%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE010+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 : 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 07:44:03 AM UTC 2026
% Result : Theorem 0.20s 5.82s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 12
% Syntax : Number of formulae : 104 ( 52 unt; 0 def)
% Number of atoms : 174 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 159 ( 89 ~; 50 |; 13 &)
% ( 4 <=>; 3 =>; 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 : 91 ( 5 sgn 32 !; 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_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(goals,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(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(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(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_19,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_20,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_17,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(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(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(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_17]) ).
cnf(c_23,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,negated_conjecture,
test(sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_25,negated_conjecture,
complement(sK0(sK2),sK2),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_26,negated_conjecture,
( complement(sK2,A)
| c(sK2) != A ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_28,negated_conjecture,
complement(sK0(sK1),sK1),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_29,negated_conjecture,
( complement(sK1,A)
| c(sK1) != A ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_37,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1)))) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_42,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_43,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_46,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_47,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_49,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_50,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_51,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_53,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_55,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_56,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_1257,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1)))) ),
inference(paramod,[status(thm)],[c_47,c_37]) ).
cnf(c_1258,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1)))) ),
inference(paramod,[status(thm)],[c_56,c_1257]) ).
cnf(c_1259,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))),multiplication(c(sK2),c(sK1)))) ),
inference(paramod,[status(thm)],[c_56,c_1258]) ).
cnf(c_1260,negated_conjecture,
( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_56,c_1259]) ).
cnf(c_1261,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_47,c_1260]) ).
cnf(c_1262,negated_conjecture,
( ~ leq(addition(addition(addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_56,c_1261]) ).
cnf(c_1263,negated_conjecture,
( ~ leq(addition(addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))),multiplication(c(sK2),c(sK1))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_56,c_1262]) ).
cnf(c_60,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2)))),one)
| ~ leq(one,addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))))) ),
inference(paramod,[status(thm)],[c_56,c_1263]) ).
cnf(c_61,plain,
complement(sK2,c(sK2)),
inference(xxres,[status(thm)],[c_26]) ).
cnf(c_62,plain,
complement(sK1,c(sK1)),
inference(xxres,[status(thm)],[c_29]) ).
cnf(c_72,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_39,c_28]) ).
cnf(c_73,plain,
addition(sK2,sK0(sK2)) = one,
inference(resolve,[status(thm)],[c_39,c_25]) ).
cnf(c_1264,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_53,c_55]) ).
cnf(c_108,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_1264]) ).
cnf(c_114,plain,
( addition(B,A) != B
| leq(A,B) ),
inference(paramod,[status(thm)],[c_56,c_42]) ).
cnf(c_1265,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_56,c_55]) ).
cnf(c_116,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_55,c_1265]) ).
cnf(c_1266,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(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_116,c_60]) ).
cnf(c_1267,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(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_116,c_1266]) ).
cnf(c_1268,negated_conjecture,
( ~ leq(addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(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_116,c_1267]) ).
cnf(c_1269,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_116,c_1268]) ).
cnf(c_1270,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_116,c_1269]) ).
cnf(c_117,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_116,c_1270]) ).
cnf(c_1271,plain,
addition(c(sK2),sK2) = one,
inference(resolve,[status(thm)],[c_61,c_39]) ).
cnf(c_120,plain,
addition(sK2,c(sK2)) = one,
inference(paramod,[status(thm)],[c_56,c_1271]) ).
cnf(c_1272,plain,
addition(c(sK1),sK1) = one,
inference(resolve,[status(thm)],[c_62,c_39]) ).
cnf(c_131,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_56,c_1272]) ).
cnf(c_1273,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_131,c_117]) ).
cnf(c_1274,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_50,c_1273]) ).
cnf(c_1275,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_56,c_1274]) ).
cnf(c_1276,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_116,c_1275]) ).
cnf(c_1277,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_49,c_1276]) ).
cnf(c_1278,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_131,c_1277]) ).
cnf(c_1279,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_51,c_1278]) ).
cnf(c_1280,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_120,c_1279]) ).
cnf(c_1281,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_56,c_1280]) ).
