%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG008-2 : 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 : n018.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 14.16s 12.26s
% Output : CNFRefutation 14.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 171 ( 91 unt; 0 def)
% Number of atoms : 321 ( 57 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 311 ( 161 ~; 150 |; 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 : 441 ( 5 sgn 61 !; 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(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(cancellation1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| ~ sum(VAR_0,VAR_3,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cancellation1) ).
cnf(c_18,plain,
( B = D
| ~ sum(A,D,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[cancellation1]) ).
fof(cancellation2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_3
| ~ sum(VAR_3,VAR_1,VAR_2)
| ~ sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cancellation2) ).
cnf(c_19,plain,
( A = D
| ~ sum(D,B,C)
| ~ sum(A,B,C) ),
inference(clausify,[status(thm)],[cancellation2]) ).
fof(x_squared_is_x,axiom,
! [VAR_0] : product(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',x_squared_is_x) ).
cnf(c_20,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_21,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_22,plain,
~ product(b,a,c),
inference(clausify,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_5673,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_5674,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_5673,c_4]) ).
cnf(c_29,plain,
sum(A,add(additive_inverse(A),B),B),
inference(resolve,[status(thm)],[c_5674,c_1]) ).
cnf(c_5675,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_5676,plain,
( sum(additive_inverse(C),add(C,A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_5675,c_4]) ).
cnf(c_38,plain,
sum(additive_inverse(A),add(A,B),B),
inference(resolve,[status(thm)],[c_5676,c_1]) ).
cnf(c_5677,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_5678,plain,
( sum(A,add(B,C),D)
| ~ sum(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_5677,c_4]) ).
cnf(c_47,plain,
sum(A,add(B,C),add(add(A,B),C)),
inference(resolve,[status(thm)],[c_5678,c_4]) ).
cnf(c_5679,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_5680,plain,
( sum(add(A,C),additive_inverse(C),B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_5679,c_6]) ).
cnf(c_74,plain,
sum(add(A,B),additive_inverse(B),A),
inference(resolve,[status(thm)],[c_5680,c_2]) ).
cnf(c_5681,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_5682,plain,
( sum(add(A,additive_inverse(C)),C,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_5681,c_5]) ).
cnf(c_77,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(resolve,[status(thm)],[c_5682,c_2]) ).
cnf(c_94,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_5683,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_5684,plain,
( sum(multiply(D,A),multiply(D,B),E)
| ~ product(D,C,E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5683,c_3]) ).
cnf(c_5685,plain,
( sum(multiply(A,B),multiply(A,C),D)
| ~ product(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_5684,c_4]) ).
cnf(c_99,plain,
sum(multiply(A,B),multiply(A,C),multiply(A,add(B,C))),
inference(resolve,[status(thm)],[c_5685,c_3]) ).
cnf(c_5686,plain,
( additive_identity = B
| ~ sum(A,additive_inverse(A),B) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_5687,plain,
additive_identity = add(A,additive_inverse(A)),
inference(resolve,[status(thm)],[c_5686,c_4]) ).
cnf(c_117,plain,
add(A,additive_inverse(A)) = additive_identity,
inference(copy,[status(thm)],[c_5687]) ).
cnf(c_5688,plain,
( additive_identity = B
| ~ sum(A,additive_inverse(A),B) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_5689,plain,
additive_identity = additive_inverse(additive_identity),
inference(resolve,[status(thm)],[c_5688,c_1]) ).
cnf(c_118,plain,
additive_inverse(additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_5689]) ).
cnf(c_5690,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_120,plain,
add(A,additive_identity) = A,
inference(resolve,[status(thm)],[c_5690,c_2]) ).
cnf(c_5691,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_121,plain,
add(additive_identity,A) = A,
inference(resolve,[status(thm)],[c_5691,c_1]) ).
cnf(c_5692,plain,
( additive_inverse(A) = B
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_18,c_6]) ).
cnf(c_122,plain,
additive_inverse(additive_inverse(A)) = A,
inference(resolve,[status(thm)],[c_5692,c_5]) ).
