%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD047-4 : 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 : n002.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 07:11:36 AM UTC 2026
% Result : Unsatisfiable 4.41s 6.28s
% Output : CNFRefutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of formulae : 93 ( 52 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 178 ( 99 ~; 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 : 10 ( 10 usr; 8 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(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(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_30,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(t_is_defined,axiom,
defined(t),
file('theBenchmark.p',t_is_defined) ).
cnf(c_32,plain,
defined(t),
inference(clausify,[status(thm)],[t_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,c,additive_identity),
file('theBenchmark.p',not_sum_8) ).
cnf(c_34,plain,
~ sum(additive_identity,c,additive_identity),
inference(clausify,[status(thm)],[not_sum_8]) ).
fof(product_9,axiom,
product(a,multiplicative_inverse(b),u),
file('theBenchmark.p',product_9) ).
cnf(c_35,plain,
product(a,multiplicative_inverse(b),u),
inference(clausify,[status(thm)],[product_9]) ).
fof(product_10,axiom,
product(a,c,s),
file('theBenchmark.p',product_10) ).
cnf(c_36,plain,
product(a,c,s),
inference(clausify,[status(thm)],[product_10]) ).
fof(product_11,axiom,
product(b,c,t),
file('theBenchmark.p',product_11) ).
cnf(c_37,plain,
product(b,c,t),
inference(clausify,[status(thm)],[product_11]) ).
fof(not_product_12,axiom,
~ product(s,multiplicative_inverse(t),u),
file('theBenchmark.p',not_product_12) ).
cnf(c_38,plain,
~ product(s,multiplicative_inverse(t),u),
inference(clausify,[status(thm)],[not_product_12]) ).
cnf(c_41,plain,
( ~ sum(D,B,D)
| ~ sum(C,D,A)
| sum(A,B,A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_47,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_60,plain,
( ~ product(B,C,A)
| ~ sum(B,B,B)
| sum(A,A,A) ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_65,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_67,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_105,plain,
product(multiplicative_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_3929,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_3929]) ).
cnf(c_121,plain,
product(multiplicative_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_122,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_3930,plain,
( sum(additive_identity,c,additive_identity)
| product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_29,c_9]) ).
cnf(c_136,plain,
product(multiplicative_inverse(c),c,multiplicative_identity),
inference(resolve,[status(thm)],[c_34,c_3930]) ).
cnf(c_153,plain,
product(multiplicative_identity,u,u),
inference(resolve,[status(thm)],[c_30,c_8]) ).
cnf(c_184,plain,
( sum(additive_identity,t,additive_identity)
| product(multiplicative_inverse(t),t,multiplicative_identity) ),
inference(resolve,[status(thm)],[c_32,c_9]) ).
cnf(c_185,plain,
product(multiplicative_identity,t,t),
inference(resolve,[status(thm)],[c_32,c_8]) ).
cnf(c_187,plain,
sum(additive_identity,t,t),
inference(resolve,[status(thm)],[c_32,c_3]) ).
cnf(c_195,plain,
( ~ product(a,C,B)
| ~ product(multiplicative_inverse(b),A,C)
| product(u,A,B) ),
inference(resolve,[status(thm)],[c_35,c_7]) ).
cnf(c_204,plain,
( ~ product(C,c,B)
| ~ product(A,C,a)
| product(A,B,s) ),
inference(resolve,[status(thm)],[c_36,c_6]) ).
cnf(c_208,plain,
product(c,b,t),
inference(resolve,[status(thm)],[c_37,c_10]) ).
cnf(c_215,plain,
~ product(multiplicative_inverse(t),s,u),
inference(resolve,[status(thm)],[c_10,c_38]) ).
cnf(c_272,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_65,c_10]) ).
cnf(c_386,plain,
product(a,multiplicative_identity,a),
inference(resolve,[status(thm)],[c_105,c_10]) ).
cnf(c_443,plain,
product(b,multiplicative_identity,b),
inference(resolve,[status(thm)],[c_121,c_10]) ).
cnf(c_592,plain,
product(t,multiplicative_identity,t),
inference(resolve,[status(thm)],[c_185,c_10]) ).
cnf(c_3931,plain,
( ~ sum(B,b,B)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_41,c_33]) ).
cnf(c_1747,plain,
~ sum(b,b,b),
inference(resolve,[status(thm)],[c_3931,c_122]) ).
cnf(c_3932,plain,
( ~ product(A,B,b)
| ~ sum(A,A,A) ),
inference(resolve,[status(thm)],[c_60,c_1747]) ).
cnf(c_1777,plain,
~ product(additive_identity,A,b),
inference(resolve,[status(thm)],[c_3932,c_67]) ).
cnf(c_1824,plain,
~ product(A,additive_identity,b),
inference(resolve,[status(thm)],[c_10,c_1777]) ).
