%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD012-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 07:11:27 AM UTC 2026
% Result : Unsatisfiable 8.33s 1.60s
% Output : CNFRefutation 8.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of formulae : 89 ( 48 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 181 ( 102 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 124 ( 7 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_3,VAR_5,VAR_2)
| ~ sum(VAR_4,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_2) ).
cnf(c_2,plain,
( ~ sum(D,F,C)
| ~ sum(E,B,F)
| ~ sum(D,E,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_2]) ).
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(associativity_multiplication_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_4,VAR_5,VAR_2)
| ~ product(VAR_3,VAR_5,VAR_1)
| ~ product(VAR_0,VAR_3,VAR_4)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_1) ).
cnf(c_6,plain,
( ~ product(E,F,C)
| ~ product(D,F,B)
| ~ product(A,D,E)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_1]) ).
fof(associativity_multiplication_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ product(VAR_3,VAR_5,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_5)
| ~ product(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_multiplication_2) ).
cnf(c_7,plain,
( ~ product(D,F,C)
| ~ product(E,B,F)
| ~ product(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[associativity_multiplication_2]) ).
fof(existence_of_identity_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| product(multiplicative_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_multiplication) ).
cnf(c_8,plain,
( ~ defined(A)
| product(multiplicative_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_multiplication]) ).
fof(existence_of_inverse_multiplication,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,additive_identity)
| product(multiplicative_inverse(VAR_0),VAR_0,multiplicative_identity) ),
file('theBenchmark.p',existence_of_inverse_multiplication) ).
cnf(c_9,plain,
( ~ defined(A)
| sum(additive_identity,A,additive_identity)
| product(multiplicative_inverse(A),A,multiplicative_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_multiplication]) ).
fof(commutativity_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_multiplication) ).
cnf(c_10,plain,
( ~ product(B,A,C)
| product(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_multiplication]) ).
fof(distributivity_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ product(VAR_4,VAR_6,VAR_1)
| ~ product(VAR_3,VAR_6,VAR_0)
| ~ product(VAR_5,VAR_6,VAR_2)
| ~ sum(VAR_3,VAR_4,VAR_5)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_1) ).
cnf(c_11,plain,
( ~ product(E,V6,B)
| ~ product(D,V6,A)
| ~ product(F,V6,C)
| ~ sum(D,E,F)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_1]) ).
fof(distributivity_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( ~ sum(VAR_5,VAR_6,VAR_2)
| ~ product(VAR_4,VAR_1,VAR_6)
| ~ product(VAR_3,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',distributivity_2) ).
cnf(c_12,plain,
( ~ sum(F,V6,C)
| ~ product(E,B,V6)
| ~ product(D,B,F)
| ~ sum(D,E,A)
| product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity_2]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_14,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_28,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_29,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(v_is_defined,axiom,
defined(v),
file('theBenchmark.p',v_is_defined) ).
cnf(c_30,plain,
defined(v),
inference(clausify,[status(thm)],[v_is_defined]) ).
fof(not_sum_5,axiom,
~ sum(additive_identity,a,additive_identity),
file('theBenchmark.p',not_sum_5) ).
cnf(c_31,plain,
~ sum(additive_identity,a,additive_identity),
inference(clausify,[status(thm)],[not_sum_5]) ).
fof(not_sum_6,axiom,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_6) ).
cnf(c_32,plain,
~ sum(additive_identity,b,additive_identity),
inference(clausify,[status(thm)],[not_sum_6]) ).
fof(product_7,axiom,
product(a,b,u),
file('theBenchmark.p',product_7) ).
cnf(c_33,plain,
product(a,b,u),
inference(clausify,[status(thm)],[product_7]) ).
fof(product_8,axiom,
product(multiplicative_inverse(a),multiplicative_inverse(b),v),
file('theBenchmark.p',product_8) ).
