%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO012-1 : 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 : n008.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 06:55:04 AM UTC 2026
% Result : Unsatisfiable 1.21s 0.57s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 18 unt; 0 def)
% Number of atoms : 64 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 37 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 25 !; 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(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(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity2) ).
cnf(c_10,plain,
( product(A,F,V6)
| ~ sum(C,E,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity2]) ).
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(additive_inverse1,axiom,
! [VAR_0] : sum(inverse(VAR_0),VAR_0,multiplicative_identity),
file('theBenchmark.p',additive_inverse1) ).
cnf(c_17,plain,
sum(inverse(A),A,multiplicative_identity),
inference(clausify,[status(thm)],[additive_inverse1]) ).
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_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(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(prove_inverse_is_an_involution,axiom,
inverse(inverse(x)) != x,
file('theBenchmark.p',prove_inverse_is_an_involution) ).
cnf(c_23,plain,
inverse(inverse(x)) != x,
inference(clausify,[status(thm)],[prove_inverse_is_an_involution]) ).
cnf(c_984,plain,
( sum(additive_identity,C,E)
| ~ product(D,inverse(B),E)
| ~ sum(B,A,D)
| ~ product(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_11,c_20]) ).
cnf(c_985,plain,
( sum(additive_identity,multiply(B,inverse(A)),D)
| ~ product(C,inverse(A),D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_984,c_2]) ).
cnf(c_986,plain,
( sum(additive_identity,multiply(A,inverse(inverse(A))),B)
| ~ product(multiplicative_identity,inverse(inverse(A)),B) ),
inference(resolve,[status(thm)],[c_985,c_17]) ).
cnf(c_769,plain,
sum(additive_identity,multiply(A,inverse(inverse(A))),inverse(inverse(A))),
inference(resolve,[status(thm)],[c_986,c_7]) ).
cnf(c_987,plain,
( B = A
| ~ product(A,multiplicative_identity,B) ),
inference(resolve,[status(thm)],[c_22,c_8]) ).
cnf(c_843,plain,
~ product(x,multiplicative_identity,inverse(inverse(x))),
inference(resolve,[status(thm)],[c_987,c_23]) ).
cnf(c_988,plain,
( product(A,D,E)
| ~ sum(additive_identity,C,E)
| ~ sum(inverse(A),B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_10,c_20]) ).
cnf(c_989,plain,
( product(A,C,D)
| ~ sum(additive_identity,multiply(A,B),D)
| ~ sum(inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_988,c_2]) ).
cnf(c_990,plain,
( product(A,multiplicative_identity,B)
| ~ sum(additive_identity,multiply(A,inverse(inverse(A))),B) ),
inference(resolve,[status(thm)],[c_989,c_18]) ).
cnf(c_982,plain,
~ sum(additive_identity,multiply(x,inverse(inverse(x))),inverse(inverse(x))),
inference(resolve,[status(thm)],[c_990,c_843]) ).
cnf(c_983,plain,
$false,
inference(resolve,[status(thm)],[c_982,c_769]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 22:35:39 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 528401 was started by sandbox2 on n008,
% 0.11/0.36 % Sat Sep 26 22:35:39 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 1.21/0.57
% 1.21/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.21/0.57
% 1.21/0.57 % Proof 1 at 0.13 (+ 0.06) seconds.
% 1.21/0.57 % Length of proof is 14.
% 1.21/0.57 % Level of proof is 3.
% 1.21/0.57 % Maximum clause weight is 20.000.
% 1.21/0.57 % Given clauses 25.
% 1.21/0.57
% 1.21/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------