%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 54.45s 7.34s
% Output : CNFRefutation 54.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 19
% Syntax : Number of formulae : 153 ( 85 unt; 0 def)
% Number of atoms : 285 ( 35 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 273 ( 141 ~; 132 |; 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 : 397 ( 2 sgn 58 !; 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(x_times_identity_x_is_identity,axiom,
! [VAR_0] : product(VAR_0,additive_identity,additive_identity),
file('theBenchmark.p',x_times_identity_x_is_identity) ).
cnf(c_18,plain,
product(A,additive_identity,additive_identity),
inference(clausify,[status(thm)],[x_times_identity_x_is_identity]) ).
fof(identity_times_x_is_identity,axiom,
! [VAR_0] : product(additive_identity,VAR_0,additive_identity),
file('theBenchmark.p',identity_times_x_is_identity) ).
cnf(c_19,plain,
product(additive_identity,A,additive_identity),
inference(clausify,[status(thm)],[identity_times_x_is_identity]) ).
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_10633,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_10634,plain,
( sum(A,additive_identity,B)
| ~ sum(additive_identity,additive_inverse(additive_inverse(A)),B) ),
inference(resolve,[status(thm)],[c_10633,c_6]) ).
cnf(c_24,plain,
sum(A,additive_identity,additive_inverse(additive_inverse(A))),
inference(resolve,[status(thm)],[c_10634,c_1]) ).
cnf(c_10635,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_10636,plain,
( sum(C,add(additive_inverse(C),A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_10635,c_4]) ).
cnf(c_29,plain,
sum(A,add(additive_inverse(A),B),B),
inference(resolve,[status(thm)],[c_10636,c_1]) ).
cnf(c_10637,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_10638,plain,
( sum(additive_inverse(C),add(C,A),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_10637,c_4]) ).
cnf(c_38,plain,
sum(additive_inverse(A),add(A,B),B),
inference(resolve,[status(thm)],[c_10638,c_1]) ).
cnf(c_10639,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_10640,plain,
( sum(A,add(B,C),D)
| ~ sum(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_10639,c_4]) ).
cnf(c_47,plain,
sum(A,add(B,C),add(add(A,B),C)),
inference(resolve,[status(thm)],[c_10640,c_4]) ).
cnf(c_10641,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_10642,plain,
( sum(add(A,additive_inverse(C)),C,B)
| ~ sum(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_10641,c_5]) ).
cnf(c_77,plain,
sum(add(A,additive_inverse(B)),B,A),
inference(resolve,[status(thm)],[c_10642,c_2]) ).
cnf(c_10643,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_10644,plain,
( sum(add(A,B),C,D)
| ~ sum(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_10643,c_4]) ).
cnf(c_79,plain,
sum(add(A,B),C,add(A,add(B,C))),
inference(resolve,[status(thm)],[c_10644,c_4]) ).
cnf(c_94,plain,
sum(A,B,add(B,A)),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_10645,plain,
( product(A,E,F)
| ~ sum(multiply(A,D),C,F)
| ~ sum(D,B,E)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_10646,plain,
( product(D,C,E)
| ~ sum(multiply(D,A),multiply(D,B),E)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_10645,c_3]) ).
cnf(c_10647,plain,
( product(A,add(B,C),D)
| ~ sum(multiply(A,B),multiply(A,C),D) ),
inference(resolve,[status(thm)],[c_10646,c_4]) ).
cnf(c_104,plain,
product(A,add(B,C),add(multiply(A,B),multiply(A,C))),
inference(resolve,[status(thm)],[c_10647,c_4]) ).
cnf(c_10648,plain,
( additive_identity = B
| ~ sum(A,additive_inverse(A),B) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_10649,plain,
additive_identity = additive_inverse(additive_identity),
inference(resolve,[status(thm)],[c_10648,c_1]) ).
cnf(c_118,plain,
additive_inverse(additive_identity) = additive_identity,
inference(copy,[status(thm)],[c_10649]) ).
cnf(c_10650,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_10650,c_2]) ).
cnf(c_10651,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_10651,c_1]) ).
cnf(c_10652,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_10653,plain,
( sum(multiply(A,B),B,D)
| ~ product(C,B,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_10652,c_20]) ).
cnf(c_10654,plain,
( sum(multiply(additive_inverse(A),A),A,B)
| ~ product(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_10653,c_5]) ).
cnf(c_141,plain,
sum(multiply(additive_inverse(A),A),A,additive_identity),
inference(resolve,[status(thm)],[c_10654,c_19]) ).
cnf(c_10655,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_10656,plain,
( sum(A,multiply(A,B),D)
| ~ product(A,C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_10655,c_3]) ).
cnf(c_10657,plain,
( sum(A,multiply(A,additive_inverse(A)),B)
| ~ product(A,additive_identity,B) ),
inference(resolve,[status(thm)],[c_10656,c_6]) ).
cnf(c_158,plain,
sum(A,multiply(A,additive_inverse(A)),additive_identity),
inference(resolve,[status(thm)],[c_10657,c_18]) ).
