%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG008-5 : 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 : n012.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 08:26:19 AM UTC 2026
% Result : Unsatisfiable 5.66s 1.20s
% Output : CNFRefutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 127 ( 71 unt; 0 def)
% Number of atoms : 242 ( 31 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 243 ( 128 ~; 115 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 330 ( 1 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity1,axiom,
! [VAR_0] : sum(additive_identity,VAR_0,VAR_0),
file('theBenchmark.p',additive_identity1) ).
cnf(c_1,plain,
sum(additive_identity,A,A),
inference(clausify,[status(thm)],[additive_identity1]) ).
fof(additive_identity2,axiom,
! [VAR_0] : sum(VAR_0,additive_identity,VAR_0),
file('theBenchmark.p',additive_identity2) ).
cnf(c_2,plain,
sum(A,additive_identity,A),
inference(clausify,[status(thm)],[additive_identity2]) ).
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_3,plain,
product(A,B,multiply(A,B)),
inference(clausify,[status(thm)],[closure_of_multiplication]) ).
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_4,plain,
sum(A,B,add(A,B)),
inference(clausify,[status(thm)],[closure_of_addition]) ).
fof(left_inverse,axiom,
! [VAR_0] : sum(additive_inverse(VAR_0),VAR_0,additive_identity),
file('theBenchmark.p',left_inverse) ).
cnf(c_5,plain,
sum(additive_inverse(A),A,additive_identity),
inference(clausify,[status(thm)],[left_inverse]) ).
fof(right_inverse,axiom,
! [VAR_0] : sum(VAR_0,additive_inverse(VAR_0),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(c_6,plain,
sum(A,additive_inverse(A),additive_identity),
inference(clausify,[status(thm)],[right_inverse]) ).
fof(associativity_of_addition1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition1) ).
cnf(c_7,plain,
( sum(A,E,F)
| ~ sum(C,D,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition1]) ).
fof(associativity_of_addition2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( sum(VAR_2,VAR_3,VAR_5)
| ~ sum(VAR_0,VAR_4,VAR_5)
| ~ sum(VAR_1,VAR_3,VAR_4)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_addition2) ).
cnf(c_8,plain,
( sum(C,D,F)
| ~ sum(A,E,F)
| ~ sum(B,D,E)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_addition2]) ).
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_9,plain,
( sum(B,A,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_addition]) ).
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_12,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(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_0,VAR_5,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity2) ).
cnf(c_13,plain,
( product(A,F,V6)
| ~ sum(C,E,V6)
| ~ sum(B,D,F)
| ~ product(A,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity2]) ).
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_14,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(distributivity4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( product(VAR_5,VAR_1,VAR_6)
| ~ sum(VAR_2,VAR_4,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',distributivity4) ).
cnf(c_15,plain,
( product(F,B,V6)
| ~ sum(C,E,V6)
| ~ sum(A,D,F)
| ~ product(D,B,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[distributivity4]) ).
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_16,plain,
( C = D
| ~ sum(A,B,D)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[addition_is_well_defined]) ).
fof(multiplication_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',multiplication_is_well_defined) ).
cnf(c_17,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[multiplication_is_well_defined]) ).
fof(multiply_additive_id2,axiom,
! [VAR_0] : product(additive_identity,VAR_0,additive_identity),
file('theBenchmark.p',multiply_additive_id2) ).
cnf(c_20,plain,
product(additive_identity,A,additive_identity),
inference(clausify,[status(thm)],[multiply_additive_id2]) ).
fof(multiply_additive_inverse,axiom,
! [VAR_0,VAR_1] : product(VAR_0,additive_inverse(VAR_1),additive_inverse(multiply(VAR_0,VAR_1))),
file('theBenchmark.p',multiply_additive_inverse) ).
cnf(c_22,plain,
product(A,additive_inverse(B),additive_inverse(multiply(A,B))),
inference(clausify,[status(thm)],[multiply_additive_inverse]) ).
fof(x_squared_is_x,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',x_squared_is_x) ).
cnf(c_23,plain,
product(A,A,A),
inference(clausify,[status(thm)],[x_squared_is_x]) ).
fof(a_times_b_is_c,axiom,
product(a,b,c),
file('theBenchmark.p',a_times_b_is_c) ).
cnf(c_24,plain,
product(a,b,c),
inference(clausify,[status(thm)],[a_times_b_is_c]) ).
