%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO013-1 : 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 : n017.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 0.71s 0.59s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 24 unt; 0 def)
% Number of atoms : 78 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 79 ( 42 ~; 37 |; 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 : 78 ( 0 sgn 28 !; 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(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(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(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_23,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_24,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_25,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_26,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_27,plain,
y != z,
inference(clausify,[status(thm)],[prove_both_inverse_are_equal]) ).
cnf(c_28,plain,
z != y,
inference(copy,[status(thm)],[c_27]) ).
cnf(c_959,plain,
sum(y,x,multiplicative_identity),
inference(resolve,[status(thm)],[c_23,c_3]) ).
cnf(c_1028,plain,
sum(z,x,multiplicative_identity),
inference(resolve,[status(thm)],[c_24,c_3]) ).
cnf(c_1085,plain,
product(y,x,additive_identity),
inference(resolve,[status(thm)],[c_25,c_4]) ).
cnf(c_1654,plain,
( A = B
| ~ product(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_22,c_7]) ).
cnf(c_1205,plain,
~ product(multiplicative_identity,z,y),
inference(resolve,[status(thm)],[c_1654,c_28]) ).
cnf(c_1655,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_1656,plain,
( product(B,z,C)
| ~ sum(multiply(A,z),additive_identity,C)
| ~ sum(A,x,B) ),
inference(resolve,[status(thm)],[c_1655,c_26]) ).
cnf(c_1657,plain,
( product(multiplicative_identity,z,A)
| ~ sum(multiply(y,z),additive_identity,A) ),
inference(resolve,[status(thm)],[c_1656,c_959]) ).
cnf(c_1547,plain,
~ sum(multiply(y,z),additive_identity,y),
inference(resolve,[status(thm)],[c_1657,c_1205]) ).
cnf(c_1658,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_1659,plain,
( sum(multiply(y,A),additive_identity,C)
| ~ product(y,B,C)
| ~ sum(A,x,B) ),
inference(resolve,[status(thm)],[c_1658,c_1085]) ).
cnf(c_1660,plain,
( sum(multiply(y,z),additive_identity,A)
| ~ product(y,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_1659,c_1028]) ).
cnf(c_1661,plain,
sum(multiply(y,z),additive_identity,y),
inference(resolve,[status(thm)],[c_1660,c_8]) ).
cnf(c_1653,plain,
$false,
inference(resolve,[status(thm)],[c_1547,c_1661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-1 : 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 : n017.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 22:30:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 1816702 was started by sandbox2 on n017,
% 0.12/0.38 % Sat Sep 26 22:30:50 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).
% 0.71/0.59
% 0.71/0.59 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.71/0.59
% 0.71/0.59 % SZS status Unsatisfiable for theBenchmark
% 0.71/0.59
% 0.71/0.59 % Proof 1 at 0.15 (+ 0.06) seconds.
% 0.71/0.59 % Length of proof is 20.
% 0.71/0.59 % Level of proof is 4.
% 0.71/0.59 % Maximum clause weight is 25.000.
% 0.71/0.59 % Given clauses 35.
% 0.71/0.59
% 0.71/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------