%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE027+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 : n006.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 10.74s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 50 unt; 0 def)
% Number of atoms : 119 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 81 ( 36 ~; 28 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 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 : 90 ( 8 sgn 33 !; 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(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(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(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_20,plain,
( ~ complement(A,B)
| c(A) = B
| ~ test(A) ),
inference(clausify,[status(thm)],[test_3]) ).
fof(nnf_17,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(sK0,addition(multiplication(sK0,sK2),multiplication(c(sK0),sK3))),multiplication(c(sK0),sK4)) != addition(multiplication(sK0,sK2),multiplication(c(sK0),sK4))
& test(sK5)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK5,sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK0),skolemize(X4,sK5)],[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]) ).
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(sK1(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X5,sK1(X0))],[nnf_13]) ).
fof(sk_test_1,plain,
( ! [VAR_0,VAR_1] :
( ~ complement(VAR_1,VAR_0)
| test(VAR_0) )
& ! [VAR_0] :
( complement(sK1(VAR_0),VAR_0)
| ~ test(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_test_1_sk]) ).
cnf(c_26,plain,
( complement(sK1(A),A)
| ~ test(A) ),
inference(split_conjunct,[status(thm)],[sk_test_1]) ).
cnf(c_28,negated_conjecture,
complement(sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_34,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_37,negated_conjecture,
( ~ complement(sK0,A)
| c(sK0) = A ),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_39,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
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_51,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_52,plain,
( multiplication(B,A) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_53,plain,
( multiplication(A,B) = zero
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_54,plain,
( addition(B,A) = one
| ~ 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,
addition(multiplication(sK0,addition(multiplication(sK0,sK2),multiplication(c(sK0),sK3))),multiplication(c(sK0),sK4)) != addition(multiplication(sK0,sK2),multiplication(c(sK0),sK4)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_57,negated_conjecture,
addition(multiplication(c(sK0),sK4),multiplication(sK0,addition(multiplication(sK0,sK2),multiplication(c(sK0),sK3)))) != addition(multiplication(sK0,sK2),multiplication(c(sK0),sK4)),
inference(paramod,[status(thm)],[c_39,c_56]) ).
cnf(c_66,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_34]) ).
cnf(c_932,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_932]) ).
cnf(c_91,plain,
multiplication(sK0,sK1(sK0)) = zero,
inference(resolve,[status(thm)],[c_52,c_28]) ).
cnf(c_94,plain,
multiplication(sK1(sK0),sK0) = zero,
inference(resolve,[status(thm)],[c_53,c_28]) ).
cnf(c_97,plain,
addition(sK0,sK1(sK0)) = one,
inference(resolve,[status(thm)],[c_54,c_28]) ).
cnf(c_933,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_66,c_54]) ).
cnf(c_124,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_39,c_933]) ).
cnf(c_934,plain,
( addition(sK1(sK0),sK0) != one
| multiplication(sK1(sK0),sK0) != zero
| complement(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_91,c_55]) ).
cnf(c_935,plain,
( addition(sK1(sK0),sK0) != one
| zero != zero
| complement(sK0,sK1(sK0)) ),
inference(paramod,[status(thm)],[c_94,c_934]) ).
cnf(c_936,plain,
( addition(sK0,sK1(sK0)) != one
| zero != zero
| complement(sK0,sK1(sK0)) ),
inference(paramod,[status(thm)],[c_39,c_935]) ).
cnf(c_937,plain,
( one != one
| zero != zero
| complement(sK0,sK1(sK0)) ),
inference(paramod,[status(thm)],[c_97,c_936]) ).
cnf(c_938,plain,
( one != one
| complement(sK0,sK1(sK0)) ),
inference(copy,[status(thm)],[c_937]) ).
cnf(c_164,plain,
complement(sK0,sK1(sK0)),
inference(copy,[status(thm)],[c_938]) ).
cnf(c_939,plain,
multiplication(zero,A) = multiplication(sK0,multiplication(sK1(sK0),A)),
inference(paramod,[status(thm)],[c_91,c_43]) ).
cnf(c_940,plain,
zero = multiplication(sK0,multiplication(sK1(sK0),A)),
inference(paramod,[status(thm)],[c_51,c_939]) ).
cnf(c_165,plain,
multiplication(sK0,multiplication(sK1(sK0),A)) = zero,
inference(copy,[status(thm)],[c_940]) ).
cnf(c_941,plain,
addition(multiplication(sK0,A),zero) = multiplication(sK0,addition(A,sK1(sK0))),
inference(paramod,[status(thm)],[c_91,c_47]) ).
