) ).
cnf(c_3852,plain,
addition(multiplication(A,sK0),multiplication(sK0,sK1)) = multiplication(addition(A,multiplication(sK0,sK1)),sK0),
inference(paramod,[status(thm)],[c_3834,c_86]) ).
cnf(c_3957,plain,
addition(c(sK1),multiplication(sK0,one)) = addition(multiplication(sK0,sK1),c(sK1)),
inference(paramod,[status(thm)],[c_114,c_977]) ).
cnf(c_3958,plain,
addition(c(sK1),sK0) = addition(multiplication(sK0,sK1),c(sK1)),
inference(paramod,[status(thm)],[c_44,c_3957]) ).
cnf(c_3959,plain,
addition(sK0,c(sK1)) = addition(multiplication(sK0,sK1),c(sK1)),
inference(paramod,[status(thm)],[c_39,c_3958]) ).
cnf(c_3960,plain,
addition(sK0,c(sK1)) = addition(c(sK1),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_39,c_3959]) ).
cnf(c_3863,plain,
addition(c(sK1),multiplication(sK0,sK1)) = addition(sK0,c(sK1)),
inference(copy,[status(thm)],[c_3960]) ).
cnf(c_3961,plain,
addition(multiplication(sK0,sK1),multiplication(sK1,addition(sK0,c(sK1)))) = addition(multiplication(sK1,c(sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_3863,c_976]) ).
cnf(c_3962,plain,
addition(multiplication(sK0,sK1),multiplication(sK1,sK0)) = addition(multiplication(sK1,c(sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_180,c_3961]) ).
cnf(c_3963,plain,
addition(multiplication(sK1,sK0),multiplication(sK0,sK1)) = addition(multiplication(sK1,c(sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_39,c_3962]) ).
cnf(c_3964,plain,
multiplication(addition(sK1,multiplication(sK0,sK1)),sK0) = addition(multiplication(sK1,c(sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_3852,c_3963]) ).
cnf(c_3965,plain,
multiplication(sK1,sK0) = addition(multiplication(sK1,c(sK1)),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_219,c_3964]) ).
cnf(c_3966,plain,
multiplication(sK1,sK0) = addition(zero,multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_115,c_3965]) ).
cnf(c_3967,plain,
multiplication(sK1,sK0) = multiplication(sK0,sK1),
inference(paramod,[status(thm)],[c_77,c_3966]) ).
cnf(c_3968,plain,
multiplication(sK0,sK1) = multiplication(sK1,sK0),
inference(copy,[status(thm)],[c_3967]) ).
cnf(c_3914,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_56,c_3968]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.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 19:15:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3206242 was started by sandbox on n026,
% 0.10/0.37 % Fri Sep 25 19:15:54 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 11.85/1.93
% 11.85/1.93 % SZS status Theorem for theBenchmark
% 11.85/1.93
% 11.85/1.93 % Proof 1 at 1.06 (+ 0.36) seconds.
% 11.85/1.93 % Length of proof is 77.
% 11.85/1.93 % Level of proof is 11.
% 11.85/1.93 % Maximum clause weight is 39.000.
% 11.85/1.93 % Given clauses 374.
% 11.85/1.93
% 11.85/1.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------