%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE018+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 : n016.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 07:44:05 AM UTC 2026
% Result : Theorem 175.66s 23.67s
% Output : CNFRefutation 175.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 132 ( 94 unt; 0 def)
% Number of atoms : 199 ( 102 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 105 ( 38 ~; 40 |; 17 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 147 ( 10 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(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_4,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('theBenchmark.p',test_4) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(multiplication(X0,c(X1)),X2)
=> leq(X0,addition(X1,X2)) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(multiplication(X0,c(X1)),X2)
=> leq(X0,addition(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
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_18,plain,
( ~ complement(B,A)
| test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
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]) ).
cnf(c_22,plain,
( c(A) = zero
| test(A) ),
inference(clausify,[status(thm)],[test_4]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( ~ leq(X0,addition(X1,X2))
& leq(multiplication(X0,c(X1)),X2)
& test(X2)
& test(X1)
& test(X0) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(sK1,addition(sK2,sK3))
& leq(multiplication(sK1,c(sK2)),sK3)
& test(sK3)
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[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_30,negated_conjecture,
( complement(sK2,A)
| c(sK2) != A ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_32,negated_conjecture,
complement(sK0(sK1),sK1),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_36,plain,
( complement(A,B)
| c(A) != B
| c(A) = zero ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_39,plain,
( ~ complement(C,A)
| complement(A,B)
| c(A) != B ),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_40,plain,
( complement(sK0(B),B)
| ~ complement(A,B) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_41,negated_conjecture,
~ leq(sK1,addition(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_42,negated_conjecture,
leq(multiplication(sK1,c(sK2)),sK3),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_43,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_44,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_45,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_46,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_47,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_48,plain,
( addition(A,B) = B
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_50,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_51,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_52,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_53,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_54,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_55,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_56,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_57,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_58,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_59,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_60,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_61,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_66,plain,
complement(sK2,c(sK2)),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_68,plain,
( complement(A,c(A))
| c(A) = zero ),
inference(xxres,[status(thm)],[c_36]) ).
cnf(c_79,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_44,c_32]) ).
cnf(c_83,plain,
multiplication(sK0(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_45,c_32]) ).
cnf(c_21611,negated_conjecture,
addition(multiplication(sK1,c(sK2)),sK3) = sK3,
inference(resolve,[status(thm)],[c_48,c_42]) ).
cnf(c_91,negated_conjecture,
addition(sK3,multiplication(sK1,c(sK2))) = sK3,
inference(paramod,[status(thm)],[c_61,c_21611]) ).
cnf(c_21612,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| complement(zero,one) ),
inference(resolve,[status(thm)],[c_59,c_43]) ).
cnf(c_21613,plain,
( multiplication(zero,one) != zero
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_50,c_21612]) ).
cnf(c_21614,plain,
( zero != zero
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_56,c_21613]) ).
cnf(c_21615,plain,
( zero != zero
| complement(zero,one) ),
inference(copy,[status(thm)],[c_21614]) ).
cnf(c_104,plain,
complement(zero,one),
inference(copy,[status(thm)],[c_21615]) ).
cnf(c_21616,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_58,c_60]) ).
cnf(c_112,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_21616]) ).
cnf(c_116,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_127,plain,
( complement(one,A)
| c(one) != A ),
inference(resolve,[status(thm)],[c_104,c_39]) ).
cnf(c_21617,plain,
A = addition(A,zero),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_21618,plain,
( ~ complement(B,A)
| complement(A,addition(c(A),zero)) ),
inference(resolve,[status(thm)],[c_39,c_21617]) ).
cnf(c_21619,plain,
complement(one,addition(c(one),zero)),
inference(resolve,[status(thm)],[c_21618,c_104]) ).
cnf(c_21620,plain,
complement(one,addition(zero,c(one))),
inference(paramod,[status(thm)],[c_61,c_21619]) ).
cnf(c_131,plain,
complement(one,c(one)),
inference(paramod,[status(thm)],[c_116,c_21620]) ).
cnf(c_133,plain,
multiplication(sK2,c(sK2)) = zero,
inference(resolve,[status(thm)],[c_66,c_45]) ).
cnf(c_21621,plain,
addition(c(sK2),sK2) = one,
inference(resolve,[status(thm)],[c_66,c_44]) ).
cnf(c_134,plain,
addition(sK2,c(sK2)) = one,
inference(paramod,[status(thm)],[c_61,c_21621]) ).
cnf(c_135,plain,
complement(sK0(c(sK2)),c(sK2)),
inference(resolve,[status(thm)],[c_66,c_40]) ).
cnf(c_21622,plain,
multiplication(c(one),one) = zero,
inference(resolve,[status(thm)],[c_131,c_46]) ).
cnf(c_155,plain,
c(one) = zero,
inference(paramod,[status(thm)],[c_56,c_21622]) ).
