%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE026+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 : n002.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 0.22s 10.57s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 14
% Syntax : Number of formulae : 107 ( 41 unt; 0 def)
% Number of atoms : 240 ( 141 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 248 ( 115 ~; 109 |; 14 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 108 ( 7 sgn 35 !; 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(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(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(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_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_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,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,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_20,plain,
( ~ complement(B,A)
| test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_21,plain,
( complement(sK0(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_22,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_23,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_24,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_25,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| 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_27,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_29,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| c(A) = B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_30,plain,
( test(B)
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_20]) ).
cnf(c_31,plain,
( multiplication(B,A) = zero
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_33,plain,
( addition(B,A) = one
| c(A) != B
| ~ test(A) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_34,plain,
( test(A)
| addition(A,B) != one
| multiplication(B,A) != zero
| multiplication(A,B) != zero ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
cnf(c_35,plain,
( ~ test(A)
| addition(A,sK0(A)) = one ),
inference(resolve,[status(thm)],[c_24,c_21]) ).
cnf(c_36,plain,
( ~ test(A)
| multiplication(sK0(A),A) = zero ),
inference(resolve,[status(thm)],[c_23,c_21]) ).
cnf(c_37,plain,
( ~ test(A)
| multiplication(A,sK0(A)) = zero ),
inference(resolve,[status(thm)],[c_22,c_21]) ).
fof(nnf_19,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X1,X0),multiplication(X0,X2))
& multiplication(multiplication(X1,X0),X2) = multiplication(X1,X0)
& test(X2)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ~ leq(multiplication(sK1,sK2),multiplication(sK2,sK3))
& multiplication(multiplication(sK1,sK2),sK3) = multiplication(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_38,negated_conjecture,
~ leq(multiplication(sK1,sK2),multiplication(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_39,negated_conjecture,
multiplication(multiplication(sK1,sK2),sK3) = multiplication(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_42,plain,
( c(multiplication(A,B)) = addition(c(A),c(B))
| ~ test(B)
| ~ test(A) ),
inference(clausify,[status(thm)],[test_deMorgan2]) ).
cnf(c_43,plain,
( addition(c(A),c(B)) = c(multiplication(A,B))
| ~ test(B)
| ~ test(A) ),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_47,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_49,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
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_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_59,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_61,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_66,negated_conjecture,
multiplication(sK1,multiplication(sK2,sK3)) = multiplication(sK1,sK2),
inference(paramod,[status(thm)],[c_57,c_39]) ).
cnf(c_67,plain,
( test(c(A))
| ~ test(A) ),
inference(xxres,[status(thm)],[c_30]) ).
cnf(c_68,plain,
( multiplication(c(A),A) = zero
| ~ test(A) ),
inference(xxres,[status(thm)],[c_31]) ).
cnf(c_376,plain,
( addition(c(A),A) = one
| ~ test(A) ),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_70,plain,
( addition(A,c(A)) = one
| ~ test(A) ),
inference(paramod,[status(thm)],[c_61,c_376]) ).
cnf(c_81,plain,
multiplication(sK1,sK0(sK1)) = zero,
inference(resolve,[status(thm)],[c_41,c_37]) ).
cnf(c_82,plain,
multiplication(sK0(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_41,c_36]) ).
cnf(c_83,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_41,c_35]) ).
cnf(c_377,negated_conjecture,
addition(multiplication(sK1,sK2),multiplication(sK2,sK3)) != multiplication(sK2,sK3),
inference(resolve,[status(thm)],[c_47,c_38]) ).
cnf(c_117,negated_conjecture,
addition(multiplication(sK2,sK3),multiplication(sK1,sK2)) != multiplication(sK2,sK3),
inference(paramod,[status(thm)],[c_61,c_377]) ).
cnf(c_378,plain,
( test(zero)
| addition(zero,A) != one
| multiplication(A,zero) != zero ),
inference(resolve,[status(thm)],[c_49,c_34]) ).
cnf(c_379,plain,
( test(zero)
| addition(zero,A) != one
| zero != zero ),
inference(paramod,[status(thm)],[c_50,c_378]) ).
