%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO013-3 : 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 : n002.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 06:55:05 AM UTC 2026
% Result : Unsatisfiable 0.13s 15.75s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 27 unt; 0 def)
% Number of atoms : 85 ( 11 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 83 ( 44 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 27 !; 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_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( sum(VAR_1,VAR_0,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(c_3,plain,
( sum(B,A,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
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(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(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity4) ).
cnf(c_12,plain,
( product(F,B,V6)
| ~ sum(C,E,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity4]) ).
fof(multiplication_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',multiplication_is_well_defined) ).
cnf(c_22,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[multiplication_is_well_defined]) ).
fof(sum_to_multiplicative_identity1,axiom,
sum(x,y,multiplicative_identity),
file('theBenchmark.p',sum_to_multiplicative_identity1) ).
cnf(c_24,plain,
sum(x,y,multiplicative_identity),
inference(clausify,[status(thm)],[sum_to_multiplicative_identity1]) ).
fof(sum_to_multiplicative_identity2,axiom,
sum(x,z,multiplicative_identity),
file('theBenchmark.p',sum_to_multiplicative_identity2) ).
cnf(c_25,plain,
sum(x,z,multiplicative_identity),
inference(clausify,[status(thm)],[sum_to_multiplicative_identity2]) ).
fof(product_to_additive_identity1,axiom,
product(x,y,additive_identity),
file('theBenchmark.p',product_to_additive_identity1) ).
cnf(c_26,plain,
product(x,y,additive_identity),
inference(clausify,[status(thm)],[product_to_additive_identity1]) ).
fof(product_to_additive_identity2,axiom,
product(x,z,additive_identity),
file('theBenchmark.p',product_to_additive_identity2) ).
cnf(c_27,plain,
product(x,z,additive_identity),
inference(clausify,[status(thm)],[product_to_additive_identity2]) ).
fof(prove_both_inverse_are_equal,axiom,
y != z,
file('theBenchmark.p',prove_both_inverse_are_equal) ).
cnf(c_28,plain,
y != z,
inference(clausify,[status(thm)],[prove_both_inverse_are_equal]) ).
cnf(c_29,plain,
z != y,
inference(copy,[status(thm)],[c_28]) ).
cnf(c_31,plain,
product(A,B,multiply(B,A)),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_1414,plain,
( A = B
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_22,c_7]) ).
cnf(c_1415,plain,
A = multiply(multiplicative_identity,A),
inference(resolve,[status(thm)],[c_1414,c_2]) ).
cnf(c_725,plain,
multiply(multiplicative_identity,A) = A,
inference(copy,[status(thm)],[c_1415]) ).
cnf(c_777,plain,
sum(y,x,multiplicative_identity),
inference(resolve,[status(thm)],[c_3,c_24]) ).
cnf(c_833,plain,
sum(z,x,multiplicative_identity),
inference(resolve,[status(thm)],[c_3,c_25]) ).
cnf(c_1416,plain,
( A = B
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_22,c_7]) ).
cnf(c_953,plain,
~ product(multiplicative_identity,z,y),
inference(resolve,[status(thm)],[c_1416,c_29]) ).
cnf(c_1417,plain,
( product(E,B,F)
| ~ sum(multiply(D,B),C,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_2]) ).
cnf(c_1418,plain,
( product(B,z,C)
| ~ sum(multiply(A,z),additive_identity,C)
| ~ sum(A,x,B) ),
inference(resolve,[status(thm)],[c_1417,c_27]) ).
cnf(c_1419,plain,
( product(multiplicative_identity,z,A)
| ~ sum(multiply(y,z),additive_identity,A) ),
inference(resolve,[status(thm)],[c_1418,c_777]) ).
cnf(c_1242,plain,
~ sum(multiply(y,z),additive_identity,y),
inference(resolve,[status(thm)],[c_1419,c_953]) ).
cnf(c_1420,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_22,c_2]) ).
cnf(c_1288,plain,
multiply(A,B) = multiply(B,A),
inference(resolve,[status(thm)],[c_1420,c_31]) ).
cnf(c_1421,plain,
( sum(multiply(B,D),C,F)
| ~ product(E,B,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_11,c_31]) ).
cnf(c_1422,plain,
( sum(multiply(y,A),additive_identity,C)
| ~ product(B,y,C)
| ~ sum(A,x,B) ),
inference(resolve,[status(thm)],[c_1421,c_26]) ).
cnf(c_1423,plain,
( sum(multiply(y,z),additive_identity,A)
| ~ product(multiplicative_identity,y,A) ),
inference(resolve,[status(thm)],[c_1422,c_833]) ).
cnf(c_1424,plain,
sum(multiply(y,z),additive_identity,multiply(y,multiplicative_identity)),
inference(resolve,[status(thm)],[c_1423,c_31]) ).
cnf(c_1425,plain,
sum(multiply(y,z),additive_identity,multiply(multiplicative_identity,y)),
inference(paramod,[status(thm)],[c_1288,c_1424]) ).
cnf(c_1412,plain,
sum(multiply(y,z),additive_identity,y),
inference(paramod,[status(thm)],[c_725,c_1425]) ).
cnf(c_1413,plain,
$false,
inference(resolve,[status(thm)],[c_1412,c_1242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.37 % Computer : n002.cluster.edu
% 0.10/15.37 % Model : x86_64 x86_64
% 0.10/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.37 % Memory : 8046.5625MB
% 0.10/15.37 % OS : Linux 6.8.0-71-generic
% 0.10/15.37 % CPULimit : 300
% 0.10/15.37 % WCLimit : 300
% 0.10/15.37 % DateTime : Sat Sep 26 22:38:37 UTC 2026
% 0.10/15.37 % CPUTime :
% 0.10/15.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/15.37 % Process 2860286 was started by sandbox on n002,
% 0.10/15.37 % Sat Sep 26 22:38:37 2026
% 0.10/15.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/15.38
% 0.10/15.38 % From the command line: assign(max_seconds, 300).
% 0.13/15.75
% 0.13/15.75 % SZS status Unsatisfiable for theBenchmark
% 0.13/15.75
% 0.13/15.75 % Proof 1 at 0.27 (+ 0.10) seconds.
% 0.13/15.75 % Length of proof is 22.
% 0.13/15.75 % Level of proof is 4.
% 0.13/15.75 % Maximum clause weight is 20.000.
% 0.13/15.75 % Given clauses 38.
% 0.13/15.75
% 0.13/15.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------