cnf(c_163,plain,
( complement(one,A)
| zero != A ),
inference(paramod,[status(thm)],[c_155,c_127]) ).
cnf(c_21623,plain,
addition(multiplication(A,sK1),zero) = multiplication(addition(A,sK0(sK1)),sK1),
inference(paramod,[status(thm)],[c_83,c_52]) ).
cnf(c_21624,plain,
addition(zero,multiplication(A,sK1)) = multiplication(addition(A,sK0(sK1)),sK1),
inference(paramod,[status(thm)],[c_61,c_21623]) ).
cnf(c_21625,plain,
multiplication(A,sK1) = multiplication(addition(A,sK0(sK1)),sK1),
inference(paramod,[status(thm)],[c_116,c_21624]) ).
cnf(c_190,plain,
multiplication(addition(A,sK0(sK1)),sK1) = multiplication(A,sK1),
inference(copy,[status(thm)],[c_21625]) ).
cnf(c_21626,plain,
addition(zero,multiplication(sK2,A)) = multiplication(sK2,addition(c(sK2),A)),
inference(paramod,[status(thm)],[c_133,c_54]) ).
cnf(c_21627,plain,
multiplication(sK2,A) = multiplication(sK2,addition(c(sK2),A)),
inference(paramod,[status(thm)],[c_116,c_21626]) ).
cnf(c_252,plain,
multiplication(sK2,addition(c(sK2),A)) = multiplication(sK2,A),
inference(copy,[status(thm)],[c_21627]) ).
cnf(c_266,plain,
multiplication(c(sK2),sK0(c(sK2))) = zero,
inference(resolve,[status(thm)],[c_135,c_46]) ).
cnf(c_268,plain,
addition(c(sK2),sK0(c(sK2))) = one,
inference(resolve,[status(thm)],[c_135,c_44]) ).
cnf(c_21628,plain,
( complement(A,c(A))
| zero = c(A) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_302,plain,
( complement(A,c(A))
| complement(one,c(A)) ),
inference(resolve,[status(thm)],[c_163,c_21628]) ).
cnf(c_21629,plain,
addition(sK3,A) = addition(sK3,addition(multiplication(sK1,c(sK2)),A)),
inference(paramod,[status(thm)],[c_91,c_60]) ).
cnf(c_310,plain,
addition(sK3,addition(multiplication(sK1,c(sK2)),A)) = addition(sK3,A),
inference(copy,[status(thm)],[c_21629]) ).
cnf(c_21630,plain,
addition(zero,multiplication(A,sK0(c(sK2)))) = multiplication(addition(c(sK2),A),sK0(c(sK2))),
inference(paramod,[status(thm)],[c_266,c_52]) ).
cnf(c_21631,plain,
multiplication(A,sK0(c(sK2))) = multiplication(addition(c(sK2),A),sK0(c(sK2))),
inference(paramod,[status(thm)],[c_116,c_21630]) ).
cnf(c_326,plain,
multiplication(addition(c(sK2),A),sK0(c(sK2))) = multiplication(A,sK0(c(sK2))),
inference(copy,[status(thm)],[c_21631]) ).
cnf(c_354,plain,
( complement(sK0(c(A)),c(A))
| complement(A,c(A)) ),
inference(resolve,[status(thm)],[c_302,c_40]) ).
cnf(c_21632,plain,
multiplication(one,sK1) = multiplication(sK1,sK1),
inference(paramod,[status(thm)],[c_79,c_190]) ).
cnf(c_21633,plain,
sK1 = multiplication(sK1,sK1),
inference(paramod,[status(thm)],[c_55,c_21632]) ).
cnf(c_478,plain,
multiplication(sK1,sK1) = sK1,
inference(copy,[status(thm)],[c_21633]) ).
cnf(c_21634,plain,
multiplication(sK1,A) = multiplication(sK1,multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_478,c_57]) ).
cnf(c_483,plain,
multiplication(sK1,multiplication(sK1,A)) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_21634]) ).
cnf(c_21635,plain,
multiplication(sK2,one) = multiplication(sK2,sK0(c(sK2))),
inference(paramod,[status(thm)],[c_268,c_252]) ).
cnf(c_21636,plain,
sK2 = multiplication(sK2,sK0(c(sK2))),
inference(paramod,[status(thm)],[c_56,c_21635]) ).
cnf(c_855,plain,
multiplication(sK2,sK0(c(sK2))) = sK2,
inference(copy,[status(thm)],[c_21636]) ).
cnf(c_873,plain,
leq(A,addition(A,B)),
inference(resolve,[status(thm)],[c_112,c_47]) ).
cnf(c_21637,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_79,c_112]) ).
cnf(c_21638,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_61,c_21637]) ).
cnf(c_876,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_79,c_21638]) ).