fof(prove_b_times_a_is_c,axiom,
~ product(b,a,c),
file('theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_25,plain,
~ product(b,a,c),
inference(clausify,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_4071,plain,
( sum(A,C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_4072,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_4071,c_4]) ).
cnf(c_32,plain,
sum(A,add(additive_inverse(A),B),B),
inference(resolve,[status(thm)],[c_4072,c_1]) ).
cnf(c_4073,plain,
( sum(additive_inverse(A),C,D)
| ~ sum(additive_identity,B,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_4074,plain,
( sum(additive_inverse(C),add(C,A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_4073,c_4]) ).
cnf(c_39,plain,
sum(additive_inverse(A),add(A,B),B),
inference(resolve,[status(thm)],[c_4074,c_1]) ).
cnf(c_4075,plain,
( sum(D,C,E)
| ~ sum(add(D,A),B,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_4076,plain,
( sum(A,add(B,C),D)
| ~ sum(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_4075,c_4]) ).
cnf(c_48,plain,
sum(A,add(B,C),add(add(A,B),C)),
inference(resolve,[status(thm)],[c_4076,c_4]) ).
cnf(c_4077,plain,
( sum(add(D,A),B,E)
| ~ sum(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_4078,plain,
( sum(add(A,additive_inverse(C)),C,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_4077,c_5]) ).
cnf(c_78,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(resolve,[status(thm)],[c_4078,c_2]) ).
cnf(c_95,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_4079,plain,
( sum(multiply(A,D),C,F)
| ~ product(A,E,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_3]) ).
cnf(c_4080,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_4079,c_3]) ).
cnf(c_4081,plain,
( sum(multiply(A,B),multiply(A,C),D)
| ~ product(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_4080,c_4]) ).
cnf(c_100,plain,
sum(multiply(A,B),multiply(A,C),multiply(A,add(B,C))),
inference(resolve,[status(thm)],[c_4081,c_3]) ).
cnf(c_4082,plain,
( additive_identity = B
| ~ sum(A,additive_inverse(A),B) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_4083,plain,
additive_identity = additive_inverse(additive_identity),
inference(resolve,[status(thm)],[c_4082,c_1]) ).
cnf(c_119,plain,
additive_inverse(additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_4083]) ).
cnf(c_4084,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_121,plain,
add(A,additive_identity) = A,
inference(resolve,[status(thm)],[c_4084,c_2]) ).
cnf(c_4085,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_122,plain,
add(additive_identity,A) = A,
inference(resolve,[status(thm)],[c_4085,c_1]) ).
cnf(c_4086,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_4087,plain,
multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)),
inference(resolve,[status(thm)],[c_4086,c_22]) ).
cnf(c_139,plain,
additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)),
inference(copy,[status(thm)],[c_4087]) ).
cnf(c_4088,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_140,plain,
multiply(A,A) = A,
inference(resolve,[status(thm)],[c_4088,c_23]) ).
cnf(c_4089,plain,
( sum(multiply(D,B),C,F)
| ~ product(E,B,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_3]) ).
cnf(c_4090,plain,
( sum(multiply(A,B),B,D)
| ~ product(C,B,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_4089,c_23]) ).
cnf(c_4091,plain,
( sum(multiply(additive_inverse(A),A),A,B)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_4090,c_5]) ).
cnf(c_151,plain,
sum(multiply(additive_inverse(A),A),A,additive_identity),
inference(resolve,[status(thm)],[c_4091,c_20]) ).
cnf(c_4092,plain,
( product(D,B,E)
| ~ sum(additive_identity,C,E)
| ~ sum(additive_identity,A,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_4093,plain,
( product(B,C,D)
| ~ sum(additive_identity,multiply(A,C),D)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_4092,c_3]) ).
cnf(c_4094,plain,
( product(A,B,C)
| ~ sum(additive_identity,multiply(A,B),C) ),
inference(resolve,[status(thm)],[c_4093,c_1]) ).
cnf(c_216,plain,
~ sum(additive_identity,multiply(b,a),c),
inference(resolve,[status(thm)],[c_4094,c_25]) ).
cnf(c_4095,plain,
( sum(additive_identity,C,E)
| ~ product(D,B,E)
| ~ sum(additive_identity,A,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_20]) ).