cnf(c_5693,plain,
( multiply(A,B) = C
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_17,c_3]) ).
cnf(c_123,plain,
multiply(A,A) = A,
inference(resolve,[status(thm)],[c_5693,c_20]) ).
cnf(c_5694,plain,
( sum(B,C,E)
| ~ product(D,B,E)
| ~ sum(B,A,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_20]) ).
cnf(c_5695,plain,
( sum(A,multiply(B,A),D)
| ~ product(C,A,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5694,c_3]) ).
cnf(c_5696,plain,
( sum(A,multiply(additive_identity,A),B)
| ~ product(A,A,B) ),
inference(resolve,[status(thm)],[c_5695,c_2]) ).
cnf(c_133,plain,
sum(A,multiply(additive_identity,A),A),
inference(resolve,[status(thm)],[c_5696,c_20]) ).
cnf(c_5697,plain,
( sum(B,C,E)
| ~ product(D,B,E)
| ~ sum(B,A,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_14,c_20]) ).
cnf(c_5698,plain,
( sum(A,multiply(B,A),D)
| ~ product(C,A,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5697,c_3]) ).
cnf(c_5699,plain,
( sum(A,multiply(additive_inverse(A),A),B)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_5698,c_6]) ).
cnf(c_142,plain,
sum(A,multiply(additive_inverse(A),A),multiply(additive_identity,A)),
inference(resolve,[status(thm)],[c_5699,c_3]) ).
cnf(c_5700,plain,
( sum(A,C,E)
| ~ product(A,D,E)
| ~ sum(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_20]) ).
cnf(c_5701,plain,
( sum(A,multiply(A,B),D)
| ~ product(A,C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5700,c_3]) ).
cnf(c_5702,plain,
( sum(A,multiply(A,additive_identity),B)
| ~ product(A,A,B) ),
inference(resolve,[status(thm)],[c_5701,c_2]) ).
cnf(c_154,plain,
sum(A,multiply(A,additive_identity),A),
inference(resolve,[status(thm)],[c_5702,c_20]) ).
cnf(c_5703,plain,
( product(E,B,F)
| ~ sum(multiply(D,B),C,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_5704,plain,
( product(C,D,E)
| ~ sum(multiply(A,D),multiply(B,D),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5703,c_3]) ).
cnf(c_5705,plain,
( product(B,A,C)
| ~ sum(multiply(additive_identity,A),multiply(B,A),C) ),
inference(resolve,[status(thm)],[c_5704,c_1]) ).
cnf(c_220,plain,
~ sum(multiply(additive_identity,a),multiply(b,a),c),
inference(resolve,[status(thm)],[c_5705,c_22]) ).
cnf(c_5706,plain,
( sum(A,D,E)
| ~ sum(B,C,E)
| ~ sum(add(additive_inverse(A),B),C,D) ),
inference(resolve,[status(thm)],[c_7,c_29]) ).
cnf(c_5707,plain,
( sum(A,C,B)
| ~ sum(add(additive_inverse(A),additive_identity),B,C) ),
inference(resolve,[status(thm)],[c_5706,c_1]) ).
cnf(c_5708,plain,
~ sum(add(additive_inverse(multiply(additive_identity,a)),additive_identity),c,multiply(b,a)),
inference(resolve,[status(thm)],[c_5707,c_220]) ).
cnf(c_340,plain,
~ sum(additive_inverse(multiply(additive_identity,a)),c,multiply(b,a)),
inference(paramod,[status(thm)],[c_120,c_5708]) ).
cnf(c_5709,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_673,plain,
add(A,B) = add(B,A),
inference(resolve,[status(thm)],[c_5709,c_94]) ).
cnf(c_5710,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_5711,plain,
( sum(C,add(A,additive_inverse(C)),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_5710,c_94]) ).
cnf(c_5712,plain,
sum(A,add(B,additive_inverse(A)),add(B,additive_identity)),
inference(resolve,[status(thm)],[c_5711,c_94]) ).
