%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO017-1 : 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 06:55:07 AM UTC 2026
% Result : Unsatisfiable 0.87s 0.59s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 17 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 92 ( 48 ~; 44 |; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 1 sgn 29 !; 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(commutativity_of_multiplication,axiom,
! [VAR_0,VAR_1,VAR_2] :
( product(VAR_1,VAR_0,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_of_multiplication) ).
cnf(c_4,plain,
( product(B,A,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_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(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(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(x_plus_y,axiom,
sum(x,y,z),
file('theBenchmark.p',x_plus_y) ).
cnf(c_23,plain,
sum(x,y,z),
inference(clausify,[status(thm)],[x_plus_y]) ).
fof(prove_product,axiom,
~ product(x,z,x),
file('theBenchmark.p',prove_product) ).
cnf(c_24,plain,
~ product(x,z,x),
inference(clausify,[status(thm)],[prove_product]) ).
cnf(c_26,plain,
product(A,B,multiply(B,A)),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_2362,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_2363,plain,
( sum(multiply(B,A),additive_identity,D)
| ~ product(B,C,D)
| ~ sum(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_2362,c_20]) ).
cnf(c_2364,plain,
( sum(multiply(A,additive_identity),additive_identity,B)
| ~ product(A,inverse(A),B) ),
inference(resolve,[status(thm)],[c_2363,c_5]) ).
cnf(c_808,plain,
sum(multiply(A,additive_identity),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_2364,c_20]) ).
cnf(c_2365,plain,
( product(A,C,E)
| ~ sum(A,D,E)
| ~ product(additive_identity,B,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_2366,plain,
( product(x,z,B)
| ~ sum(x,A,B)
| ~ product(additive_identity,y,A) ),
inference(resolve,[status(thm)],[c_2365,c_23]) ).
cnf(c_2367,plain,
( product(x,z,x)
| ~ product(additive_identity,y,additive_identity) ),
inference(resolve,[status(thm)],[c_2366,c_6]) ).
cnf(c_952,plain,
~ product(additive_identity,y,additive_identity),
inference(resolve,[status(thm)],[c_2367,c_24]) ).
cnf(c_2368,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_2369,plain,
( product(A,B,D)
| ~ sum(C,additive_identity,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_2368,c_6]) ).
cnf(c_2370,plain,
( product(B,A,C)
| ~ sum(multiply(A,B),additive_identity,C) ),
inference(resolve,[status(thm)],[c_2369,c_26]) ).
cnf(c_2371,plain,
~ sum(multiply(y,additive_identity),additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_2370,c_952]) ).
cnf(c_2361,plain,
$false,
inference(resolve,[status(thm)],[c_808,c_2371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n010.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 22:37:31 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 196754 was started by sandbox on n010,
% 0.12/0.37 % Sat Sep 26 22:37:31 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.87/0.59
% 0.87/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.87/0.59
% 0.87/0.59 % Proof 1 at 0.15 (+ 0.05) seconds.
% 0.87/0.59 % Length of proof is 14.
% 0.87/0.59 % Level of proof is 2.
% 0.87/0.59 % Maximum clause weight is 25.000.
% 0.87/0.59 % Given clauses 35.
% 0.87/0.59
% 0.87/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------