cnf(c_10658,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_19]) ).
cnf(c_10659,plain,
( product(B,C,D)
| ~ sum(additive_identity,multiply(A,C),D)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_10658,c_3]) ).
cnf(c_10660,plain,
( product(A,B,C)
| ~ sum(additive_identity,multiply(A,B),C) ),
inference(resolve,[status(thm)],[c_10659,c_1]) ).
cnf(c_206,plain,
~ sum(additive_identity,multiply(b,a),c),
inference(resolve,[status(thm)],[c_10660,c_22]) ).
cnf(c_10661,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_10662,plain,
add(A,additive_identity) = additive_inverse(additive_inverse(A)),
inference(resolve,[status(thm)],[c_10661,c_24]) ).
cnf(c_10663,plain,
A = additive_inverse(additive_inverse(A)),
inference(paramod,[status(thm)],[c_120,c_10662]) ).
cnf(c_210,plain,
additive_inverse(additive_inverse(A)) = A,
inference(copy,[status(thm)],[c_10663]) ).
cnf(c_10664,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_10665,plain,
( sum(A,C,B)
| ~ sum(additive_inverse(A),B,C) ),
inference(resolve,[status(thm)],[c_10664,c_1]) ).
cnf(c_10666,plain,
~ sum(additive_inverse(additive_identity),c,multiply(b,a)),
inference(resolve,[status(thm)],[c_10665,c_206]) ).
cnf(c_218,plain,
~ sum(additive_identity,c,multiply(b,a)),
inference(paramod,[status(thm)],[c_118,c_10666]) ).
cnf(c_10667,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_10668,plain,
( sum(additive_identity,B,C)
| ~ sum(A,B,add(additive_inverse(additive_inverse(A)),C)) ),
inference(resolve,[status(thm)],[c_10667,c_29]) ).
cnf(c_10669,plain,
~ sum(A,c,add(additive_inverse(additive_inverse(A)),multiply(b,a))),
inference(resolve,[status(thm)],[c_10668,c_218]) ).
cnf(c_450,plain,
~ sum(A,c,add(A,multiply(b,a))),
inference(paramod,[status(thm)],[c_210,c_10669]) ).
cnf(c_10670,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_461,plain,
add(additive_inverse(A),add(A,B)) = B,
inference(resolve,[status(thm)],[c_10670,c_38]) ).
cnf(c_10671,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_657,plain,
add(A,B) = add(B,A),
inference(resolve,[status(thm)],[c_10671,c_94]) ).
cnf(c_10672,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_10673,plain,
( sum(C,add(A,additive_inverse(C)),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_10672,c_94]) ).
cnf(c_10674,plain,
sum(A,add(B,additive_inverse(A)),add(B,additive_identity)),
inference(resolve,[status(thm)],[c_10673,c_94]) ).
cnf(c_740,plain,
sum(A,add(B,additive_inverse(A)),B),
inference(paramod,[status(thm)],[c_120,c_10674]) ).
cnf(c_10675,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_10676,plain,
( sum(additive_inverse(C),add(A,C),B)
| ~ sum(additive_identity,A,B) ),
inference(resolve,[status(thm)],[c_10675,c_94]) ).
cnf(c_10677,plain,
sum(additive_inverse(A),add(B,A),add(B,additive_identity)),
inference(resolve,[status(thm)],[c_10676,c_94]) ).
cnf(c_741,plain,
sum(additive_inverse(A),add(B,A),B),
inference(paramod,[status(thm)],[c_120,c_10677]) ).
cnf(c_10678,plain,
( add(A,B) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_10679,plain,
add(A,add(B,C)) = add(add(A,B),C),
inference(resolve,[status(thm)],[c_10678,c_47]) ).
cnf(c_2001,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(copy,[status(thm)],[c_10679]) ).
cnf(c_10680,plain,
( add(add(A,B),C) = D
| ~ sum(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_16,c_47]) ).
cnf(c_10681,plain,
add(add(A,B),C) = add(add(B,C),A),
inference(resolve,[status(thm)],[c_10680,c_94]) ).
cnf(c_10682,plain,
add(A,add(B,C)) = add(add(B,C),A),
inference(paramod,[status(thm)],[c_2001,c_10681]) ).
cnf(c_10683,plain,
add(A,add(B,C)) = add(B,add(C,A)),
inference(paramod,[status(thm)],[c_2001,c_10682]) ).
cnf(c_2002,plain,
add(A,add(B,C)) = add(C,add(A,B)),
inference(copy,[status(thm)],[c_10683]) ).
cnf(c_10684,plain,
( sum(additive_identity,B,D)
| ~ sum(multiply(additive_inverse(A),A),C,D)
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_8,c_141]) ).
cnf(c_10685,plain,
( sum(additive_identity,B,C)
| ~ sum(multiply(additive_inverse(add(A,additive_inverse(B))),add(A,additive_inverse(B))),A,C) ),
inference(resolve,[status(thm)],[c_10684,c_77]) ).