cnf(c_754,plain,
sum(A,add(B,additive_inverse(A)),B),
inference(paramod,[status(thm)],[c_120,c_5712]) ).
cnf(c_5713,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_5714,plain,
( sum(additive_inverse(C),add(A,C),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_5713,c_94]) ).
cnf(c_5715,plain,
sum(additive_inverse(A),add(B,A),add(B,additive_identity)),
inference(resolve,[status(thm)],[c_5714,c_94]) ).
cnf(c_755,plain,
sum(additive_inverse(A),add(B,A),B),
inference(paramod,[status(thm)],[c_120,c_5715]) ).
cnf(c_5716,plain,
( sum(B,C,E)
| ~ sum(additive_inverse(A),D,E)
| ~ sum(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_8,c_38]) ).
cnf(c_5717,plain,
( sum(B,C,D)
| ~ sum(add(A,B),C,add(A,D)) ),
inference(resolve,[status(thm)],[c_5716,c_38]) ).
cnf(c_1049,plain,
~ sum(add(A,additive_inverse(multiply(additive_identity,a))),c,add(A,multiply(b,a))),
inference(resolve,[status(thm)],[c_5717,c_340]) ).
cnf(c_5718,plain,
( add(additive_inverse(A),C) = B
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_18,c_29]) ).
cnf(c_5719,plain,
add(additive_inverse(A),A) = multiply(additive_identity,A),
inference(resolve,[status(thm)],[c_5718,c_133]) ).
cnf(c_5720,plain,
add(A,additive_inverse(A)) = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_673,c_5719]) ).
cnf(c_5721,plain,
additive_identity = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_117,c_5720]) ).
cnf(c_1057,plain,
multiply(additive_identity,A) = additive_identity,
inference(copy,[status(thm)],[c_5721]) ).
cnf(c_5722,plain,
~ sum(add(A,additive_inverse(additive_identity)),c,add(A,multiply(b,a))),
inference(paramod,[status(thm)],[c_1057,c_1049]) ).
cnf(c_5723,plain,
~ sum(add(A,additive_identity),c,add(A,multiply(b,a))),
inference(paramod,[status(thm)],[c_118,c_5722]) ).
cnf(c_1087,plain,
~ sum(A,c,add(A,multiply(b,a))),
inference(paramod,[status(thm)],[c_120,c_5723]) ).
cnf(c_1144,plain,
sum(A,multiply(additive_inverse(A),A),additive_identity),
inference(paramod,[status(thm)],[c_1057,c_142]) ).
cnf(c_5724,plain,
( add(additive_inverse(A),C) = B
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_18,c_29]) ).
cnf(c_5725,plain,
add(additive_inverse(A),A) = multiply(A,additive_identity),
inference(resolve,[status(thm)],[c_5724,c_154]) ).
cnf(c_5726,plain,
add(A,additive_inverse(A)) = multiply(A,additive_identity),
inference(paramod,[status(thm)],[c_673,c_5725]) ).
cnf(c_5727,plain,
additive_identity = multiply(A,additive_identity),
inference(paramod,[status(thm)],[c_117,c_5726]) ).
cnf(c_1151,plain,
multiply(A,additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_5727]) ).
cnf(c_5728,plain,
( product(E,B,F)
| ~ sum(multiply(D,B),C,F)
| ~ sum(D,A,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_3]) ).
cnf(c_5729,plain,
( product(C,D,E)
| ~ sum(multiply(A,D),multiply(B,D),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5728,c_3]) ).
cnf(c_5730,plain,
( product(A,B,C)
| ~ sum(multiply(A,B),multiply(multiply(A,additive_identity),B),C) ),
inference(resolve,[status(thm)],[c_5729,c_154]) ).
cnf(c_5731,plain,
product(A,additive_identity,multiply(A,additive_identity)),
inference(resolve,[status(thm)],[c_5730,c_154]) ).
cnf(c_1152,plain,
product(A,additive_identity,additive_identity),
inference(paramod,[status(thm)],[c_1151,c_5731]) ).