cnf(c_4096,plain,
( sum(additive_identity,C,D)
| ~ product(A,B,D)
| ~ product(add(additive_inverse(additive_identity),A),B,C) ),
inference(resolve,[status(thm)],[c_4095,c_32]) ).
cnf(c_4097,plain,
( sum(additive_identity,A,c)
| ~ product(add(additive_inverse(additive_identity),a),b,A) ),
inference(resolve,[status(thm)],[c_4096,c_24]) ).
cnf(c_4098,plain,
~ product(add(additive_inverse(additive_identity),a),b,multiply(b,a)),
inference(resolve,[status(thm)],[c_4097,c_216]) ).
cnf(c_4099,plain,
~ product(add(additive_identity,a),b,multiply(b,a)),
inference(paramod,[status(thm)],[c_119,c_4098]) ).
cnf(c_275,plain,
~ product(a,b,multiply(b,a)),
inference(paramod,[status(thm)],[c_122,c_4099]) ).
cnf(c_4100,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_430,plain,
add(additive_inverse(A),add(A,B)) = B,
inference(resolve,[status(thm)],[c_4100,c_39]) ).
cnf(c_4101,plain,
( product(A,D,E)
| ~ sum(A,C,E)
| ~ sum(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_13,c_23]) ).
cnf(c_4102,plain,
( product(A,B,D)
| ~ sum(A,C,D)
| ~ product(A,add(additive_inverse(A),B),C) ),
inference(resolve,[status(thm)],[c_4101,c_32]) ).
cnf(c_4103,plain,
( product(A,B,C)
| ~ product(A,add(additive_inverse(A),B),add(additive_inverse(A),C)) ),
inference(resolve,[status(thm)],[c_4102,c_32]) ).
cnf(c_493,plain,
~ product(a,add(additive_inverse(a),b),add(additive_inverse(a),multiply(b,a))),
inference(resolve,[status(thm)],[c_4103,c_275]) ).
cnf(c_4104,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_666,plain,
add(A,B) = add(B,A),
inference(resolve,[status(thm)],[c_4104,c_95]) ).
cnf(c_4105,plain,
~ product(a,add(b,additive_inverse(a)),add(additive_inverse(a),multiply(b,a))),
inference(paramod,[status(thm)],[c_666,c_493]) ).
cnf(c_835,plain,
~ product(a,add(b,additive_inverse(a)),add(multiply(b,a),additive_inverse(a))),
inference(paramod,[status(thm)],[c_666,c_4105]) ).
cnf(c_4106,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_4107,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(resolve,[status(thm)],[c_4106,c_48]) ).
cnf(c_1037,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_4107]) ).
cnf(c_4108,plain,
( product(D,B,E)
| ~ sum(B,C,E)
| ~ sum(B,A,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_23]) ).
cnf(c_4109,plain,
( product(C,A,D)
| ~ sum(A,multiply(B,A),D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_4108,c_3]) ).
cnf(c_4110,plain,
( product(A,add(A,additive_inverse(B)),C)
| ~ sum(add(A,additive_inverse(B)),multiply(B,add(A,additive_inverse(B))),C) ),
inference(resolve,[status(thm)],[c_4109,c_78]) ).
cnf(c_4111,plain,
product(A,add(A,additive_inverse(B)),add(multiply(B,add(A,additive_inverse(B))),add(A,additive_inverse(B)))),
inference(resolve,[status(thm)],[c_4110,c_95]) ).
cnf(c_4112,plain,
product(A,add(A,additive_inverse(B)),add(add(A,additive_inverse(B)),multiply(B,add(A,additive_inverse(B))))),
inference(paramod,[status(thm)],[c_666,c_4111]) ).
cnf(c_1472,plain,
product(A,add(A,additive_inverse(B)),add(A,add(additive_inverse(B),multiply(B,add(A,additive_inverse(B)))))),
inference(paramod,[status(thm)],[c_1037,c_4112]) ).
cnf(c_4113,plain,
( sum(additive_identity,B,D)
| ~ sum(additive_inverse(A),C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_4114,plain,
( sum(additive_identity,A,B)
| ~ sum(additive_inverse(multiply(additive_inverse(A),A)),additive_identity,B) ),
inference(resolve,[status(thm)],[c_4113,c_151]) ).
cnf(c_4115,plain,
sum(additive_identity,A,add(additive_identity,additive_inverse(multiply(additive_inverse(A),A)))),
inference(resolve,[status(thm)],[c_4114,c_95]) ).