cnf(c_119,plain,
( test(zero)
| addition(zero,A) != one ),
inference(copy,[status(thm)],[c_379]) ).
cnf(c_380,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| c(zero) = one
| ~ test(zero) ),
inference(resolve,[status(thm)],[c_59,c_29]) ).
cnf(c_381,plain,
( multiplication(zero,one) != zero
| zero != zero
| c(zero) = one
| ~ test(zero) ),
inference(paramod,[status(thm)],[c_50,c_380]) ).
cnf(c_382,plain,
( zero != zero
| zero != zero
| c(zero) = one
| ~ test(zero) ),
inference(paramod,[status(thm)],[c_56,c_381]) ).
cnf(c_383,plain,
( zero != zero
| c(zero) = one
| ~ test(zero) ),
inference(copy,[status(thm)],[c_382]) ).
cnf(c_137,plain,
( c(zero) = one
| ~ test(zero) ),
inference(copy,[status(thm)],[c_383]) ).
cnf(c_148,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_384,plain,
( test(zero)
| A != one ),
inference(paramod,[status(thm)],[c_148,c_119]) ).
cnf(c_385,plain,
( test(zero)
| one != A ),
inference(copy,[status(thm)],[c_384]) ).
cnf(c_150,plain,
test(zero),
inference(copy,[status(thm)],[c_385]) ).
cnf(c_152,plain,
c(zero) = one,
inference(resolve,[status(thm)],[c_150,c_137]) ).
cnf(c_165,plain,
test(c(sK1)),
inference(resolve,[status(thm)],[c_67,c_41]) ).
cnf(c_386,plain,
( addition(c(A),c(zero)) = c(multiplication(A,zero))
| ~ test(A) ),
inference(resolve,[status(thm)],[c_150,c_43]) ).
cnf(c_387,plain,
( addition(c(A),one) = c(multiplication(A,zero))
| ~ test(A) ),
inference(paramod,[status(thm)],[c_152,c_386]) ).
cnf(c_388,plain,
( addition(one,c(A)) = c(multiplication(A,zero))
| ~ test(A) ),
inference(paramod,[status(thm)],[c_61,c_387]) ).
cnf(c_389,plain,
( addition(one,c(A)) = c(zero)
| ~ test(A) ),
inference(paramod,[status(thm)],[c_50,c_388]) ).
cnf(c_178,plain,
( addition(one,c(A)) = one
| ~ test(A) ),
inference(paramod,[status(thm)],[c_152,c_389]) ).
cnf(c_203,plain,
multiplication(c(sK1),sK1) = zero,
inference(resolve,[status(thm)],[c_68,c_41]) ).
cnf(c_251,plain,
addition(sK1,c(sK1)) = one,
inference(resolve,[status(thm)],[c_70,c_41]) ).
cnf(c_390,plain,
( addition(sK0(sK1),sK1) != one
| multiplication(sK0(sK1),sK1) != zero
| c(sK1) = sK0(sK1)
| ~ test(sK1) ),
inference(resolve,[status(thm)],[c_81,c_29]) ).
cnf(c_391,plain,
( addition(sK0(sK1),sK1) != one
| zero != zero
| c(sK1) = sK0(sK1)
| ~ test(sK1) ),
inference(paramod,[status(thm)],[c_82,c_390]) ).
cnf(c_392,plain,
( addition(sK1,sK0(sK1)) != one
| zero != zero
| c(sK1) = sK0(sK1)
| ~ test(sK1) ),
inference(paramod,[status(thm)],[c_61,c_391]) ).
cnf(c_393,plain,
( one != one
| zero != zero
| c(sK1) = sK0(sK1)
| ~ test(sK1) ),
inference(paramod,[status(thm)],[c_83,c_392]) ).
cnf(c_394,plain,
( one != one
| zero != zero
| sK0(sK1) = c(sK1)
| ~ test(sK1) ),
inference(copy,[status(thm)],[c_393]) ).
cnf(c_395,plain,
( one != one
| sK0(sK1) = c(sK1)
| ~ test(sK1) ),
inference(copy,[status(thm)],[c_394]) ).