cnf(c_5732,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_5733,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(resolve,[status(thm)],[c_5732,c_47]) ).
cnf(c_1171,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_5733]) ).
cnf(c_5734,plain,
( add(additive_inverse(A),C) = B
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_18,c_29]) ).
cnf(c_5735,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(resolve,[status(thm)],[c_5734,c_74]) ).
cnf(c_1372,plain,
add(A,additive_inverse(add(A,B))) = additive_inverse(B),
inference(paramod,[status(thm)],[c_673,c_5735]) ).
cnf(c_5736,plain,
( product(D,B,E)
| ~ sum(B,C,E)
| ~ sum(B,A,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_15,c_20]) ).
cnf(c_5737,plain,
( product(C,A,D)
| ~ sum(A,multiply(B,A),D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5736,c_3]) ).
cnf(c_5738,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_5737,c_77]) ).
cnf(c_5739,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_5738,c_94]) ).
cnf(c_5740,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_673,c_5739]) ).
cnf(c_1672,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_1171,c_5740]) ).
cnf(c_5741,plain,
( sum(A,C,E)
| ~ product(A,D,E)
| ~ sum(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_20]) ).
cnf(c_5742,plain,
( sum(a,c,B)
| ~ product(a,A,B)
| ~ sum(a,b,A) ),
inference(resolve,[status(thm)],[c_5741,c_21]) ).
cnf(c_5743,plain,
( sum(a,c,A)
| ~ product(a,add(b,a),A) ),
inference(resolve,[status(thm)],[c_5742,c_94]) ).
cnf(c_5744,plain,
~ product(a,add(b,a),add(a,multiply(b,a))),
inference(resolve,[status(thm)],[c_5743,c_1087]) ).
cnf(c_4204,plain,
~ product(a,add(a,b),add(a,multiply(b,a))),
inference(paramod,[status(thm)],[c_673,c_5744]) ).
cnf(c_5745,plain,
( add(C,A) = B
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_18,c_755]) ).
cnf(c_5746,plain,
add(additive_identity,A) = multiply(additive_inverse(additive_inverse(A)),additive_inverse(A)),
inference(resolve,[status(thm)],[c_5745,c_1144]) ).
cnf(c_5747,plain,
A = multiply(additive_inverse(additive_inverse(A)),additive_inverse(A)),
inference(paramod,[status(thm)],[c_121,c_5746]) ).
cnf(c_5748,plain,
A = multiply(A,additive_inverse(A)),
inference(paramod,[status(thm)],[c_122,c_5747]) ).
cnf(c_4599,plain,
multiply(A,additive_inverse(A)) = A,
inference(copy,[status(thm)],[c_5748]) ).
cnf(c_5749,plain,
( add(C,additive_inverse(A)) = B
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_18,c_754]) ).
cnf(c_5750,plain,
add(additive_identity,additive_inverse(A)) = multiply(additive_inverse(A),A),
inference(resolve,[status(thm)],[c_5749,c_1144]) ).
cnf(c_5751,plain,
additive_inverse(A) = multiply(additive_inverse(A),A),
inference(paramod,[status(thm)],[c_121,c_5750]) ).
cnf(c_4600,plain,
multiply(additive_inverse(A),A) = additive_inverse(A),
inference(copy,[status(thm)],[c_5751]) ).
cnf(c_5752,plain,
( sum(A,C,E)
| ~ product(A,D,E)
| ~ sum(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_12,c_20]) ).
cnf(c_5753,plain,
( sum(A,multiply(A,B),D)
| ~ product(A,C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_5752,c_3]) ).
cnf(c_5754,plain,
( sum(A,multiply(A,multiply(additive_inverse(A),A)),B)
| ~ product(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_5753,c_1144]) ).
cnf(c_5755,plain,
sum(A,multiply(A,multiply(additive_inverse(A),A)),additive_identity),
inference(resolve,[status(thm)],[c_5754,c_1152]) ).
