%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 39 unt; 0 def)
% Number of atoms : 70 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 7 |; 8 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 21 !; 2 ?)
% 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(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_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(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X0,X1),multiplication(X0,c(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]) ).
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_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(multiplication(X0,X1),multiplication(X0,c(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(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))) != one
& test(sK1)
& test(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK1),skolemize(X1,sK0)],[nnf_19]) ).
cnf(c_58,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_59,negated_conjecture,
test(sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_60,negated_conjecture,
addition(addition(addition(multiplication(sK1,sK0),multiplication(sK1,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_165,negated_conjecture,
addition(addition(multiplication(sK1,addition(sK0,c(sK0))),multiplication(c(sK1),sK0)),multiplication(c(sK1),c(sK0))) != one,
inference(paramod,[status(thm)],[c_48,c_60]) ).
cnf(c_166,negated_conjecture,
addition(addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0)))),multiplication(c(sK1),c(sK0))) != one,
inference(paramod,[status(thm)],[c_40,c_165]) ).
cnf(c_61,negated_conjecture,
addition(multiplication(c(sK1),c(sK0)),addition(multiplication(c(sK1),sK0),multiplication(sK1,addition(sK0,c(sK0))))) != one,
inference(paramod,[status(thm)],[c_40,c_166]) ).
cnf(c_167,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_167]) ).
cnf(c_71,negated_conjecture,
addition(multiplication(c(sK1),sK0),addition(multiplication(c(sK1),c(sK0)),multiplication(sK1,addition(sK0,c(sK0))))) != one,
inference(paramod,[status(thm)],[c_69,c_61]) ).
cnf(c_168,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_168]) ).
cnf(c_169,negated_conjecture,
addition(multiplication(c(sK1),addition(sK0,c(sK0))),multiplication(sK1,addition(sK0,c(sK0)))) != one,
inference(paramod,[status(thm)],[c_80,c_71]) ).
cnf(c_170,negated_conjecture,
addition(multiplication(sK1,addition(sK0,c(sK0))),multiplication(c(sK1),addition(sK0,c(sK0)))) != one,
inference(paramod,[status(thm)],[c_40,c_169]) ).
cnf(c_84,negated_conjecture,
multiplication(addition(sK1,c(sK1)),addition(sK0,c(sK0))) != one,
inference(paramod,[status(thm)],[c_50,c_170]) ).
cnf(c_171,negated_conjecture,
( c(sK0) != A
| addition(A,sK0) = one ),
inference(resolve,[status(thm)],[c_38,c_58]) ).
cnf(c_172,plain,
A = multiplication(one,A),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_173,negated_conjecture,
addition(multiplication(one,c(sK0)),sK0) = one,
inference(resolve,[status(thm)],[c_171,c_172]) ).
cnf(c_174,negated_conjecture,
addition(c(sK0),sK0) = one,
inference(paramod,[status(thm)],[c_46,c_173]) ).
cnf(c_135,negated_conjecture,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_40,c_174]) ).
cnf(c_175,negated_conjecture,
multiplication(addition(sK1,c(sK1)),one) != one,
inference(paramod,[status(thm)],[c_135,c_84]) ).
cnf(c_141,negated_conjecture,
addition(sK1,c(sK1)) != one,
inference(paramod,[status(thm)],[c_45,c_175]) ).
cnf(c_176,negated_conjecture,
( c(sK1) != A
| addition(A,sK1) = one ),
inference(resolve,[status(thm)],[c_38,c_59]) ).
cnf(c_177,plain,
A = multiplication(one,A),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_178,negated_conjecture,
addition(multiplication(one,c(sK1)),sK1) = one,
inference(resolve,[status(thm)],[c_176,c_177]) ).
cnf(c_179,negated_conjecture,
addition(c(sK1),sK1) = one,
inference(paramod,[status(thm)],[c_46,c_178]) ).
cnf(c_180,negated_conjecture,
addition(sK1,c(sK1)) = one,
inference(paramod,[status(thm)],[c_40,c_179]) ).
cnf(c_164,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_141,c_180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 19:11:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2644814 was started by sandbox on n011,
% 0.10/0.37 % Fri Sep 25 19:11:30 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.40 % Length of proof is 31.
% 0.10/0.40 % Level of proof is 7.
% 0.10/0.40 % Maximum clause weight is 54.000.
% 0.10/0.40 % Given clauses 26.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------