%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 06:55:00 AM UTC 2026
% Result : Unsatisfiable 0.75s 0.50s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 59 ( 31 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(closure_of_multiplication,axiom,
! [VAR_0,VAR_1] : product(VAR_0,VAR_1,multiply(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_multiplication) ).
cnf(c_2,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_6,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
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(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(distributivity7,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_2,VAR_4,VAR_6)
| ~ sum(VAR_5,VAR_1,VAR_6)
| ~ product(VAR_0,VAR_3,VAR_5)
| ~ sum(VAR_3,VAR_1,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity7) ).
cnf(c_15,plain,
( product(C,E,V6)
| ~ sum(F,B,V6)
| ~ product(A,D,F)
| ~ sum(D,B,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[distributivity7]) ).
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(multiplicative_inverse1,axiom,
! [VAR_0] : product(inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',multiplicative_inverse1) ).
cnf(c_19,plain,
product(inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[multiplicative_inverse1]) ).
fof(prove_both_equalities,axiom,
~ product(x,x,x),
file('theBenchmark.p',prove_both_equalities) ).
cnf(c_23,plain,
~ product(x,x,x),
inference(clausify,[status(thm)],[prove_both_equalities]) ).
cnf(c_876,plain,
( sum(multiply(D,B),C,F)
| ~ product(E,B,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_11,c_2]) ).
cnf(c_877,plain,
( sum(multiply(A,B),additive_identity,D)
| ~ product(C,B,D)
| ~ sum(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_876,c_19]) ).
cnf(c_878,plain,
( sum(multiply(A,A),additive_identity,B)
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_877,c_18]) ).
cnf(c_620,plain,
sum(multiply(A,A),additive_identity,A),
inference(resolve,[status(thm)],[c_878,c_7]) ).
cnf(c_879,plain,
( product(C,B,E)
| ~ sum(D,additive_identity,E)
| ~ product(C,A,D)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_880,plain,
( product(A,B,D)
| ~ sum(C,additive_identity,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_879,c_6]) ).
cnf(c_881,plain,
( product(A,B,C)
| ~ sum(multiply(A,B),additive_identity,C) ),
inference(resolve,[status(thm)],[c_880,c_2]) ).
cnf(c_882,plain,
~ sum(multiply(x,x),additive_identity,x),
inference(resolve,[status(thm)],[c_881,c_23]) ).
cnf(c_875,plain,
$false,
inference(resolve,[status(thm)],[c_620,c_882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 22:32:47 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3269823 was started by sandbox2 on n005,
% 0.12/0.38 % Sat Sep 26 22:32:47 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.75/0.50
% 0.75/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.75/0.50
% 0.75/0.50 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.75/0.50 % Length of proof is 10.
% 0.75/0.50 % Level of proof is 2.
% 0.75/0.50 % Maximum clause weight is 25.000.
% 0.75/0.50 % Given clauses 23.
% 0.75/0.50
% 0.75/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------