%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE024+2 : 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 : n018.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 18.01s 3.31s
% Output : CNFRefutation 18.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 99 ( 50 unt; 0 def)
% Number of atoms : 204 ( 129 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 192 ( 87 ~; 82 |; 14 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 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 : 100 ( 5 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
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(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_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_deMorgan1,axiom,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> c(addition(X0,X1)) = multiplication(c(X0),c(X1)) ),
file('theBenchmark.p',test_deMorgan1) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ),
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]) ).
cnf(c_27,plain,
( multiplication(B,A) = 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_32,plain,
( multiplication(sK0(A),A) = zero
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_26]) ).
cnf(c_33,plain,
( multiplication(A,sK0(A)) = zero
| ~ test(A) ),
inference(resolve,[status(thm)],[c_29,c_27]) ).
cnf(c_34,plain,
( c(B) != A
| ~ test(B)
| test(A) ),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_36,plain,
( c(B) != A
| ~ test(B)
| multiplication(A,B) = zero ),
inference(resolve,[status(thm)],[c_27,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_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_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_52,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_54,plain,
( c(addition(A,B)) = multiplication(c(A),c(B))
| ~ test(B)
| ~ test(A) ),
inference(clausify,[status(thm)],[test_deMorgan1]) ).
cnf(c_55,plain,
( multiplication(c(A),c(B)) = c(addition(A,B))
| ~ test(B)
| ~ test(A) ),
inference(copy,[status(thm)],[c_54]) ).
fof(nnf_19,plain,
? [X0,X1,X2] :
( multiplication(multiplication(X1,X0),c(X2)) != zero
& multiplication(c(X1),X0) = addition(multiplication(X0,c(X2)),multiplication(c(X1),X0))
& test(X2)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( multiplication(multiplication(sK1,sK2),c(sK3)) != zero
& multiplication(c(sK1),sK2) = addition(multiplication(sK2,c(sK3)),multiplication(c(sK1),sK2))
& test(sK3)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK3,sK2]),skolemize(X0,sK2),skolemize(X1,sK1),skolemize(X2,sK3)],[nnf_19]) ).
cnf(c_58,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_60,negated_conjecture,
multiplication(c(sK1),sK2) = addition(multiplication(sK2,c(sK3)),multiplication(c(sK1),sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_61,negated_conjecture,
addition(multiplication(sK2,c(sK3)),multiplication(c(sK1),sK2)) = multiplication(c(sK1),sK2),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_62,negated_conjecture,
multiplication(multiplication(sK1,sK2),c(sK3)) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_63,negated_conjecture,
multiplication(sK1,multiplication(sK2,c(sK3))) != zero,
inference(paramod,[status(thm)],[c_44,c_62]) ).
cnf(c_6797,plain,
( multiplication(c(A),c(A)) = c(addition(A,A))
| ~ test(A) ),
inference(factor,[status(thm)],[c_55]) ).
cnf(c_66,plain,
( multiplication(c(A),c(A)) = c(A)
| ~ test(A) ),
inference(paramod,[status(thm)],[c_43,c_6797]) ).
cnf(c_68,plain,
( ~ test(A)
| test(c(A)) ),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_69,plain,
( ~ test(A)
| multiplication(c(A),A) = zero ),
inference(xxres,[status(thm)],[c_36]) ).
cnf(c_6798,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_80,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_6798]) ).
cnf(c_119,plain,
( c(sK1) != A
| addition(A,sK1) = one ),
inference(resolve,[status(thm)],[c_58,c_38]) ).
cnf(c_123,plain,
multiplication(sK1,sK0(sK1)) = zero,
inference(resolve,[status(thm)],[c_58,c_33]) ).
cnf(c_124,plain,
multiplication(sK0(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_58,c_32]) ).
cnf(c_125,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_58,c_31]) ).
cnf(c_153,plain,
test(c(sK1)),
inference(resolve,[status(thm)],[c_68,c_58]) ).
cnf(c_179,plain,
multiplication(c(c(sK1)),c(c(sK1))) = c(c(sK1)),
inference(resolve,[status(thm)],[c_153,c_66]) ).
cnf(c_197,plain,
multiplication(c(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_69,c_58]) ).
cnf(c_6799,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_6800,plain,
addition(addition(zero,c(sK1)),sK1) = one,
inference(resolve,[status(thm)],[c_119,c_6799]) ).
cnf(c_6801,plain,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_80,c_6800]) ).
cnf(c_223,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_40,c_6801]) ).
cnf(c_6802,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| addition(sK0(sK1),sK1) != one
| multiplication(sK0(sK1),sK1) != zero ),
inference(resolve,[status(thm)],[c_123,c_39]) ).
cnf(c_6803,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| addition(sK0(sK1),sK1) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_124,c_6802]) ).
cnf(c_6804,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| addition(sK1,sK0(sK1)) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_40,c_6803]) ).
cnf(c_6805,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_125,c_6804]) ).
cnf(c_6806,plain,
( sK0(sK1) = c(sK1)
| ~ test(sK1)
| one != one
| zero != zero ),
inference(copy,[status(thm)],[c_6805]) ).
cnf(c_6807,plain,
( sK0(sK1) = c(sK1)
| ~ test(sK1)
| one != one ),
inference(copy,[status(thm)],[c_6806]) ).
cnf(c_6808,plain,
( sK0(sK1) = c(sK1)
| ~ test(sK1) ),
inference(copy,[status(thm)],[c_6807]) ).
cnf(c_229,negated_conjecture,
sK0(sK1) = c(sK1),
inference(resolve,[status(thm)],[c_58,c_6808]) ).