cnf(c_910,plain,
leq(A,addition(B,A)),
inference(paramod,[status(thm)],[c_61,c_873]) ).
cnf(c_21639,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_876,c_52]) ).
cnf(c_21640,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_55,c_21639]) ).
cnf(c_933,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_55,c_21640]) ).
cnf(c_977,plain,
leq(A,addition(B,addition(C,A))),
inference(paramod,[status(thm)],[c_60,c_910]) ).
cnf(c_2565,plain,
leq(multiplication(sK1,A),addition(B,A)),
inference(paramod,[status(thm)],[c_933,c_977]) ).
cnf(c_2908,plain,
leq(multiplication(sK1,addition(multiplication(sK1,c(sK2)),A)),addition(sK3,A)),
inference(paramod,[status(thm)],[c_310,c_2565]) ).
cnf(c_21641,plain,
multiplication(addition(c(sK2),sK2),sK0(c(sK2))) = sK2,
inference(paramod,[status(thm)],[c_855,c_326]) ).
cnf(c_21642,plain,
multiplication(addition(sK2,c(sK2)),sK0(c(sK2))) = sK2,
inference(paramod,[status(thm)],[c_61,c_21641]) ).
cnf(c_21643,plain,
multiplication(one,sK0(c(sK2))) = sK2,
inference(paramod,[status(thm)],[c_134,c_21642]) ).
cnf(c_3154,plain,
sK0(c(sK2)) = sK2,
inference(paramod,[status(thm)],[c_55,c_21643]) ).
cnf(c_21644,plain,
( complement(sK0(c(A)),c(A))
| complement(sK0(c(A)),c(A)) ),
inference(resolve,[status(thm)],[c_354,c_40]) ).
cnf(c_3327,plain,
complement(sK0(c(A)),c(A)),
inference(copy,[status(thm)],[c_21644]) ).
cnf(c_3336,plain,
addition(c(A),sK0(c(A))) = one,
inference(resolve,[status(thm)],[c_3327,c_44]) ).
cnf(c_21645,plain,
addition(multiplication(sK1,A),multiplication(sK1,B)) = multiplication(sK1,addition(multiplication(sK1,A),B)),
inference(paramod,[status(thm)],[c_483,c_54]) ).
cnf(c_21646,plain,
multiplication(sK1,addition(A,B)) = multiplication(sK1,addition(multiplication(sK1,A),B)),
inference(paramod,[status(thm)],[c_54,c_21645]) ).
cnf(c_7305,plain,
multiplication(sK1,addition(multiplication(sK1,A),B)) = multiplication(sK1,addition(A,B)),
inference(copy,[status(thm)],[c_21646]) ).
cnf(c_7311,plain,
leq(multiplication(sK1,addition(c(sK2),A)),addition(sK3,A)),
inference(paramod,[status(thm)],[c_7305,c_2908]) ).
cnf(c_21647,plain,
leq(multiplication(sK1,one),addition(sK3,sK0(c(sK2)))),
inference(paramod,[status(thm)],[c_3336,c_7311]) ).
cnf(c_21648,plain,
leq(sK1,addition(sK3,sK0(c(sK2)))),
inference(paramod,[status(thm)],[c_56,c_21647]) ).
cnf(c_21649,plain,
leq(sK1,addition(sK3,sK2)),
inference(paramod,[status(thm)],[c_3154,c_21648]) ).
cnf(c_21650,plain,
leq(sK1,addition(sK2,sK3)),
inference(paramod,[status(thm)],[c_61,c_21649]) ).
cnf(c_21610,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_41,c_21650]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:18:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3079517 was started by sandbox2 on n016,
% 0.09/0.37 % Fri Sep 25 19:18:45 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 175.66/23.67
% 175.66/23.67 % given #500 (W,wt=8): 2214 leq(addition(c(c1),A),addition(A,one)). [back_rewrite(1636),rewrite([2120(2)])].
% 175.66/23.67
% 175.66/23.67 % given #1000 (T,wt=9): 5195 leq(multiplication(c1,addition(c3,A)),addition(A,one)). [para(61(a,1),2664(a,1,2))].
% 175.66/23.67
% 175.66/23.67 % given #1500 (T,wt=10): 3891 leq(multiplication(c2,multiplication(c(A),c3)),one). [para(3624(a,1),2570(a,2)),rewrite([57(5)])].
% 175.66/23.67
% 175.66/23.67 % SZS status Theorem for theBenchmark
% 175.66/23.67
% 175.66/23.67 % Proof 1 at 5.43 (+ 1.69) seconds.
% 175.66/23.67 % Length of proof is 86.
% 175.66/23.67 % Level of proof is 10.
% 175.66/23.67 % Maximum clause weight is 18.000.
% 175.66/23.67 % Given clauses 1609.
% 175.66/23.67
% 175.66/23.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------