%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO006-1 : 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 : n010.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 0.77s 0.47s
% Output : CNFRefutation 0.77s
% 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_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_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_5,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
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(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( sum(VAR_2,VAR_4,VAR_6)
| ~ product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_0,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity1) ).
cnf(c_9,plain,
( sum(C,E,V6)
| ~ product(A,F,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity1]) ).
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(multiplicative_inverse2,axiom,
! [VAR_0] : product(VAR_0,inverse(VAR_0),additive_identity),
file('theBenchmark.p',multiplicative_inverse2) ).
cnf(c_20,plain,
product(A,inverse(A),additive_identity),
inference(clausify,[status(thm)],[multiplicative_inverse2]) ).
fof(prove_equations,axiom,
~ product(x,additive_identity,additive_identity),
file('theBenchmark.p',prove_equations) ).
cnf(c_23,plain,
~ product(x,additive_identity,additive_identity),
inference(clausify,[status(thm)],[prove_equations]) ).
cnf(c_875,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_2]) ).
cnf(c_876,plain,
( sum(multiply(B,A),additive_identity,D)
| ~ product(B,C,D)
| ~ sum(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_875,c_20]) ).
cnf(c_877,plain,
( sum(multiply(A,additive_identity),additive_identity,B)
| ~ product(A,inverse(A),B) ),
inference(resolve,[status(thm)],[c_876,c_5]) ).
cnf(c_835,plain,
sum(multiply(A,additive_identity),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_877,c_20]) ).
cnf(c_878,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_879,plain,
( product(A,B,D)
| ~ sum(C,additive_identity,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_878,c_6]) ).
cnf(c_880,plain,
( product(A,B,C)
| ~ sum(multiply(A,B),additive_identity,C) ),
inference(resolve,[status(thm)],[c_879,c_2]) ).
cnf(c_881,plain,
~ sum(multiply(x,additive_identity),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_880,c_23]) ).
cnf(c_874,plain,
$false,
inference(resolve,[status(thm)],[c_835,c_881]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n010.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 22:34:30 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 187630 was started by sandbox on n010,
% 0.07/0.35 % Sat Sep 26 22:34:30 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.77/0.47
% 0.77/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.77/0.47
% 0.77/0.47 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.77/0.47 % Length of proof is 9.
% 0.77/0.47 % Level of proof is 2.
% 0.77/0.47 % Maximum clause weight is 25.000.
% 0.77/0.47 % Given clauses 23.
% 0.77/0.47
% 0.77/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------