cnf(c_942,plain,
addition(zero,multiplication(sK0,A)) = multiplication(sK0,addition(A,sK1(sK0))),
inference(paramod,[status(thm)],[c_39,c_941]) ).
cnf(c_943,plain,
multiplication(sK0,A) = multiplication(sK0,addition(A,sK1(sK0))),
inference(paramod,[status(thm)],[c_78,c_942]) ).
cnf(c_167,plain,
multiplication(sK0,addition(A,sK1(sK0))) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_943]) ).
cnf(c_944,negated_conjecture,
c(sK0) = sK1(sK0),
inference(resolve,[status(thm)],[c_164,c_37]) ).
cnf(c_173,negated_conjecture,
sK1(sK0) = c(sK0),
inference(copy,[status(thm)],[c_944]) ).
cnf(c_178,plain,
multiplication(sK0,addition(A,c(sK0))) = multiplication(sK0,A),
inference(paramod,[status(thm)],[c_173,c_167]) ).
cnf(c_180,plain,
multiplication(sK0,multiplication(c(sK0),A)) = zero,
inference(paramod,[status(thm)],[c_173,c_165]) ).
cnf(c_945,plain,
multiplication(sK0,one) = multiplication(sK0,sK0),
inference(paramod,[status(thm)],[c_124,c_178]) ).
cnf(c_946,plain,
sK0 = multiplication(sK0,sK0),
inference(paramod,[status(thm)],[c_44,c_945]) ).
cnf(c_862,plain,
multiplication(sK0,sK0) = sK0,
inference(copy,[status(thm)],[c_946]) ).
cnf(c_947,plain,
multiplication(sK0,A) = multiplication(sK0,multiplication(sK0,A)),
inference(paramod,[status(thm)],[c_862,c_43]) ).
cnf(c_867,plain,
multiplication(sK0,multiplication(sK0,A)) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_947]) ).
cnf(c_948,plain,
addition(multiplication(sK0,A),zero) = multiplication(sK0,addition(A,multiplication(c(sK0),B))),
inference(paramod,[status(thm)],[c_180,c_47]) ).
cnf(c_949,plain,
addition(zero,multiplication(sK0,A)) = multiplication(sK0,addition(A,multiplication(c(sK0),B))),
inference(paramod,[status(thm)],[c_39,c_948]) ).
cnf(c_950,plain,
multiplication(sK0,A) = multiplication(sK0,addition(A,multiplication(c(sK0),B))),
inference(paramod,[status(thm)],[c_78,c_949]) ).
cnf(c_928,plain,
multiplication(sK0,addition(A,multiplication(c(sK0),B))) = multiplication(sK0,A),
inference(copy,[status(thm)],[c_950]) ).
cnf(c_951,negated_conjecture,
addition(multiplication(c(sK0),sK4),multiplication(sK0,multiplication(sK0,sK2))) != addition(multiplication(sK0,sK2),multiplication(c(sK0),sK4)),
inference(paramod,[status(thm)],[c_928,c_57]) ).
cnf(c_952,negated_conjecture,
addition(multiplication(c(sK0),sK4),multiplication(sK0,sK2)) != addition(multiplication(sK0,sK2),multiplication(c(sK0),sK4)),
inference(paramod,[status(thm)],[c_867,c_951]) ).
cnf(c_953,negated_conjecture,
addition(multiplication(sK0,sK2),multiplication(c(sK0),sK4)) != addition(multiplication(sK0,sK2),multiplication(c(sK0),sK4)),
inference(paramod,[status(thm)],[c_39,c_952]) ).
cnf(c_931,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE027+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.58 % Computer : n006.cluster.edu
% 0.09/10.58 % Model : x86_64 x86_64
% 0.09/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.58 % Memory : 8046.5625MB
% 0.09/10.58 % OS : Linux 6.8.0-71-generic
% 0.09/10.58 % CPULimit : 300
% 0.09/10.58 % WCLimit : 300
% 0.09/10.58 % DateTime : Fri Sep 25 19:14:51 UTC 2026
% 0.09/10.58 % CPUTime :
% 0.09/10.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.58 % Process 3536244 was started by sandbox2 on n006,
% 0.09/10.58 % Fri Sep 25 19:14:51 2026
% 0.09/10.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/10.59
% 0.09/10.59 % From the command line: assign(max_seconds, 300).
% 0.14/10.74
% 0.14/10.74 % SZS status Theorem for theBenchmark
% 0.14/10.74
% 0.14/10.74 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.14/10.74 % Length of proof is 46.
% 0.14/10.74 % Level of proof is 9.
% 0.14/10.74 % Maximum clause weight is 36.000.
% 0.14/10.74 % Given clauses 165.
% 0.14/10.74
% 0.14/10.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------