%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE026+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 : n018.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 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 35 unt; 0 def)
% Number of atoms : 69 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 14 ~; 5 |; 10 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 25 !; 3 ?)
% 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_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('theBenchmark.p',multiplicative_associativity) ).
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(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('theBenchmark.p',order) ).
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] :
( ( 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]) ).
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] :
( ~ 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(sK0,sK1),multiplication(sK1,sK2))
& multiplication(multiplication(sK0,sK1),sK2) = multiplication(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_23,negated_conjecture,
test(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_29,negated_conjecture,
( complement(sK0,A)
| c(sK0) != A ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_37,negated_conjecture,
~ leq(multiplication(sK0,sK1),multiplication(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_38,negated_conjecture,
multiplication(multiplication(sK0,sK1),sK2) = multiplication(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_40,plain,
( addition(B,A) = one
| ~ complement(A,B) ),
inference(clausify,[status(thm)],[test_2]) ).
cnf(c_43,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(clausify,[status(thm)],[order]) ).
cnf(c_47,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_48,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_51,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_53,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(clausify,[status(thm)],[multiplicative_associativity]) ).
cnf(c_54,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_56,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_57,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_61,negated_conjecture,
multiplication(sK0,multiplication(sK1,sK2)) = multiplication(sK0,sK1),
inference(paramod,[status(thm)],[c_53,c_38]) ).
cnf(c_63,plain,
complement(sK0,c(sK0)),
inference(xxres,[status(thm)],[c_29]) ).
cnf(c_362,negated_conjecture,
addition(multiplication(sK0,sK1),multiplication(sK1,sK2)) != multiplication(sK1,sK2),
inference(resolve,[status(thm)],[c_43,c_37]) ).
cnf(c_82,negated_conjecture,
addition(multiplication(sK1,sK2),multiplication(sK0,sK1)) != multiplication(sK1,sK2),
inference(paramod,[status(thm)],[c_57,c_362]) ).
cnf(c_363,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_51,c_48]) ).
cnf(c_90,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_363]) ).
cnf(c_364,plain,
addition(A,B) = addition(A,addition(A,B)),
inference(paramod,[status(thm)],[c_54,c_56]) ).
cnf(c_106,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(copy,[status(thm)],[c_364]) ).
cnf(c_365,plain,
addition(c(sK0),sK0) = one,
inference(resolve,[status(thm)],[c_63,c_40]) ).
cnf(c_137,plain,
addition(sK0,c(sK0)) = one,
inference(paramod,[status(thm)],[c_57,c_365]) ).
cnf(c_366,plain,
multiplication(addition(one,sK0),multiplication(sK1,sK2)) = addition(multiplication(sK1,sK2),multiplication(sK0,sK1)),
inference(paramod,[status(thm)],[c_61,c_90]) ).
cnf(c_266,plain,
addition(multiplication(sK1,sK2),multiplication(sK0,sK1)) = multiplication(addition(one,sK0),multiplication(sK1,sK2)),
inference(copy,[status(thm)],[c_366]) ).
cnf(c_267,negated_conjecture,
multiplication(addition(one,sK0),multiplication(sK1,sK2)) != multiplication(sK1,sK2),
inference(paramod,[status(thm)],[c_266,c_82]) ).
cnf(c_367,plain,
addition(sK0,one) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_137,c_106]) ).
cnf(c_368,plain,
addition(one,sK0) = addition(sK0,c(sK0)),
inference(paramod,[status(thm)],[c_57,c_367]) ).
cnf(c_356,plain,
addition(one,sK0) = one,
inference(paramod,[status(thm)],[c_137,c_368]) ).
cnf(c_369,negated_conjecture,
multiplication(one,multiplication(sK1,sK2)) != multiplication(sK1,sK2),
inference(paramod,[status(thm)],[c_356,c_267]) ).
cnf(c_370,negated_conjecture,
multiplication(sK1,sK2) != multiplication(sK1,sK2),
inference(paramod,[status(thm)],[c_51,c_369]) ).
cnf(c_361,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE026+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 19:17:21 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2622080 was started by sandbox2 on n018,
% 0.17/0.43 % Fri Sep 25 19:17:21 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.17/0.49
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49
% 0.17/0.49 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.17/0.49 % Length of proof is 34.
% 0.17/0.49 % Level of proof is 6.
% 0.17/0.49 % Maximum clause weight is 32.000.
% 0.17/0.49 % Given clauses 103.
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------