cnf(c_34,plain,
product(multiplicative_inverse(a),multiplicative_inverse(b),v),
inference(clausify,[status(thm)],[product_8]) ).
fof(not_product_9,axiom,
~ product(multiplicative_identity,multiplicative_inverse(u),v),
file('theBenchmark.p',not_product_9) ).
cnf(c_35,plain,
~ product(multiplicative_identity,multiplicative_inverse(u),v),
inference(clausify,[status(thm)],[not_product_9]) ).
cnf(c_38,plain,
( ~ sum(D,B,D)
| ~ sum(C,D,A)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_44,plain,
( ~ product(D,E,B)
| ~ product(C,E,A)
| ~ sum(C,D,C)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_57,plain,
( ~ product(B,C,A)
| ~ sum(B,B,B)
| sum(A,A,A) ),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_62,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_64,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_10085,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_101,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolve,[status(thm)],[c_31,c_10085]) ).
cnf(c_102,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_103,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_10086,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_117,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_32,c_10086]) ).
cnf(c_133,plain,
( sum(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_29,c_9]) ).
cnf(c_134,plain,
product(multiplicative_identity,u,u),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_136,plain,
sum(additive_identity,u,u),
inference(resolve,[status(thm)],[c_29,c_3]) ).
cnf(c_150,plain,
product(multiplicative_identity,v,v),
inference(resolve,[status(thm)],[c_30,c_8]) ).
cnf(c_157,plain,
product(b,a,u),
inference(resolve,[status(thm)],[c_33,c_10]) ).
cnf(c_160,plain,
( ~ product(a,C,B)
| ~ product(b,A,C)
| product(u,A,B) ),
inference(resolve,[status(thm)],[c_33,c_7]) ).
cnf(c_165,plain,
product(multiplicative_inverse(b),multiplicative_inverse(a),v),
inference(resolve,[status(thm)],[c_34,c_10]) ).
cnf(c_172,plain,
~ product(multiplicative_inverse(u),multiplicative_identity,v),
inference(resolve,[status(thm)],[c_10,c_35]) ).
cnf(c_214,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_62,c_10]) ).
cnf(c_327,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_102,c_10]) ).
cnf(c_408,plain,
product(u,multiplicative_identity,u),
inference(resolve,[status(thm)],[c_134,c_10]) ).
cnf(c_1181,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(resolve,[status(thm)],[c_101,c_10]) ).
cnf(c_10087,plain,
( ~ sum(B,a,B)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_38,c_31]) ).
cnf(c_1218,plain,
~ sum(a,a,a),
inference(resolve,[status(thm)],[c_10087,c_103]) ).
cnf(c_10088,plain,
( ~ product(A,B,a)
| ~ sum(A,A,A) ),
inference(resolve,[status(thm)],[c_57,c_1218]) ).
cnf(c_1246,plain,
~ product(additive_identity,A,a),
inference(resolve,[status(thm)],[c_10088,c_64]) ).
cnf(c_1284,plain,
~ product(A,additive_identity,a),
inference(resolve,[status(thm)],[c_10,c_1246]) ).
cnf(c_1402,plain,
product(b,multiplicative_inverse(b),multiplicative_identity),
inference(resolve,[status(thm)],[c_117,c_10]) ).
cnf(c_10089,plain,
( ~ product(C,D,a)
| ~ product(B,D,additive_identity)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_1284]) ).
cnf(c_10090,plain,
( ~ product(multiplicative_identity,A,a)
| ~ product(b,A,additive_identity) ),
inference(resolve,[status(thm)],[c_10089,c_117]) ).
cnf(c_1423,plain,
~ product(b,a,additive_identity),
inference(resolve,[status(thm)],[c_10090,c_102]) ).
cnf(c_10091,plain,
( ~ product(B,C,additive_identity)
| ~ product(A,C,a)
| ~ product(b,A,B) ),
inference(resolve,[status(thm)],[c_6,c_1423]) ).