cnf(c_1282,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_131,c_1281]) ).
cnf(c_1283,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_50,c_1282]) ).
cnf(c_1284,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_56,c_1283]) ).
cnf(c_1285,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_116,c_1284]) ).
cnf(c_1286,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_49,c_1285]) ).
cnf(c_1287,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_131,c_1286]) ).
cnf(c_1288,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),addition(sK2,c(sK2))),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_51,c_1287]) ).
cnf(c_1289,negated_conjecture,
( ~ leq(addition(multiplication(sK2,sK1),one),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_120,c_1288]) ).
cnf(c_135,negated_conjecture,
( ~ leq(addition(one,multiplication(sK2,sK1)),one)
| ~ leq(one,addition(one,multiplication(sK2,sK1))) ),
inference(paramod,[status(thm)],[c_56,c_1289]) ).
cnf(c_394,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_108,c_42]) ).
cnf(c_1290,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_72,c_108]) ).
cnf(c_1291,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_56,c_1290]) ).
cnf(c_398,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_72,c_1291]) ).
cnf(c_1292,plain,
addition(sK2,one) = addition(sK2,sK0(sK2)),
inference(paramod,[status(thm)],[c_73,c_108]) ).
cnf(c_1293,plain,
addition(one,sK2) = addition(sK2,sK0(sK2)),
inference(paramod,[status(thm)],[c_56,c_1292]) ).
cnf(c_399,plain,
addition(one,sK2) = one,
inference(paramod,[status(thm)],[c_73,c_1293]) ).
cnf(c_407,negated_conjecture,
~ leq(addition(one,multiplication(sK2,sK1)),one),
inference(resolve,[status(thm)],[c_394,c_135]) ).
cnf(c_1294,negated_conjecture,
addition(one,addition(one,multiplication(sK2,sK1))) != one,
inference(resolve,[status(thm)],[c_114,c_407]) ).
cnf(c_422,negated_conjecture,
addition(one,multiplication(sK2,sK1)) != one,
inference(paramod,[status(thm)],[c_108,c_1294]) ).
cnf(c_426,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_56,c_394]) ).
cnf(c_1295,plain,
addition(multiplication(A,one),multiplication(A,sK1)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_398,c_49]) ).
cnf(c_1296,plain,
addition(A,multiplication(A,sK1)) = multiplication(A,one),
inference(paramod,[status(thm)],[c_51,c_1295]) ).
cnf(c_464,plain,
addition(A,multiplication(A,sK1)) = A,
inference(paramod,[status(thm)],[c_51,c_1296]) ).
cnf(c_485,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_55,c_426]) ).
cnf(c_822,plain,
leq(multiplication(A,sK1),addition(B,A)),
inference(paramod,[status(thm)],[c_464,c_485]) ).
cnf(c_1247,plain,
leq(multiplication(sK2,sK1),one),
inference(paramod,[status(thm)],[c_399,c_822]) ).
cnf(c_1297,plain,
addition(multiplication(sK2,sK1),one) = one,
inference(resolve,[status(thm)],[c_1247,c_43]) ).
cnf(c_1298,plain,
addition(one,multiplication(sK2,sK1)) = one,
inference(paramod,[status(thm)],[c_56,c_1297]) ).
cnf(c_1256,plain,
$false,
inference(resolve,[status(thm)],[c_422,c_1298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n011.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Fri Sep 25 19:12:49 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.42 % Process 2648669 was started by sandbox2 on n011,
% 0.16/5.42 % Fri Sep 25 19:12:49 2026
% 0.16/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.43
% 0.16/5.43 % From the command line: assign(max_seconds, 300).
% 0.20/5.82
% 0.20/5.82 % SZS status Theorem for theBenchmark
% 0.20/5.82
% 0.20/5.82 % Proof 1 at 0.24 (+ 0.12) seconds.
% 0.20/5.82 % Length of proof is 56.
% 0.20/5.82 % Level of proof is 8.
% 0.20/5.82 % Maximum clause weight is 50.000.
% 0.20/5.82 % Given clauses 197.
% 0.20/5.82
% 0.20/5.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------