%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO010-1 : 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 : n016.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 06:55:03 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.48s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 19 unt; 0 def)
% Number of atoms : 88 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 103 ( 54 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 1 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(closure_of_addition,axiom,
! [VAR_0,VAR_1] : sum(VAR_0,VAR_1,add(VAR_0,VAR_1)),
file('theBenchmark.p',closure_of_addition) ).
cnf(c_1,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
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(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(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(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(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(addition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ sum(VAR_0,VAR_1,VAR_3)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',addition_is_well_defined) ).
cnf(c_21,plain,
( C = D
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(prove_equations,axiom,
~ sum(x,multiply(x,y),x),
file('theBenchmark.p',prove_equations) ).
cnf(c_23,plain,
~ sum(x,multiply(x,y),x),
inference(clausify,[status(thm)],[prove_equations]) ).
cnf(c_24,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_993,plain,
( product(add(D,B),C,F)
| ~ sum(E,B,F)
| ~ product(D,A,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_1]) ).
cnf(c_994,plain,
( product(add(A,B),multiplicative_identity,D)
| ~ sum(C,B,D)
| ~ product(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_993,c_17]) ).
cnf(c_995,plain,
( product(add(multiplicative_identity,A),multiplicative_identity,B)
| ~ sum(inverse(A),A,B) ),
inference(resolve,[status(thm)],[c_994,c_7]) ).
cnf(c_251,plain,
product(add(multiplicative_identity,A),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_995,c_17]) ).
cnf(c_996,plain,
( sum(A,C,E)
| ~ product(A,D,E)
| ~ sum(multiplicative_identity,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_997,plain,
( sum(C,multiply(C,A),D)
| ~ product(C,B,D)
| ~ sum(multiplicative_identity,A,B) ),
inference(resolve,[status(thm)],[c_996,c_2]) ).
cnf(c_998,plain,
( sum(B,multiply(B,A),B)
| ~ sum(multiplicative_identity,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_997,c_8]) ).
cnf(c_856,plain,
~ sum(multiplicative_identity,y,multiplicative_identity),
inference(resolve,[status(thm)],[c_998,c_23]) ).
cnf(c_999,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_21,c_1]) ).
cnf(c_860,plain,
add(A,B) = add(B,A),
inference(resolve,[status(thm)],[c_999,c_24]) ).
cnf(c_1000,plain,
( sum(C,B,E)
| ~ product(D,multiplicative_identity,E)
| ~ sum(C,A,D)
| ~ product(A,multiplicative_identity,B) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_1001,plain,
( sum(A,B,D)
| ~ product(C,multiplicative_identity,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_1000,c_8]) ).
cnf(c_1002,plain,
( sum(B,A,C)
| ~ product(add(A,B),multiplicative_identity,C) ),
inference(resolve,[status(thm)],[c_1001,c_24]) ).
cnf(c_1003,plain,
~ product(add(y,multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_1002,c_856]) ).
cnf(c_991,plain,
~ product(add(multiplicative_identity,y),multiplicative_identity,multiplicative_identity),
inference(paramod,[status(thm)],[c_860,c_1003]) ).
cnf(c_992,plain,
$false,
inference(resolve,[status(thm)],[c_991,c_251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:40:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1889629 was started by sandbox on n016,
% 0.09/0.37 % Sat Sep 26 22:40:18 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.48
% 0.09/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.48
% 0.09/0.48 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.09/0.48 % Length of proof is 17.
% 0.09/0.48 % Level of proof is 4.
% 0.09/0.48 % Maximum clause weight is 20.000.
% 0.09/0.48 % Given clauses 25.
% 0.09/0.48
% 0.09/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------