cnf(c_10092,plain,
( ~ product(u,A,additive_identity)
| ~ product(a,A,a) ),
inference(resolve,[status(thm)],[c_10091,c_157]) ).
cnf(c_1428,plain,
~ product(u,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_10092,c_327]) ).
cnf(c_10093,plain,
( ~ sum(C,D,additive_identity)
| ~ product(B,multiplicative_identity,D)
| ~ product(A,multiplicative_identity,C)
| ~ sum(A,B,u) ),
inference(resolve,[status(thm)],[c_12,c_1428]) ).
cnf(c_10094,plain,
( ~ sum(A,B,additive_identity)
| ~ product(u,multiplicative_identity,B)
| ~ product(additive_identity,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_10093,c_136]) ).
cnf(c_10095,plain,
( ~ sum(additive_identity,A,additive_identity)
| ~ product(u,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_10094,c_214]) ).
cnf(c_1436,plain,
~ sum(additive_identity,u,additive_identity),
inference(resolve,[status(thm)],[c_10095,c_408]) ).
cnf(c_1437,plain,
product(multiplicative_inverse(u),u,multiplicative_identity),
inference(resolve,[status(thm)],[c_1436,c_133]) ).
cnf(c_1917,plain,
( ~ product(b,A,multiplicative_identity)
| product(u,A,a) ),
inference(resolve,[status(thm)],[c_160,c_327]) ).
cnf(c_9988,plain,
product(u,multiplicative_inverse(b),a),
inference(resolve,[status(thm)],[c_1402,c_1917]) ).
cnf(c_10096,plain,
( ~ product(B,C,v)
| ~ product(A,C,multiplicative_identity)
| ~ product(multiplicative_inverse(u),A,B) ),
inference(resolve,[status(thm)],[c_6,c_172]) ).
cnf(c_10097,plain,
( ~ product(multiplicative_identity,A,v)
| ~ product(u,A,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_10096,c_1437]) ).
cnf(c_10072,plain,
~ product(u,v,multiplicative_identity),
inference(resolve,[status(thm)],[c_10097,c_150]) ).
cnf(c_10098,plain,
( ~ product(B,C,multiplicative_identity)
| ~ product(A,C,v)
| ~ product(u,A,B) ),
inference(resolve,[status(thm)],[c_6,c_10072]) ).
cnf(c_10099,plain,
( ~ product(A,multiplicative_inverse(a),multiplicative_identity)
| ~ product(u,multiplicative_inverse(b),A) ),
inference(resolve,[status(thm)],[c_10098,c_165]) ).
cnf(c_10100,plain,
~ product(u,multiplicative_inverse(b),a),
inference(resolve,[status(thm)],[c_10099,c_1181]) ).
cnf(c_10084,plain,
$false,
inference(resolve,[status(thm)],[c_9988,c_10100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD012-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 02:21:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1627698 was started by sandbox2 on n009,
% 0.09/0.36 % Sun Sep 27 02:21:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 8.33/1.60
% 8.33/1.60 % given #500 (A,wt=17): 215 product(A,B,additive_identity) | -product(multiplicative_identity,C,A) | -product(C,B,additive_identity). [resolve(62,a,7,d)].
% 8.33/1.60
% 8.33/1.60 % given #1000 (F,wt=15): 8836 -sum(additive_inverse(multiplicative_identity),v,v). [ur(5,a,1893,a)].
% 8.33/1.60
% 8.33/1.60 % SZS status Unsatisfiable for theBenchmark
% 8.33/1.60
% 8.33/1.60 % Proof 1 at 1.01 (+ 0.20) seconds.
% 8.33/1.60 % Length of proof is 53.
% 8.33/1.60 % Level of proof is 10.
% 8.33/1.60 % Maximum clause weight is 25.000.
% 8.33/1.60 % Given clauses 1010.
% 8.33/1.60
% 8.33/1.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------