%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE010+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 : n016.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 07:44:03 AM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 61 unt; 0 def)
% Number of atoms : 110 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 40 ~; 15 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 30 !; 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_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
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(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_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
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] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
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_25,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
fof(nnf_13,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X2] : complement(X2,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(X2,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_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_38,plain,
( c(B) != A
| ~ test(B)
| addition(A,B) = one ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_40,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_41,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_43,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_45,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_46,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
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_49,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_50,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_49]) ).
fof(nnf_19,plain,
? [X0,X1] :
( addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) != one
& test(X0)
& test(X1) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))) != one
& test(sK2)
& test(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK2),skolemize(X1,sK1)],[nnf_19]) ).
cnf(c_58,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_59,negated_conjecture,
test(sK2),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_60,negated_conjecture,
addition(addition(addition(addition(multiplication(sK1,sK2),multiplication(c(sK1),sK2)),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_385,negated_conjecture,
addition(addition(addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(sK2,sK1)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))) != one,
inference(paramod,[status(thm)],[c_50,c_60]) ).
cnf(c_386,negated_conjecture,
addition(addition(addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2)),multiplication(c(sK2),sK1)),multiplication(c(sK2),c(sK1))) != one,
inference(paramod,[status(thm)],[c_40,c_385]) ).
cnf(c_387,negated_conjecture,
addition(addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2))),multiplication(c(sK2),c(sK1))) != one,
inference(paramod,[status(thm)],[c_40,c_386]) ).
cnf(c_61,negated_conjecture,
addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),addition(multiplication(sK2,sK1),multiplication(addition(sK1,c(sK1)),sK2)))) != one,
inference(paramod,[status(thm)],[c_40,c_387]) ).
cnf(c_388,plain,
addition(addition(A,B),C) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_40,c_41]) ).
cnf(c_69,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(paramod,[status(thm)],[c_41,c_388]) ).
cnf(c_389,negated_conjecture,
addition(multiplication(c(sK2),c(sK1)),addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2)))) != one,
inference(paramod,[status(thm)],[c_69,c_61]) ).
cnf(c_390,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),c(sK1)),addition(multiplication(c(sK2),sK1),multiplication(addition(sK1,c(sK1)),sK2)))) != one,
inference(paramod,[status(thm)],[c_69,c_389]) ).
cnf(c_71,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),sK1),addition(multiplication(c(sK2),c(sK1)),multiplication(addition(sK1,c(sK1)),sK2)))) != one,
inference(paramod,[status(thm)],[c_69,c_390]) ).
cnf(c_391,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_75,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_391]) ).
cnf(c_392,plain,
addition(multiplication(A,addition(B,C)),D) = addition(multiplication(A,B),addition(multiplication(A,C),D)),
inference(paramod,[status(thm)],[c_48,c_41]) ).
cnf(c_80,plain,
addition(multiplication(A,B),addition(multiplication(A,C),D)) = addition(multiplication(A,addition(B,C)),D),
inference(copy,[status(thm)],[c_392]) ).
cnf(c_393,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_45,c_48]) ).
cnf(c_81,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_393]) ).
cnf(c_394,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(c(sK2),addition(sK1,c(sK1))),multiplication(addition(sK1,c(sK1)),sK2))) != one,
inference(paramod,[status(thm)],[c_80,c_71]) ).
cnf(c_84,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(addition(sK1,c(sK1)),sK2),multiplication(c(sK2),addition(sK1,c(sK1))))) != one,
inference(paramod,[status(thm)],[c_40,c_394]) ).
cnf(c_128,plain,
addition(sK1,sK0(sK1)) = one,
inference(resolve,[status(thm)],[c_58,c_31]) ).
cnf(c_395,negated_conjecture,
( c(sK1) != A
| addition(A,sK1) = one ),
inference(resolve,[status(thm)],[c_38,c_58]) ).
cnf(c_396,plain,
A = multiplication(one,A),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_397,negated_conjecture,
addition(multiplication(one,c(sK1)),sK1) = one,
inference(resolve,[status(thm)],[c_395,c_396]) ).