cnf(c_5756,plain,
sum(A,multiply(A,additive_inverse(A)),additive_identity),
inference(paramod,[status(thm)],[c_4600,c_5755]) ).
cnf(c_4614,plain,
sum(A,A,additive_identity),
inference(paramod,[status(thm)],[c_4599,c_5756]) ).
cnf(c_5757,plain,
( additive_inverse(C) = A
| ~ sum(A,add(B,C),B) ),
inference(resolve,[status(thm)],[c_19,c_755]) ).
cnf(c_5758,plain,
additive_inverse(A) = add(additive_identity,A),
inference(resolve,[status(thm)],[c_5757,c_4614]) ).
cnf(c_4621,plain,
additive_inverse(A) = A,
inference(paramod,[status(thm)],[c_121,c_5758]) ).
cnf(c_5759,plain,
product(A,add(A,B),add(A,add(additive_inverse(B),multiply(B,add(A,additive_inverse(B)))))),
inference(paramod,[status(thm)],[c_4621,c_1672]) ).
cnf(c_5760,plain,
product(A,add(A,B),add(A,add(B,multiply(B,add(A,additive_inverse(B)))))),
inference(paramod,[status(thm)],[c_4621,c_5759]) ).
cnf(c_5493,plain,
product(A,add(A,B),add(A,add(B,multiply(B,add(A,B))))),
inference(paramod,[status(thm)],[c_4621,c_5760]) ).
cnf(c_5761,plain,
add(A,add(A,B)) = additive_inverse(B),
inference(paramod,[status(thm)],[c_4621,c_1372]) ).
cnf(c_5525,plain,
add(A,add(A,B)) = B,
inference(paramod,[status(thm)],[c_4621,c_5761]) ).
cnf(c_5762,plain,
( add(B,A) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_94]) ).
cnf(c_5763,plain,
add(multiply(A,B),multiply(A,C)) = multiply(A,add(C,B)),
inference(resolve,[status(thm)],[c_5762,c_99]) ).
cnf(c_5649,plain,
multiply(A,add(B,C)) = add(multiply(A,C),multiply(A,B)),
inference(copy,[status(thm)],[c_5763]) ).
cnf(c_5764,plain,
product(A,add(A,B),add(A,add(B,add(multiply(B,B),multiply(B,A))))),
inference(paramod,[status(thm)],[c_5649,c_5493]) ).
cnf(c_5765,plain,
product(A,add(A,B),add(A,add(B,add(B,multiply(B,A))))),
inference(paramod,[status(thm)],[c_123,c_5764]) ).
cnf(c_5671,plain,
product(A,add(A,B),add(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_5525,c_5765]) ).
cnf(c_5672,plain,
$false,
inference(resolve,[status(thm)],[c_5671,c_4204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.42 % Computer : n018.cluster.edu
% 0.13/10.42 % Model : x86_64 x86_64
% 0.13/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.42 % Memory : 8046.5625MB
% 0.13/10.42 % OS : Linux 6.8.0-71-generic
% 0.13/10.42 % CPULimit : 300
% 0.13/10.42 % WCLimit : 300
% 0.13/10.42 % DateTime : Sat Sep 26 05:47:01 UTC 2026
% 0.13/10.43 % CPUTime :
% 0.13/10.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/10.43 % Process 3856782 was started by sandbox on n018,
% 0.13/10.43 % Sat Sep 26 05:47:01 2026
% 0.13/10.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/10.43
% 0.13/10.43 % From the command line: assign(max_seconds, 300).
% 14.16/12.26
% 14.16/12.26 % SZS status Unsatisfiable for theBenchmark
% 14.16/12.26
% 14.16/12.26 % Proof 1 at 1.41 (+ 0.40) seconds.
% 14.16/12.26 % Length of proof is 59.
% 14.16/12.26 % Level of proof is 10.
% 14.16/12.26 % Maximum clause weight is 20.000.
% 14.16/12.26 % Given clauses 104.
% 14.16/12.26
% 14.16/12.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------