%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO016-1 : 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 : 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 06:55:06 AM UTC 2026
% Result : Unsatisfiable 2.26s 0.77s
% Output : CNFRefutation 2.26s
% 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; 4 con; 0-2 aty)
% Number of variables : 105 ( 1 sgn 33 !; 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(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(x_times_y,axiom,
product(x,y,z),
file('theBenchmark.p',x_times_y) ).
cnf(c_23,plain,
product(x,y,z),
inference(clausify,[status(thm)],[x_times_y]) ).
fof(prove_sum,axiom,
~ sum(x,z,x),
file('theBenchmark.p',prove_sum) ).
cnf(c_24,plain,
~ sum(x,z,x),
inference(clausify,[status(thm)],[prove_sum]) ).
cnf(c_25,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_1346,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_1347,plain,
( product(add(A,B),multiplicative_identity,D)
| ~ sum(C,B,D)
| ~ product(A,inverse(B),C) ),
inference(resolve,[status(thm)],[c_1346,c_17]) ).
cnf(c_1348,plain,
( product(add(multiplicative_identity,A),multiplicative_identity,B)
| ~ sum(inverse(A),A,B) ),
inference(resolve,[status(thm)],[c_1347,c_7]) ).
cnf(c_252,plain,
product(add(multiplicative_identity,A),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_1348,c_17]) ).
cnf(c_1349,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_1350,plain,
( sum(x,z,B)
| ~ product(x,A,B)
| ~ sum(multiplicative_identity,y,A) ),
inference(resolve,[status(thm)],[c_1349,c_23]) ).
cnf(c_1351,plain,
( sum(x,z,x)
| ~ sum(multiplicative_identity,y,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_1350,c_8]) ).
cnf(c_917,plain,
~ sum(multiplicative_identity,y,multiplicative_identity),
inference(resolve,[status(thm)],[c_1351,c_24]) ).
cnf(c_1352,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_21,c_1]) ).
cnf(c_921,plain,
add(A,B) = add(B,A),
inference(resolve,[status(thm)],[c_1352,c_25]) ).
cnf(c_1353,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_1354,plain,
( sum(A,B,D)
| ~ product(C,multiplicative_identity,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_1353,c_8]) ).
cnf(c_1355,plain,
( sum(B,A,C)
| ~ product(add(A,B),multiplicative_identity,C) ),
inference(resolve,[status(thm)],[c_1354,c_25]) ).
cnf(c_1356,plain,
~ product(add(y,multiplicative_identity),multiplicative_identity,multiplicative_identity),
inference(resolve,[status(thm)],[c_1355,c_917]) ).
cnf(c_1344,plain,
~ product(add(multiplicative_identity,y),multiplicative_identity,multiplicative_identity),
inference(paramod,[status(thm)],[c_921,c_1356]) ).
cnf(c_1345,plain,
$false,
inference(resolve,[status(thm)],[c_1344,c_252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n010.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 22:36:46 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.42 % Process 193418 was started by sandbox2 on n010,
% 0.14/0.42 % Sat Sep 26 22:36:46 2026
% 0.14/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.42
% 0.14/0.42 % From the command line: assign(max_seconds, 300).
% 2.26/0.77
% 2.26/0.77 % SZS status Unsatisfiable for theBenchmark
% 2.26/0.77
% 2.26/0.77 % Proof 1 at 0.24 (+ 0.09) seconds.
% 2.26/0.77 % Length of proof is 17.
% 2.26/0.77 % Level of proof is 4.
% 2.26/0.77 % Maximum clause weight is 25.000.
% 2.26/0.77 % Given clauses 36.
% 2.26/0.77
% 2.26/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------