cnf(c_396,plain,
( sK0(sK1) = c(sK1)
| ~ test(sK1) ),
inference(copy,[status(thm)],[c_395]) ).
cnf(c_279,negated_conjecture,
sK0(sK1) = c(sK1),
inference(resolve,[status(thm)],[c_41,c_396]) ).
cnf(c_397,plain,
( addition(sK1,sK0(sK1)) != one
| multiplication(sK0(sK1),sK1) != zero
| c(sK0(sK1)) = sK1
| ~ test(sK0(sK1)) ),
inference(resolve,[status(thm)],[c_81,c_29]) ).
cnf(c_398,plain,
( addition(sK1,sK0(sK1)) != one
| multiplication(sK0(sK1),sK1) != zero
| c(sK0(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(paramod,[status(thm)],[c_279,c_397]) ).
cnf(c_399,plain,
( addition(sK1,sK0(sK1)) != one
| multiplication(sK0(sK1),sK1) != zero
| c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(paramod,[status(thm)],[c_279,c_398]) ).
cnf(c_400,plain,
( addition(sK1,sK0(sK1)) != one
| multiplication(c(sK1),sK1) != zero
| c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(paramod,[status(thm)],[c_279,c_399]) ).
cnf(c_401,plain,
( addition(sK1,sK0(sK1)) != one
| zero != zero
| c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(paramod,[status(thm)],[c_203,c_400]) ).
cnf(c_402,plain,
( addition(sK1,c(sK1)) != one
| zero != zero
| c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(paramod,[status(thm)],[c_279,c_401]) ).
cnf(c_403,plain,
( one != one
| zero != zero
| c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(paramod,[status(thm)],[c_251,c_402]) ).
cnf(c_404,plain,
( one != one
| c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(copy,[status(thm)],[c_403]) ).
cnf(c_405,plain,
( c(c(sK1)) = sK1
| ~ test(c(sK1)) ),
inference(copy,[status(thm)],[c_404]) ).
cnf(c_280,plain,
c(c(sK1)) = sK1,
inference(resolve,[status(thm)],[c_165,c_405]) ).
cnf(c_406,plain,
addition(one,c(c(sK1))) = one,
inference(resolve,[status(thm)],[c_178,c_165]) ).
cnf(c_353,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_280,c_406]) ).
cnf(c_407,plain,
addition(multiplication(one,A),multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_353,c_52]) ).
cnf(c_408,plain,
addition(A,multiplication(sK1,A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_55,c_407]) ).
cnf(c_362,plain,
addition(A,multiplication(sK1,A)) = A,
inference(paramod,[status(thm)],[c_55,c_408]) ).
cnf(c_409,plain,
addition(multiplication(sK2,sK3),multiplication(sK1,sK2)) = multiplication(sK2,sK3),
inference(paramod,[status(thm)],[c_66,c_362]) ).
cnf(c_375,plain,
$false,
inference(resolve,[status(thm)],[c_117,c_409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/10.45 % Computer : n002.cluster.edu
% 0.19/10.45 % Model : x86_64 x86_64
% 0.19/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.45 % Memory : 8046.5625MB
% 0.19/10.45 % OS : Linux 6.8.0-71-generic
% 0.19/10.45 % CPULimit : 300
% 0.19/10.45 % WCLimit : 300
% 0.19/10.45 % DateTime : Fri Sep 25 19:18:00 UTC 2026
% 0.19/10.46 % CPUTime :
% 0.19/10.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/10.46 % Process 3915702 was started by sandbox2 on n002,
% 0.19/10.46 % Fri Sep 25 19:18:00 2026
% 0.19/10.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/10.47
% 0.19/10.47 % From the command line: assign(max_seconds, 300).
% 0.22/10.57
% 0.22/10.57 % SZS status Theorem for theBenchmark
% 0.22/10.57
% 0.22/10.57 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.22/10.57 % Length of proof is 67.
% 0.22/10.57 % Level of proof is 9.
% 0.22/10.57 % Maximum clause weight is 31.000.
% 0.22/10.57 % Given clauses 108.
% 0.22/10.57
% 0.22/10.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------