cnf(c_3933,plain,
( ~ product(C,D,b)
| ~ product(B,D,additive_identity)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_6,c_1824]) ).
cnf(c_3934,plain,
( ~ product(multiplicative_identity,A,b)
| ~ product(c,A,additive_identity) ),
inference(resolve,[status(thm)],[c_3933,c_136]) ).
cnf(c_1921,plain,
~ product(c,b,additive_identity),
inference(resolve,[status(thm)],[c_3934,c_121]) ).
cnf(c_3935,plain,
( ~ product(B,C,additive_identity)
| ~ product(A,C,b)
| ~ product(c,A,B) ),
inference(resolve,[status(thm)],[c_6,c_1921]) ).
cnf(c_3936,plain,
( ~ product(t,A,additive_identity)
| ~ product(b,A,b) ),
inference(resolve,[status(thm)],[c_3935,c_208]) ).
cnf(c_1926,plain,
~ product(t,multiplicative_identity,additive_identity),
inference(resolve,[status(thm)],[c_3936,c_443]) ).
cnf(c_3937,plain,
( ~ sum(C,D,additive_identity)
| ~ product(B,multiplicative_identity,D)
| ~ product(A,multiplicative_identity,C)
| ~ sum(A,B,t) ),
inference(resolve,[status(thm)],[c_12,c_1926]) ).
cnf(c_3938,plain,
( ~ sum(A,B,additive_identity)
| ~ product(t,multiplicative_identity,B)
| ~ product(additive_identity,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_3937,c_187]) ).
cnf(c_3939,plain,
( ~ sum(additive_identity,A,additive_identity)
| ~ product(t,multiplicative_identity,A) ),
inference(resolve,[status(thm)],[c_3938,c_272]) ).
cnf(c_1935,plain,
~ sum(additive_identity,t,additive_identity),
inference(resolve,[status(thm)],[c_3939,c_592]) ).
cnf(c_1936,plain,
product(multiplicative_inverse(t),t,multiplicative_identity),
inference(resolve,[status(thm)],[c_1935,c_184]) ).
cnf(c_2643,plain,
( ~ product(a,multiplicative_identity,A)
| product(u,b,A) ),
inference(resolve,[status(thm)],[c_195,c_120]) ).
cnf(c_2679,plain,
( ~ product(A,b,a)
| product(A,t,s) ),
inference(resolve,[status(thm)],[c_204,c_37]) ).
cnf(c_3013,plain,
product(u,b,a),
inference(resolve,[status(thm)],[c_2643,c_386]) ).
cnf(c_3904,plain,
product(u,t,s),
inference(resolve,[status(thm)],[c_2679,c_3013]) ).
cnf(c_3910,plain,
product(t,u,s),
inference(resolve,[status(thm)],[c_3904,c_10]) ).
cnf(c_3940,plain,
( ~ product(B,C,u)
| ~ product(A,C,s)
| ~ product(multiplicative_inverse(t),A,B) ),
inference(resolve,[status(thm)],[c_6,c_215]) ).
cnf(c_3941,plain,
( ~ product(A,u,u)
| ~ product(multiplicative_inverse(t),t,A) ),
inference(resolve,[status(thm)],[c_3940,c_3910]) ).
cnf(c_3942,plain,
~ product(multiplicative_inverse(t),t,multiplicative_identity),
inference(resolve,[status(thm)],[c_3941,c_153]) ).
cnf(c_3928,plain,
$false,
inference(resolve,[status(thm)],[c_1936,c_3942]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD047-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.65 % Computer : n002.cluster.edu
% 0.18/5.65 % Model : x86_64 x86_64
% 0.18/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.65 % Memory : 8046.5625MB
% 0.18/5.65 % OS : Linux 6.8.0-71-generic
% 0.18/5.65 % CPULimit : 300
% 0.18/5.65 % WCLimit : 300
% 0.18/5.65 % DateTime : Sun Sep 27 02:31:13 UTC 2026
% 0.18/5.65 % CPUTime :
% 0.18/5.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.66 % Process 3141879 was started by sandbox2 on n002,
% 0.18/5.66 % Sun Sep 27 02:31:13 2026
% 0.18/5.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.66
% 0.18/5.66 % From the command line: assign(max_seconds, 300).
% 4.41/6.28
% 4.41/6.28 % given #500 (T,wt=13): 847 product(s,A,s) | -product(multiplicative_identity,A,multiplicative_identity). [resolve(566,a,45,b)].
% 4.41/6.28
% 4.41/6.28 % SZS status Unsatisfiable for theBenchmark
% 4.41/6.28
% 4.41/6.28 % Proof 1 at 0.50 (+ 0.11) seconds.
% 4.41/6.28 % Length of proof is 57.
% 4.41/6.28 % Level of proof is 9.
% 4.41/6.28 % Maximum clause weight is 25.000.
% 4.41/6.28 % Given clauses 580.
% 4.41/6.28
% 4.41/6.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------