%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE011+4 : 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 : n013.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 0.15s 10.77s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 111 ( 57 unt; 0 def)
% Number of atoms : 186 ( 69 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 163 ( 88 ~; 53 |; 14 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 108 ( 5 sgn 35 !; 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_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(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
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] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
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(sK0(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,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_21,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_24,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_26,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_33,plain,
( addition(B,A) = one
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_35,plain,
( ~ test(A)
| addition(A,sK0(A)) = one ),
inference(resolve,[status(thm)],[c_24,c_21]) ).
fof(nnf_19,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1)))) )
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK2),skolemize(X1,sK1)],[nnf_19]) ).
cnf(c_38,negated_conjecture,
( ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1)))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,negated_conjecture,
test(sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_40,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,plain,
( c(multiplication(A,B)) = addition(c(A),c(B))
| ~ test(B)
| ~ test(A) ),
inference(clausify,[status(thm)],[test_deMorgan2]) ).
cnf(c_44,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_45,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
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_50,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_51,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_52,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_53,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_55,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_56,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_57,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_58,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_907,plain,
( c(multiplication(A,A)) = addition(c(A),c(A))
| ~ test(A) ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_61,plain,
( c(multiplication(A,A)) = c(A)
| ~ test(A) ),
inference(paramod,[status(thm)],[c_55,c_907]) ).
cnf(c_908,negated_conjecture,
( ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK2),c(sK1)))) ),
inference(paramod,[status(thm)],[c_58,c_38]) ).
cnf(c_909,negated_conjecture,
( ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(addition(sK2,c(sK2)),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)))) ),
inference(paramod,[status(thm)],[c_58,c_908]) ).
cnf(c_910,negated_conjecture,
( ~ leq(addition(addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)))) ),
inference(paramod,[status(thm)],[c_58,c_909]) ).
cnf(c_63,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2)))) ),
inference(paramod,[status(thm)],[c_58,c_910]) ).
cnf(c_66,plain,
addition(sK2,sK0(sK2)) = one,
inference(resolve,[status(thm)],[c_39,c_35]) ).
cnf(c_67,plain,
( addition(A,sK2) = one
| c(sK2) != A ),
inference(resolve,[status(thm)],[c_39,c_33]) ).
cnf(c_75,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_40,c_35]) ).
cnf(c_76,plain,
( addition(A,sK1) = one
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_40,c_33]) ).
cnf(c_129,plain,
addition(multiplication(addition(A,B),C),D) = addition(multiplication(A,C),addition(multiplication(B,C),D)),
inference(paramod,[status(thm)],[c_49,c_57]) ).
cnf(c_911,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_55,c_57]) ).
cnf(c_132,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_911]) ).
cnf(c_912,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(addition(sK2,c(sK2)),sK1),multiplication(addition(sK1,c(sK1)),sK2))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_129,c_63]) ).
cnf(c_137,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_129,c_912]) ).
cnf(c_139,plain,
( addition(B,A) != B
| leq(A,B) ),
inference(paramod,[status(thm)],[c_58,c_44]) ).
cnf(c_140,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_58,c_56]) ).
cnf(c_913,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_58,c_57]) ).
cnf(c_141,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_57,c_913]) ).
cnf(c_914,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_141,c_137]) ).
cnf(c_915,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_141,c_914]) ).
cnf(c_916,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_141,c_915]) ).
cnf(c_143,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_141,c_916]) ).
cnf(c_145,plain,
c(multiplication(sK1,sK1)) = c(sK1),
inference(resolve,[status(thm)],[c_61,c_40]) ).
cnf(c_917,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_918,plain,
addition(addition(zero,c(sK2)),sK2) = one,
inference(resolve,[status(thm)],[c_67,c_917]) ).
cnf(c_919,plain,
addition(c(sK2),sK2) = one,
inference(paramod,[status(thm)],[c_140,c_918]) ).
cnf(c_186,plain,
addition(sK2,c(sK2)) = one,
inference(paramod,[status(thm)],[c_58,c_919]) ).
cnf(c_920,plain,
c(sK1) = c(multiplication(sK1,sK1)),
inference(copy,[status(thm)],[c_145]) ).
cnf(c_921,plain,
addition(c(multiplication(sK1,sK1)),sK1) = one,
inference(resolve,[status(thm)],[c_76,c_920]) ).
cnf(c_922,plain,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_145,c_921]) ).
cnf(c_281,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_58,c_922]) ).
cnf(c_923,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(one,sK2))))) ),
inference(paramod,[status(thm)],[c_281,c_143]) ).
cnf(c_924,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),sK2)))) ),
inference(paramod,[status(thm)],[c_52,c_923]) ).
cnf(c_925,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(sK2,multiplication(c(sK2),c(sK1)))))) ),
inference(paramod,[status(thm)],[c_58,c_924]) ).
