%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE027+3 : 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 : 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 07:44:08 AM UTC 2026
% Result : Theorem 0.14s 5.57s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 11
% Syntax : Number of formulae : 99 ( 50 unt; 0 def)
% Number of atoms : 200 ( 125 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 191 ( 90 ~; 82 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 114 ( 9 sgn 35 !; 7 ?)
% 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,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
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) )
& ( ? [X5] : complement(X5,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(X5,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,X3,X4] :
( addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2))
& test(X4)
& test(X3) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( addition(multiplication(sK1,addition(multiplication(sK1,sK2),multiplication(c(sK1),sK3))),multiplication(c(sK1),sK4)) != addition(multiplication(sK1,sK2),multiplication(c(sK1),sK4))
& test(sK5)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK5,sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK1),skolemize(X4,sK5)],[nnf_19]) ).
cnf(c_58,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_60,negated_conjecture,
addition(multiplication(sK1,addition(multiplication(sK1,sK2),multiplication(c(sK1),sK3))),multiplication(c(sK1),sK4)) != addition(multiplication(sK1,sK2),multiplication(c(sK1),sK4)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_61,negated_conjecture,
addition(multiplication(c(sK1),sK4),multiplication(sK1,addition(multiplication(sK1,sK2),multiplication(c(sK1),sK3)))) != addition(multiplication(sK1,sK2),multiplication(c(sK1),sK4)),
inference(paramod,[status(thm)],[c_40,c_60]) ).
cnf(c_1649,plain,
( multiplication(c(A),c(A)) = c(addition(A,A))
| ~ test(A) ),
inference(factor,[status(thm)],[c_55]) ).
cnf(c_64,plain,
( multiplication(c(A),c(A)) = c(A)
| ~ test(A) ),
inference(paramod,[status(thm)],[c_43,c_1649]) ).
cnf(c_66,plain,
( ~ test(A)
| test(c(A)) ),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_67,plain,
( ~ test(A)
| multiplication(c(A),A) = zero ),
inference(xxres,[status(thm)],[c_36]) ).
cnf(c_1650,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_78,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_1650]) ).
cnf(c_117,plain,
( c(sK1) != A
| addition(A,sK1) = one ),
inference(resolve,[status(thm)],[c_58,c_38]) ).
cnf(c_121,plain,
multiplication(sK1,sK0(sK1)) = zero,
inference(resolve,[status(thm)],[c_58,c_33]) ).
cnf(c_122,plain,
multiplication(sK0(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_58,c_32]) ).
cnf(c_123,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_58,c_31]) ).
cnf(c_147,plain,
test(c(sK1)),
inference(resolve,[status(thm)],[c_66,c_58]) ).
cnf(c_173,plain,
multiplication(c(c(sK1)),c(c(sK1))) = c(c(sK1)),
inference(resolve,[status(thm)],[c_147,c_64]) ).
cnf(c_191,plain,
multiplication(c(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_67,c_58]) ).
cnf(c_1651,plain,
A = addition(zero,A),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_1652,plain,
addition(addition(zero,c(sK1)),sK1) = one,
inference(resolve,[status(thm)],[c_117,c_1651]) ).
cnf(c_1653,plain,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_78,c_1652]) ).
cnf(c_217,plain,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_40,c_1653]) ).
cnf(c_1654,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| addition(sK0(sK1),sK1) != one
| multiplication(sK0(sK1),sK1) != zero ),
inference(resolve,[status(thm)],[c_121,c_39]) ).
cnf(c_1655,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| addition(sK0(sK1),sK1) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_122,c_1654]) ).
cnf(c_1656,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| addition(sK1,sK0(sK1)) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_40,c_1655]) ).
cnf(c_1657,plain,
( c(sK1) = sK0(sK1)
| ~ test(sK1)
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_123,c_1656]) ).
cnf(c_1658,plain,
( sK0(sK1) = c(sK1)
| ~ test(sK1)
| one != one
| zero != zero ),
inference(copy,[status(thm)],[c_1657]) ).
cnf(c_1659,plain,
( sK0(sK1) = c(sK1)
| ~ test(sK1)
| one != one ),
inference(copy,[status(thm)],[c_1658]) ).
cnf(c_1660,plain,
( sK0(sK1) = c(sK1)
| ~ test(sK1) ),
inference(copy,[status(thm)],[c_1659]) ).
cnf(c_223,negated_conjecture,
sK0(sK1) = c(sK1),
inference(resolve,[status(thm)],[c_58,c_1660]) ).
cnf(c_1661,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,sK0(sK1)) != one
| multiplication(sK0(sK1),sK1) != zero ),
inference(resolve,[status(thm)],[c_121,c_39]) ).
cnf(c_1662,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,sK0(sK1)) != one
| multiplication(c(sK1),sK1) != zero ),
inference(paramod,[status(thm)],[c_223,c_1661]) ).
cnf(c_1663,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,sK0(sK1)) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_191,c_1662]) ).
cnf(c_1664,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| addition(sK1,c(sK1)) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_223,c_1663]) ).
cnf(c_1665,plain,
( c(sK0(sK1)) = sK1
| ~ test(sK0(sK1))
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_217,c_1664]) ).