cnf(c_6809,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,sK0(sK1)) != one
| multiplication(sK0(sK1),sK1) != zero ),
inference(resolve,[status(thm)],[c_123,c_39]) ).
cnf(c_6810,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,sK0(sK1)) != one
| multiplication(c(sK1),sK1) != zero ),
inference(paramod,[status(thm)],[c_229,c_6809]) ).
cnf(c_6811,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,sK0(sK1)) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_197,c_6810]) ).
cnf(c_6812,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,c(sK1)) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_229,c_6811]) ).
cnf(c_6813,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_223,c_6812]) ).
cnf(c_6814,plain,
( c(sK0(sK1)) = sK1
| ~ test(c(sK1))
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_229,c_6813]) ).
cnf(c_6815,plain,
( c(c(sK1)) = sK1
| ~ test(c(sK1))
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_229,c_6814]) ).
cnf(c_6816,plain,
( c(c(sK1)) = sK1
| ~ test(c(sK1))
| one != one ),
inference(copy,[status(thm)],[c_6815]) ).
cnf(c_6817,plain,
( c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(copy,[status(thm)],[c_6816]) ).
cnf(c_230,plain,
c(c(sK1)) = sK1,
inference(resolve,[status(thm)],[c_153,c_6817]) ).
cnf(c_6818,plain,
multiplication(zero,A) = multiplication(sK1,multiplication(sK0(sK1),A)),
inference(paramod,[status(thm)],[c_123,c_44]) ).
cnf(c_6819,plain,
zero = multiplication(sK1,multiplication(sK0(sK1),A)),
inference(paramod,[status(thm)],[c_52,c_6818]) ).
cnf(c_6820,plain,
zero = multiplication(sK1,multiplication(c(sK1),A)),
inference(paramod,[status(thm)],[c_229,c_6819]) ).
cnf(c_231,plain,
multiplication(sK1,multiplication(c(sK1),A)) = zero,
inference(copy,[status(thm)],[c_6820]) ).
cnf(c_6821,plain,
multiplication(sK1,c(c(sK1))) = c(c(sK1)),
inference(paramod,[status(thm)],[c_230,c_179]) ).
cnf(c_6822,plain,
multiplication(sK1,sK1) = c(c(sK1)),
inference(paramod,[status(thm)],[c_230,c_6821]) ).
cnf(c_246,plain,
multiplication(sK1,sK1) = sK1,
inference(paramod,[status(thm)],[c_230,c_6822]) ).
cnf(c_6823,plain,
multiplication(sK1,A) = multiplication(sK1,multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_246,c_44]) ).
cnf(c_251,plain,
multiplication(sK1,multiplication(sK1,A)) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_6823]) ).
cnf(c_6824,plain,
addition(multiplication(sK1,A),multiplication(sK1,B)) = multiplication(sK1,addition(A,multiplication(sK1,B))),
inference(paramod,[status(thm)],[c_251,c_48]) ).
cnf(c_6825,plain,
multiplication(sK1,addition(A,B)) = multiplication(sK1,addition(A,multiplication(sK1,B))),
inference(paramod,[status(thm)],[c_48,c_6824]) ).
cnf(c_848,plain,
multiplication(sK1,addition(A,multiplication(sK1,B))) = multiplication(sK1,addition(A,B)),
inference(copy,[status(thm)],[c_6825]) ).
cnf(c_6826,plain,
multiplication(sK1,addition(multiplication(sK2,c(sK3)),multiplication(sK1,multiplication(c(sK1),sK2)))) = multiplication(sK1,multiplication(c(sK1),sK2)),
inference(paramod,[status(thm)],[c_61,c_848]) ).
cnf(c_6827,plain,
multiplication(sK1,addition(multiplication(sK2,c(sK3)),zero)) = multiplication(sK1,multiplication(c(sK1),sK2)),
inference(paramod,[status(thm)],[c_231,c_6826]) ).
cnf(c_6828,plain,
multiplication(sK1,addition(zero,multiplication(sK2,c(sK3)))) = multiplication(sK1,multiplication(c(sK1),sK2)),
inference(paramod,[status(thm)],[c_40,c_6827]) ).
cnf(c_6829,plain,
multiplication(sK1,multiplication(sK2,c(sK3))) = multiplication(sK1,multiplication(c(sK1),sK2)),
inference(paramod,[status(thm)],[c_80,c_6828]) ).
cnf(c_6830,plain,
multiplication(sK1,multiplication(sK2,c(sK3))) = zero,
inference(paramod,[status(thm)],[c_231,c_6829]) ).
cnf(c_6796,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_6830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE024+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n018.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Fri Sep 25 19:16:37 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.58 % Process 2619592 was started by sandbox on n018,
% 0.11/0.58 % Fri Sep 25 19:16:37 2026
% 0.11/0.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.59
% 0.11/0.59 % From the command line: assign(max_seconds, 300).
% 18.01/3.31
% 18.01/3.31 % given #500 (W,wt=33): 580 addition(A,multiplication(addition(one,B),A)) = addition(A,multiplication(B,A)). [para(94(a,2),82(a,1,2))].
% 18.01/3.31
% 18.01/3.31 % SZS status Theorem for theBenchmark
% 18.01/3.31
% 18.01/3.31 % Proof 1 at 1.83 (+ 0.53) seconds.
% 18.01/3.31 % Length of proof is 59.
% 18.01/3.31 % Level of proof is 9.
% 18.01/3.31 % Maximum clause weight is 37.000.
% 18.01/3.31 % Given clauses 517.
% 18.01/3.31
% 18.01/3.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------