%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:11:37 AM UTC 2026
% Result : Unsatisfiable 0.21s 1.67s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 49 ( 31 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 41 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_29,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(d_is_defined,axiom,
defined(d),
file('theBenchmark.p',d_is_defined) ).
cnf(c_30,plain,
defined(d),
inference(clausify,[status(thm)],[d_is_defined]) ).
fof(s_is_defined,axiom,
defined(s),
file('theBenchmark.p',s_is_defined) ).
cnf(c_32,plain,
defined(s),
inference(clausify,[status(thm)],[s_is_defined]) ).
fof(not_sum_7,axiom,
~ sum(additive_identity,b,additive_identity),
file('theBenchmark.p',not_sum_7) ).
cnf(c_33,plain,
~ sum(additive_identity,b,additive_identity),
inference(clausify,[status(thm)],[not_sum_7]) ).
fof(not_sum_8,axiom,
~ sum(additive_identity,d,additive_identity),
file('theBenchmark.p',not_sum_8) ).
cnf(c_34,plain,
~ sum(additive_identity,d,additive_identity),
inference(clausify,[status(thm)],[not_sum_8]) ).
fof(product_9,axiom,
product(a,multiplicative_inverse(b),s),
file('theBenchmark.p',product_9) ).
cnf(c_35,plain,
product(a,multiplicative_inverse(b),s),
inference(clausify,[status(thm)],[product_9]) ).
fof(product_10,axiom,
product(a,d,k),
file('theBenchmark.p',product_10) ).
cnf(c_36,plain,
product(a,d,k),
inference(clausify,[status(thm)],[product_10]) ).
fof(product_11,axiom,
product(b,c,k),
file('theBenchmark.p',product_11) ).
cnf(c_37,plain,
product(b,c,k),
inference(clausify,[status(thm)],[product_11]) ).
fof(not_product_12,axiom,
~ product(c,multiplicative_inverse(d),s),
file('theBenchmark.p',not_product_12) ).
cnf(c_38,plain,
~ product(c,multiplicative_inverse(d),s),
inference(clausify,[status(thm)],[not_product_12]) ).
cnf(c_4639,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_28,c_9]) ).
cnf(c_120,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(resolve,[status(thm)],[c_33,c_4639]) ).
cnf(c_137,plain,
product(multiplicative_identity,c,c),
inference(resolve,[status(thm)],[c_29,c_8]) ).
cnf(c_4640,plain,
( sum(additive_identity,d,additive_identity)
| product(multiplicative_inverse(d),d,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_30,c_9]) ).
cnf(c_152,plain,
product(multiplicative_inverse(d),d,multiplicative_identity),
inference(resolve,[status(thm)],[c_34,c_4640]) ).
cnf(c_185,plain,
product(multiplicative_identity,s,s),
inference(resolve,[status(thm)],[c_32,c_8]) ).
cnf(c_192,plain,
product(multiplicative_inverse(b),a,s),
inference(resolve,[status(thm)],[c_35,c_10]) ).
cnf(c_213,plain,
( ~ product(C,c,B)
| ~ product(A,b,C)
| product(A,k,B) ),
inference(resolve,[status(thm)],[c_37,c_6]) ).
cnf(c_215,plain,
~ product(multiplicative_inverse(d),c,s),
inference(resolve,[status(thm)],[c_10,c_38]) ).
cnf(c_4641,plain,
( ~ product(B,C,s)
| ~ product(A,C,c)
| ~ product(multiplicative_inverse(d),A,B) ),
inference(resolve,[status(thm)],[c_6,c_215]) ).
cnf(c_4642,plain,
( ~ product(multiplicative_identity,A,s)
| ~ product(d,A,c) ),
inference(resolve,[status(thm)],[c_4641,c_152]) ).
cnf(c_2389,plain,
~ product(d,s,c),
inference(resolve,[status(thm)],[c_4642,c_185]) ).
cnf(c_2438,plain,
~ product(s,d,c),
inference(resolve,[status(thm)],[c_10,c_2389]) ).
cnf(c_4643,plain,
( ~ product(A,C,c)
| ~ product(B,d,C)
| ~ product(A,B,s) ),
inference(resolve,[status(thm)],[c_7,c_2438]) ).
cnf(c_4644,plain,
( ~ product(multiplicative_inverse(b),A,c)
| ~ product(a,d,A) ),
inference(resolve,[status(thm)],[c_4643,c_192]) ).
cnf(c_3049,plain,
~ product(multiplicative_inverse(b),k,c),
inference(resolve,[status(thm)],[c_4644,c_36]) ).
cnf(c_3214,plain,
( ~ product(A,b,multiplicative_identity)
| product(A,k,c) ),
inference(resolve,[status(thm)],[c_213,c_137]) ).
cnf(c_4645,plain,
product(multiplicative_inverse(b),k,c),
inference(resolve,[status(thm)],[c_3214,c_120]) ).
cnf(c_4638,plain,
$false,
inference(resolve,[status(thm)],[c_3049,c_4645]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/1.06 % Computer : n008.cluster.edu
% 0.17/1.06 % Model : x86_64 x86_64
% 0.17/1.06 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/1.06 % Memory : 8046.5625MB
% 0.17/1.06 % OS : Linux 6.8.0-71-generic
% 0.17/1.06 % CPULimit : 300
% 0.17/1.06 % WCLimit : 300
% 0.17/1.06 % DateTime : Sun Sep 27 02:30:41 UTC 2026
% 0.17/1.06 % CPUTime :
% 0.17/1.06 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/1.06 % Process 845358 was started by sandbox on n008,
% 0.17/1.06 % Sun Sep 27 02:30:41 2026
% 0.17/1.06 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/1.07
% 0.17/1.07 % From the command line: assign(max_seconds, 300).
% 0.21/1.67
% 0.21/1.67 % given #500 (T,wt=13): 1307 sum(additive_identity,A,additive_identity) | -sum(a,A,a). [resolve(106,a,41,b)].
% 0.21/1.67
% 0.21/1.67 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.67
% 0.21/1.67 % Proof 1 at 0.48 (+ 0.10) seconds.
% 0.21/1.67 % Length of proof is 27.
% 0.21/1.67 % Level of proof is 5.
% 0.21/1.67 % Maximum clause weight is 21.000.
% 0.21/1.67 % Given clauses 604.
% 0.21/1.67
% 0.21/1.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------