cnf(c_398,negated_conjecture,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_46,c_397]) ).
cnf(c_135,negated_conjecture,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_40,c_398]) ).
cnf(c_399,negated_conjecture,
addition(multiplication(sK2,sK1),addition(multiplication(one,sK2),multiplication(c(sK2),addition(sK1,c(sK1))))) != one,
inference(paramod,[status(thm)],[c_135,c_84]) ).
cnf(c_400,negated_conjecture,
addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),addition(sK1,c(sK1))))) != one,
inference(paramod,[status(thm)],[c_46,c_399]) ).
cnf(c_401,negated_conjecture,
addition(multiplication(sK2,sK1),addition(sK2,multiplication(c(sK2),one))) != one,
inference(paramod,[status(thm)],[c_135,c_400]) ).
cnf(c_402,negated_conjecture,
addition(multiplication(sK2,sK1),addition(sK2,c(sK2))) != one,
inference(paramod,[status(thm)],[c_45,c_401]) ).
cnf(c_403,negated_conjecture,
addition(sK2,addition(multiplication(sK2,sK1),c(sK2))) != one,
inference(paramod,[status(thm)],[c_69,c_402]) ).
cnf(c_141,negated_conjecture,
addition(sK2,addition(c(sK2),multiplication(sK2,sK1))) != one,
inference(paramod,[status(thm)],[c_40,c_403]) ).
cnf(c_404,negated_conjecture,
( c(sK2) != A
| addition(A,sK2) = one ),
inference(resolve,[status(thm)],[c_38,c_59]) ).
cnf(c_405,plain,
A = multiplication(one,A),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_406,negated_conjecture,
addition(multiplication(one,c(sK2)),sK2) = one,
inference(resolve,[status(thm)],[c_404,c_405]) ).
cnf(c_407,negated_conjecture,
addition(c(sK2),sK2) = one,
inference(paramod,[status(thm)],[c_46,c_406]) ).
cnf(c_164,negated_conjecture,
addition(sK2,c(sK2)) = one,
inference(paramod,[status(thm)],[c_40,c_407]) ).
cnf(c_408,plain,
addition(c(sK2),addition(sK2,multiplication(sK2,sK1))) != one,
inference(paramod,[status(thm)],[c_69,c_141]) ).
cnf(c_300,plain,
addition(c(sK2),multiplication(sK2,addition(one,sK1))) != one,
inference(paramod,[status(thm)],[c_81,c_408]) ).
cnf(c_409,plain,
addition(sK1,one) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_128,c_75]) ).
cnf(c_410,plain,
addition(one,sK1) = addition(sK1,sK0(sK1)),
inference(paramod,[status(thm)],[c_40,c_409]) ).
cnf(c_382,plain,
addition(one,sK1) = one,
inference(paramod,[status(thm)],[c_128,c_410]) ).
cnf(c_411,plain,
addition(c(sK2),multiplication(sK2,one)) != one,
inference(paramod,[status(thm)],[c_382,c_300]) ).
cnf(c_412,plain,
addition(c(sK2),sK2) != one,
inference(paramod,[status(thm)],[c_45,c_411]) ).
cnf(c_413,plain,
addition(sK2,c(sK2)) != one,
inference(paramod,[status(thm)],[c_40,c_412]) ).
cnf(c_414,plain,
one != one,
inference(paramod,[status(thm)],[c_164,c_413]) ).
cnf(c_384,plain,
$false,
inference(copy,[status(thm)],[c_414]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:17:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3075701 was started by sandbox2 on n016,
% 0.09/0.37 % Fri Sep 25 19:17:15 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.46
% 0.09/0.46 % SZS status Theorem for theBenchmark
% 0.09/0.46
% 0.09/0.46 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.46 % Length of proof is 42.
% 0.09/0.46 % Level of proof is 8.
% 0.09/0.46 % Maximum clause weight is 68.000.
% 0.09/0.46 % Given clauses 64.
% 0.09/0.46
% 0.09/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------