%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE024+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 : n001.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 12.34s 2.13s
% Output : CNFRefutation 12.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 46 unt; 0 def)
% Number of atoms : 134 ( 82 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 99 ( 43 ~; 37 |; 10 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 92 ( 7 sgn 27 !; 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_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(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_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(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) )
=> ( 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_20,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_21,plain,
( c(A) = zero
| test(A) ),
inference(clausify,[status(thm)],[test_4]) ).
fof(nnf_17,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(sK0,sK1),c(sK2)) != zero
& multiplication(c(sK0),sK1) = addition(multiplication(sK1,c(sK2)),multiplication(c(sK0),sK1))
& test(sK2)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(X0,sK1),skolemize(X1,sK0),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_22,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,plain,
( complement(A,B)
| c(A) != B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
cnf(c_25,plain,
( ~ complement(B,A)
| test(A) ),
inference(clausify,[status(thm)],[test_1]) ).
cnf(c_31,plain,
( ~ complement(B,C)
| c(B) = C
| ~ complement(A,B) ),
inference(resolve,[status(thm)],[c_25,c_20]) ).
cnf(c_32,plain,
( complement(B,C)
| c(B) != C
| ~ complement(A,B) ),
inference(resolve,[status(thm)],[c_25,c_24]) ).
cnf(c_34,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_38,plain,
( c(A) = zero
| ~ complement(A,B)
| c(A) = B ),
inference(resolve,[status(thm)],[c_20,c_21]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_40,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_41,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_43,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_44,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_47,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_50,plain,
multiplication(A,zero) = zero,
inference(clausify,[status(thm)],[right_annihilation]) ).
cnf(c_51,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_53,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_55,plain,
( addition(B,A) != one
| multiplication(A,B) != zero
| multiplication(B,A) != zero
| complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_56,negated_conjecture,
multiplication(c(sK0),sK1) = addition(multiplication(sK1,c(sK2)),multiplication(c(sK0),sK1)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_4024,negated_conjecture,
multiplication(c(sK0),sK1) = addition(multiplication(c(sK0),sK1),multiplication(sK1,c(sK2))),
inference(paramod,[status(thm)],[c_39,c_56]) ).
cnf(c_57,negated_conjecture,
addition(multiplication(c(sK0),sK1),multiplication(sK1,c(sK2))) = multiplication(c(sK0),sK1),
inference(copy,[status(thm)],[c_4024]) ).
cnf(c_58,negated_conjecture,
multiplication(multiplication(sK0,sK1),c(sK2)) != zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_59,negated_conjecture,
multiplication(sK0,multiplication(sK1,c(sK2))) != zero,
inference(paramod,[status(thm)],[c_43,c_58]) ).
cnf(c_61,plain,
( ~ complement(A,zero)
| c(A) = zero ),
inference(factor,[status(thm)],[c_38]) ).
cnf(c_67,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_4025,plain,
A = addition(zero,A),
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_78,plain,
addition(zero,A) = A,
inference(copy,[status(thm)],[c_4025]) ).
cnf(c_82,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_47,c_40]) ).
cnf(c_4026,plain,
( multiplication(zero,one) != zero
| multiplication(one,zero) != zero
| complement(zero,one) ),
inference(resolve,[status(thm)],[c_55,c_41]) ).
cnf(c_4027,plain,
( multiplication(zero,one) != zero
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_50,c_4026]) ).
cnf(c_4028,plain,
( zero != zero
| zero != zero
| complement(zero,one) ),
inference(paramod,[status(thm)],[c_44,c_4027]) ).
cnf(c_4029,plain,
( zero != zero
| complement(zero,one) ),
inference(copy,[status(thm)],[c_4028]) ).
cnf(c_100,plain,
complement(zero,one),
inference(copy,[status(thm)],[c_4029]) ).
cnf(c_115,plain,
( complement(one,A)
| c(one) != A ),
inference(resolve,[status(thm)],[c_100,c_32]) ).
cnf(c_117,plain,
( ~ complement(one,A)
| c(one) = A ),
inference(resolve,[status(thm)],[c_100,c_31]) ).
cnf(c_126,plain,
multiplication(sK0,c(sK0)) = zero,
inference(resolve,[status(thm)],[c_67,c_53]) ).
cnf(c_4030,plain,
( multiplication(one,zero) != zero
| multiplication(zero,one) != zero
| complement(one,zero) ),
inference(resolve,[status(thm)],[c_78,c_55]) ).
cnf(c_4031,plain,
( multiplication(one,zero) != zero
| zero != zero
| complement(one,zero) ),
inference(paramod,[status(thm)],[c_44,c_4030]) ).
