%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 06:55:01 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 13 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 31 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(closure_of_addition,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,VAR_1,add(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_addition) ).
cnf(c_1,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
fof(multiplicative_identity1,axiom,
! [VAR_0] : product(multiplicative_identity,VAR_0,VAR_0),
file('theBenchmark.p',multiplicative_identity1) ).
cnf(c_7,plain,
product(multiplicative_identity,A,A),
inference(clausify,[status(thm)],[multiplicative_identity1]) ).
fof(multiplicative_identity2,axiom,
! [VAR_0] : product(VAR_0,multiplicative_identity,VAR_0),
file('theBenchmark.p',multiplicative_identity2) ).
cnf(c_8,plain,
product(A,multiplicative_identity,A),
inference(clausify,[status(thm)],[multiplicative_identity2]) ).
fof(distributivity3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_0,VAR_3,VAR_5)
| ~ product(VAR_3,VAR_1,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity3) ).
cnf(c_11,plain,
( sum(C,E,V6)
| ~ product(F,B,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity3]) ).
fof(distributivity5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_2,VAR_4,VAR_6)
| ~ sum(VAR_0,VAR_5,VAR_6)
| ~ product(VAR_1,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity5) ).
cnf(c_13,plain,
( product(C,E,V6)
| ~ sum(A,F,V6)
| ~ product(B,D,F)
| ~ sum(A,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[distributivity5]) ).
fof(additive_inverse2,axiom,
! [VAR_0] : sum(VAR_0,inverse(VAR_0),multiplicative_identity),
file('theBenchmark.p',additive_inverse2) ).
cnf(c_18,plain,
sum(A,inverse(A),multiplicative_identity),
inference(clausify,[status(thm)],[additive_inverse2]) ).
fof(prove_equations,axiom,
~ sum(x,multiplicative_identity,multiplicative_identity),
file('theBenchmark.p',prove_equations) ).
cnf(c_23,plain,
~ sum(x,multiplicative_identity,multiplicative_identity),
inference(clausify,[status(thm)],[prove_equations]) ).
cnf(c_1027,plain,
( product(add(A,D),C,F)
| ~ sum(A,E,F)
| ~ product(D,B,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_13,c_1]) ).
cnf(c_1028,plain,
( product(add(B,A),multiplicative_identity,D)
| ~ sum(B,C,D)
| ~ product(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_1027,c_18]) ).
cnf(c_1029,plain,
( product(add(A,multiplicative_identity),multiplicative_identity,B)
| ~ sum(A,inverse(A),B) ),
inference(resolve,[status(thm)],[c_1028,c_7]) ).
cnf(c_562,plain,
product(add(A,multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_1029,c_18]) ).
cnf(c_1030,plain,
( sum(C,B,E)
| ~ product(D,multiplicative_identity,E)
| ~ sum(C,A,D)
| ~ product(A,multiplicative_identity,B) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_1031,plain,
( sum(A,B,D)
| ~ product(C,multiplicative_identity,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_1030,c_8]) ).
cnf(c_1032,plain,
( sum(A,B,C)
| ~ product(add(A,B),multiplicative_identity,C) ),
inference(resolve,[status(thm)],[c_1031,c_1]) ).
cnf(c_1033,plain,
~ product(add(x,multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_1032,c_23]) ).
cnf(c_1026,plain,
$false,
inference(resolve,[status(thm)],[c_562,c_1033]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 22:39:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1886164 was started by sandbox on n016,
% 0.09/0.36 % Sat Sep 26 22:39:00 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.04 (+ 0.03) seconds.
% 0.13/0.44 % Length of proof is 9.
% 0.13/0.44 % Level of proof is 2.
% 0.13/0.44 % Maximum clause weight is 25.000.
% 0.13/0.44 % Given clauses 23.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------