cnf(c_1666,plain,
( c(sK0(sK1)) = sK1
| ~ test(c(sK1))
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_223,c_1665]) ).
cnf(c_1667,plain,
( c(c(sK1)) = sK1
| ~ test(c(sK1))
| one != one
| zero != zero ),
inference(paramod,[status(thm)],[c_223,c_1666]) ).
cnf(c_1668,plain,
( c(c(sK1)) = sK1
| ~ test(c(sK1))
| one != one ),
inference(copy,[status(thm)],[c_1667]) ).
cnf(c_1669,plain,
( c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(copy,[status(thm)],[c_1668]) ).
cnf(c_224,plain,
c(c(sK1)) = sK1,
inference(resolve,[status(thm)],[c_147,c_1669]) ).
cnf(c_1670,plain,
multiplication(zero,A) = multiplication(sK1,multiplication(sK0(sK1),A)),
inference(paramod,[status(thm)],[c_121,c_44]) ).
cnf(c_1671,plain,
zero = multiplication(sK1,multiplication(sK0(sK1),A)),
inference(paramod,[status(thm)],[c_52,c_1670]) ).
cnf(c_1672,plain,
zero = multiplication(sK1,multiplication(c(sK1),A)),
inference(paramod,[status(thm)],[c_223,c_1671]) ).
cnf(c_225,plain,
multiplication(sK1,multiplication(c(sK1),A)) = zero,
inference(copy,[status(thm)],[c_1672]) ).
cnf(c_1673,plain,
multiplication(sK1,c(c(sK1))) = c(c(sK1)),
inference(paramod,[status(thm)],[c_224,c_173]) ).
cnf(c_1674,plain,
multiplication(sK1,sK1) = c(c(sK1)),
inference(paramod,[status(thm)],[c_224,c_1673]) ).
cnf(c_240,plain,
multiplication(sK1,sK1) = sK1,
inference(paramod,[status(thm)],[c_224,c_1674]) ).
cnf(c_1675,plain,
multiplication(sK1,A) = multiplication(sK1,multiplication(sK1,A)),
inference(paramod,[status(thm)],[c_240,c_44]) ).
cnf(c_244,plain,
multiplication(sK1,multiplication(sK1,A)) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_1675]) ).
cnf(c_1676,plain,
addition(multiplication(sK1,A),multiplication(sK1,B)) = multiplication(sK1,addition(multiplication(sK1,A),B)),
inference(paramod,[status(thm)],[c_244,c_48]) ).
cnf(c_1677,plain,
multiplication(sK1,addition(A,B)) = multiplication(sK1,addition(multiplication(sK1,A),B)),
inference(paramod,[status(thm)],[c_48,c_1676]) ).
cnf(c_837,plain,
multiplication(sK1,addition(multiplication(sK1,A),B)) = multiplication(sK1,addition(A,B)),
inference(copy,[status(thm)],[c_1677]) ).
cnf(c_844,negated_conjecture,
addition(multiplication(c(sK1),sK4),multiplication(sK1,addition(sK2,multiplication(c(sK1),sK3)))) != addition(multiplication(sK1,sK2),multiplication(c(sK1),sK4)),
inference(paramod,[status(thm)],[c_837,c_61]) ).
cnf(c_1678,plain,
addition(multiplication(sK1,A),zero) = multiplication(sK1,addition(A,multiplication(c(sK1),B))),
inference(paramod,[status(thm)],[c_225,c_48]) ).
cnf(c_1679,plain,
addition(zero,multiplication(sK1,A)) = multiplication(sK1,addition(A,multiplication(c(sK1),B))),
inference(paramod,[status(thm)],[c_40,c_1678]) ).
cnf(c_1680,plain,
multiplication(sK1,A) = multiplication(sK1,addition(A,multiplication(c(sK1),B))),
inference(paramod,[status(thm)],[c_78,c_1679]) ).
cnf(c_1645,plain,
multiplication(sK1,addition(A,multiplication(c(sK1),B))) = multiplication(sK1,A),
inference(copy,[status(thm)],[c_1680]) ).
cnf(c_1681,negated_conjecture,
addition(multiplication(c(sK1),sK4),multiplication(sK1,sK2)) != addition(multiplication(sK1,sK2),multiplication(c(sK1),sK4)),
inference(paramod,[status(thm)],[c_1645,c_844]) ).
cnf(c_1682,negated_conjecture,
addition(multiplication(sK1,sK2),multiplication(c(sK1),sK4)) != addition(multiplication(sK1,sK2),multiplication(c(sK1),sK4)),
inference(paramod,[status(thm)],[c_40,c_1681]) ).
cnf(c_1648,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE027+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n013.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 19:14:31 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 980466 was started by sandbox2 on n013,
% 0.09/5.37 % Fri Sep 25 19:14:31 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.14/5.57
% 0.14/5.57 % SZS status Theorem for theBenchmark
% 0.14/5.57
% 0.14/5.57 % Proof 1 at 0.12 (+ 0.05) seconds.
% 0.14/5.57 % Length of proof is 59.
% 0.14/5.57 % Level of proof is 10.
% 0.14/5.57 % Maximum clause weight is 54.000.
% 0.14/5.57 % Given clauses 244.
% 0.14/5.57
% 0.14/5.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------