cnf(c_4116,plain,
sum(additive_identity,A,add(additive_identity,multiply(additive_inverse(A),additive_inverse(A)))),
inference(paramod,[status(thm)],[c_139,c_4115]) ).
cnf(c_4117,plain,
sum(additive_identity,A,add(additive_identity,additive_inverse(A))),
inference(paramod,[status(thm)],[c_140,c_4116]) ).
cnf(c_2190,plain,
sum(additive_identity,A,additive_inverse(A)),
inference(paramod,[status(thm)],[c_122,c_4117]) ).
cnf(c_4118,plain,
( add(B,A) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_95]) ).
cnf(c_4119,plain,
add(A,additive_identity) = additive_inverse(A),
inference(resolve,[status(thm)],[c_4118,c_2190]) ).
cnf(c_4120,plain,
A = additive_inverse(A),
inference(paramod,[status(thm)],[c_121,c_4119]) ).
cnf(c_2369,plain,
additive_inverse(A) = A,
inference(copy,[status(thm)],[c_4120]) ).
cnf(c_4121,plain,
product(A,add(A,B),add(A,add(additive_inverse(B),multiply(B,add(A,additive_inverse(B)))))),
inference(paramod,[status(thm)],[c_2369,c_1472]) ).
cnf(c_4122,plain,
product(A,add(A,B),add(A,add(B,multiply(B,add(A,additive_inverse(B)))))),
inference(paramod,[status(thm)],[c_2369,c_4121]) ).
cnf(c_2779,plain,
product(A,add(A,B),add(A,add(B,multiply(B,add(A,B))))),
inference(paramod,[status(thm)],[c_2369,c_4122]) ).
cnf(c_4123,plain,
~ product(a,add(b,a),add(multiply(b,a),additive_inverse(a))),
inference(paramod,[status(thm)],[c_2369,c_835]) ).
cnf(c_4124,plain,
~ product(a,add(a,b),add(multiply(b,a),additive_inverse(a))),
inference(paramod,[status(thm)],[c_666,c_4123]) ).
cnf(c_4125,plain,
~ product(a,add(a,b),add(multiply(b,a),a)),
inference(paramod,[status(thm)],[c_2369,c_4124]) ).
cnf(c_2940,plain,
~ product(a,add(a,b),add(a,multiply(b,a))),
inference(paramod,[status(thm)],[c_666,c_4125]) ).
cnf(c_2997,plain,
add(A,add(A,B)) = B,
inference(paramod,[status(thm)],[c_2369,c_430]) ).
cnf(c_4126,plain,
( add(B,A) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_95]) ).
cnf(c_4127,plain,
add(multiply(A,B),multiply(A,C)) = multiply(A,add(C,B)),
inference(resolve,[status(thm)],[c_4126,c_100]) ).
cnf(c_3928,plain,
multiply(A,add(B,C)) = add(multiply(A,C),multiply(A,B)),
inference(copy,[status(thm)],[c_4127]) ).
cnf(c_4128,plain,
product(A,add(A,B),add(A,add(B,add(multiply(B,B),multiply(B,A))))),
inference(paramod,[status(thm)],[c_3928,c_2779]) ).
cnf(c_4129,plain,
product(A,add(A,B),add(A,add(B,add(B,multiply(B,A))))),
inference(paramod,[status(thm)],[c_140,c_4128]) ).
cnf(c_4069,plain,
product(A,add(A,B),add(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_2997,c_4129]) ).
cnf(c_4070,plain,
$false,
inference(resolve,[status(thm)],[c_4069,c_2940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG008-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sat Sep 26 05:45:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 4018883 was started by sandbox on n012,
% 0.03/0.31 % Sat Sep 26 05:45:05 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.32
% 0.03/0.32 % From the command line: assign(max_seconds, 300).
% 5.66/1.20
% 5.66/1.20 % SZS status Unsatisfiable for theBenchmark
% 5.66/1.20
% 5.66/1.20 % Proof 1 at 0.60 (+ 0.22) seconds.
% 5.66/1.20 % Length of proof is 48.
% 5.66/1.20 % Level of proof is 6.
% 5.66/1.20 % Maximum clause weight is 20.000.
% 5.66/1.20 % Given clauses 98.
% 5.66/1.20
% 5.66/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------