cnf(c_926,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(sK2,addition(multiplication(c(sK2),sK1),multiplication(c(sK2),c(sK1)))))) ),
inference(paramod,[status(thm)],[c_141,c_925]) ).
cnf(c_927,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),addition(sK1,c(sK1)))))) ),
inference(paramod,[status(thm)],[c_51,c_926]) ).
cnf(c_928,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),one)))) ),
inference(paramod,[status(thm)],[c_281,c_927]) ).
cnf(c_929,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),addition(sK2,c(sK2)))) ),
inference(paramod,[status(thm)],[c_53,c_928]) ).
cnf(c_930,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(sK2,sK1),one)) ),
inference(paramod,[status(thm)],[c_186,c_929]) ).
cnf(c_931,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_58,c_930]) ).
cnf(c_932,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(one,sK2)))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_281,c_931]) ).
cnf(c_933,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),sK2))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_52,c_932]) ).
cnf(c_934,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(sK2,multiplication(c(sK2),c(sK1))))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_58,c_933]) ).
cnf(c_935,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(sK2,addition(multiplication(c(sK2),sK1),multiplication(c(sK2),c(sK1))))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_141,c_934]) ).
cnf(c_936,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_51,c_935]) ).
cnf(c_937,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),one))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_281,c_936]) ).
cnf(c_938,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(sK2,c(sK2))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_53,c_937]) ).
cnf(c_939,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),one),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_186,c_938]) ).
cnf(c_282,negated_conjecture,
( ~ leq(addition(one,multiplication(sK2,sK1)),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_58,c_939]) ).
cnf(c_571,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_132,c_44]) ).
cnf(c_940,plain,
addition(sK2,one) = addition(sK2,sK0(sK2)),
inference(paramod,[status(thm)],[c_66,c_132]) ).
cnf(c_941,plain,
addition(one,sK2) = addition(sK2,sK0(sK2)),
inference(paramod,[status(thm)],[c_58,c_940]) ).
cnf(c_575,plain,
addition(one,sK2) = one,
inference(paramod,[status(thm)],[c_66,c_941]) ).
cnf(c_942,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_75,c_132]) ).
cnf(c_943,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_58,c_942]) ).
cnf(c_576,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_75,c_943]) ).
cnf(c_578,negated_conjecture,
~ leq(addition(one,multiplication(sK2,sK1)),one),
inference(resolve,[status(thm)],[c_571,c_282]) ).
cnf(c_582,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_58,c_571]) ).
cnf(c_944,negated_conjecture,
addition(one,addition(one,multiplication(sK2,sK1))) != one,
inference(resolve,[status(thm)],[c_139,c_578]) ).
cnf(c_595,negated_conjecture,
addition(one,multiplication(sK2,sK1)) != one,
inference(paramod,[status(thm)],[c_132,c_944]) ).
cnf(c_945,plain,
addition(multiplication(one,A),multiplication(sK2,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_575,c_49]) ).
cnf(c_946,plain,
addition(A,multiplication(sK2,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_52,c_945]) ).
cnf(c_598,plain,
addition(A,multiplication(sK2,A)) = A,
inference(paramod,[status(thm)],[c_52,c_946]) ).
cnf(c_610,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_57,c_582]) ).
cnf(c_702,plain,
leq(multiplication(sK2,A),addition(B,A)),
inference(paramod,[status(thm)],[c_598,c_610]) ).
cnf(c_872,plain,
leq(multiplication(sK2,sK1),one),
inference(paramod,[status(thm)],[c_576,c_702]) ).
cnf(c_947,plain,
addition(multiplication(sK2,sK1),one) = one,
inference(resolve,[status(thm)],[c_872,c_45]) ).
cnf(c_948,plain,
addition(one,multiplication(sK2,sK1)) = one,
inference(paramod,[status(thm)],[c_58,c_947]) ).
cnf(c_906,plain,
$false,
inference(resolve,[status(thm)],[c_595,c_948]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.58 % Computer : n013.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Fri Sep 25 19:12:19 UTC 2026
% 0.10/10.58 % CPUTime :
% 0.10/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.58 % Process 976937 was started by sandbox on n013,
% 0.10/10.58 % Fri Sep 25 19:12:19 2026
% 0.10/10.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/10.59
% 0.10/10.59 % From the command line: assign(max_seconds, 300).
% 0.15/10.77
% 0.15/10.77 % SZS status Theorem for theBenchmark
% 0.15/10.77
% 0.15/10.77 % Proof 1 at 0.13 (+ 0.04) seconds.
% 0.15/10.77 % Length of proof is 63.
% 0.15/10.77 % Level of proof is 9.
% 0.15/10.77 % Maximum clause weight is 46.000.
% 0.15/10.77 % Given clauses 218.
% 0.15/10.77
% 0.15/10.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------