cnf(c_4032,plain,
( zero != zero
| zero != zero
| complement(one,zero) ),
inference(paramod,[status(thm)],[c_50,c_4031]) ).
cnf(c_4033,plain,
( zero != zero
| complement(one,zero) ),
inference(copy,[status(thm)],[c_4032]) ).
cnf(c_133,plain,
complement(one,zero),
inference(copy,[status(thm)],[c_4033]) ).
cnf(c_135,plain,
c(one) = zero,
inference(resolve,[status(thm)],[c_133,c_61]) ).
cnf(c_139,plain,
( ~ complement(one,A)
| zero = A ),
inference(paramod,[status(thm)],[c_135,c_117]) ).
cnf(c_140,plain,
( complement(one,A)
| zero != A ),
inference(paramod,[status(thm)],[c_135,c_115]) ).
cnf(c_4034,plain,
multiplication(zero,A) = multiplication(sK0,multiplication(c(sK0),A)),
inference(paramod,[status(thm)],[c_126,c_43]) ).
cnf(c_4035,plain,
zero = multiplication(sK0,multiplication(c(sK0),A)),
inference(paramod,[status(thm)],[c_51,c_4034]) ).
cnf(c_200,plain,
multiplication(sK0,multiplication(c(sK0),A)) = zero,
inference(copy,[status(thm)],[c_4035]) ).
cnf(c_4036,negated_conjecture,
zero != multiplication(sK0,multiplication(sK1,c(sK2))),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_223,negated_conjecture,
~ complement(one,multiplication(sK0,multiplication(sK1,c(sK2)))),
inference(resolve,[status(thm)],[c_139,c_4036]) ).
cnf(c_4037,plain,
addition(multiplication(A,multiplication(c(sK0),sK1)),B) = addition(multiplication(A,multiplication(c(sK0),sK1)),addition(multiplication(A,multiplication(sK1,c(sK2))),B)),
inference(paramod,[status(thm)],[c_57,c_82]) ).
cnf(c_266,plain,
addition(multiplication(A,multiplication(c(sK0),sK1)),addition(multiplication(A,multiplication(sK1,c(sK2))),B)) = addition(multiplication(A,multiplication(c(sK0),sK1)),B),
inference(copy,[status(thm)],[c_4037]) ).
cnf(c_4038,plain,
addition(zero,addition(multiplication(sK0,multiplication(sK1,c(sK2))),A)) = addition(multiplication(sK0,multiplication(c(sK0),sK1)),A),
inference(paramod,[status(thm)],[c_200,c_266]) ).
cnf(c_4039,plain,
addition(multiplication(sK0,multiplication(sK1,c(sK2))),A) = addition(multiplication(sK0,multiplication(c(sK0),sK1)),A),
inference(paramod,[status(thm)],[c_78,c_4038]) ).
cnf(c_4040,plain,
addition(multiplication(sK0,multiplication(sK1,c(sK2))),A) = addition(zero,A),
inference(paramod,[status(thm)],[c_200,c_4039]) ).
cnf(c_3956,plain,
addition(multiplication(sK0,multiplication(sK1,c(sK2))),A) = A,
inference(paramod,[status(thm)],[c_78,c_4040]) ).
cnf(c_4041,plain,
( complement(one,A)
| A != zero ),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_4042,plain,
complement(one,addition(multiplication(sK0,multiplication(sK1,c(sK2))),zero)),
inference(resolve,[status(thm)],[c_3956,c_4041]) ).
cnf(c_4043,plain,
complement(one,addition(zero,multiplication(sK0,multiplication(sK1,c(sK2))))),
inference(paramod,[status(thm)],[c_39,c_4042]) ).
cnf(c_4044,plain,
complement(one,multiplication(sK0,multiplication(sK1,c(sK2)))),
inference(paramod,[status(thm)],[c_78,c_4043]) ).
cnf(c_4023,plain,
$false,
inference(resolve,[status(thm)],[c_223,c_4044]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE024+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 19:20:11 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 4010397 was started by sandbox2 on n001,
% 0.16/0.44 % Fri Sep 25 19:20:11 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 12.34/2.13
% 12.34/2.13 % SZS status Theorem for theBenchmark
% 12.34/2.13
% 12.34/2.13 % Proof 1 at 1.25 (+ 0.40) seconds.
% 12.34/2.13 % Length of proof is 54.
% 12.34/2.13 % Level of proof is 7.
% 12.34/2.13 % Maximum clause weight is 24.000.
% 12.34/2.13 % Given clauses 333.
% 12.34/2.13
% 12.34/2.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------