cnf(c_10686,plain,
sum(additive_identity,A,multiply(additive_inverse(add(additive_identity,additive_inverse(A))),add(additive_identity,additive_inverse(A)))),
inference(resolve,[status(thm)],[c_10685,c_2]) ).
cnf(c_10687,plain,
sum(additive_identity,A,multiply(additive_inverse(additive_inverse(A)),add(additive_identity,additive_inverse(A)))),
inference(paramod,[status(thm)],[c_121,c_10686]) ).
cnf(c_10688,plain,
sum(additive_identity,A,multiply(A,add(additive_identity,additive_inverse(A)))),
inference(paramod,[status(thm)],[c_210,c_10687]) ).
cnf(c_2395,plain,
sum(additive_identity,A,multiply(A,additive_inverse(A))),
inference(paramod,[status(thm)],[c_121,c_10688]) ).
cnf(c_10689,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_10690,plain,
( sum(a,c,B)
| ~ product(a,A,B)
| ~ sum(a,b,A) ),
inference(resolve,[status(thm)],[c_10689,c_21]) ).
cnf(c_10691,plain,
( sum(a,c,A)
| ~ product(a,add(b,a),A) ),
inference(resolve,[status(thm)],[c_10690,c_94]) ).
cnf(c_10692,plain,
~ product(a,add(b,a),add(a,multiply(b,a))),
inference(resolve,[status(thm)],[c_10691,c_450]) ).
cnf(c_5461,plain,
~ product(a,add(a,b),add(a,multiply(b,a))),
inference(paramod,[status(thm)],[c_657,c_10692]) ).
cnf(c_10693,plain,
( product(F,add(B,C),V6)
| ~ sum(add(multiply(E,B),multiply(E,C)),D,V6)
| ~ sum(E,A,F)
| ~ product(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_15,c_104]) ).
cnf(c_10694,plain,
( product(D,add(B,C),E)
| ~ sum(add(multiply(A,B),multiply(A,C)),add(B,C),E)
| ~ sum(A,add(B,C),D) ),
inference(resolve,[status(thm)],[c_10693,c_20]) ).
cnf(c_10695,plain,
( product(B,add(B,additive_inverse(A)),C)
| ~ sum(add(multiply(A,B),multiply(A,additive_inverse(A))),add(B,additive_inverse(A)),C) ),
inference(resolve,[status(thm)],[c_10694,c_740]) ).
cnf(c_10696,plain,
product(A,add(A,additive_inverse(B)),add(multiply(B,A),add(multiply(B,additive_inverse(B)),add(A,additive_inverse(B))))),
inference(resolve,[status(thm)],[c_10695,c_79]) ).
cnf(c_8644,plain,
product(A,add(A,additive_inverse(B)),add(multiply(B,A),add(additive_inverse(B),add(multiply(B,additive_inverse(B)),A)))),
inference(paramod,[status(thm)],[c_2002,c_10696]) ).
cnf(c_10697,plain,
( B = C
| ~ sum(A,add(B,additive_inverse(A)),C) ),
inference(resolve,[status(thm)],[c_16,c_740]) ).
cnf(c_10698,plain,
A = multiply(add(A,additive_inverse(additive_identity)),additive_inverse(add(A,additive_inverse(additive_identity)))),
inference(resolve,[status(thm)],[c_10697,c_2395]) ).
cnf(c_10699,plain,
A = multiply(add(A,additive_identity),additive_inverse(add(A,additive_inverse(additive_identity)))),
inference(paramod,[status(thm)],[c_118,c_10698]) ).
cnf(c_10700,plain,
A = multiply(A,additive_inverse(add(A,additive_inverse(additive_identity)))),
inference(paramod,[status(thm)],[c_120,c_10699]) ).
cnf(c_10701,plain,
A = multiply(A,additive_inverse(add(A,additive_identity))),
inference(paramod,[status(thm)],[c_118,c_10700]) ).
cnf(c_10702,plain,
A = multiply(A,additive_inverse(A)),
inference(paramod,[status(thm)],[c_120,c_10701]) ).
cnf(c_9898,plain,
multiply(A,additive_inverse(A)) = A,
inference(copy,[status(thm)],[c_10702]) ).
cnf(c_10703,plain,
( sum(additive_inverse(B),D,E)
| ~ sum(A,C,E)
| ~ sum(add(A,B),C,D) ),
inference(resolve,[status(thm)],[c_7,c_741]) ).
cnf(c_10704,plain,
( sum(additive_inverse(B),additive_identity,C)
| ~ sum(A,multiply(add(A,B),additive_inverse(add(A,B))),C) ),
inference(resolve,[status(thm)],[c_10703,c_158]) ).
cnf(c_10705,plain,
sum(additive_inverse(A),additive_identity,multiply(multiply(add(additive_identity,A),additive_inverse(add(additive_identity,A))),additive_inverse(multiply(add(additive_identity,A),additive_inverse(add(additive_identity,A)))))),
inference(resolve,[status(thm)],[c_10704,c_2395]) ).
cnf(c_10706,plain,
sum(additive_inverse(A),additive_identity,multiply(multiply(A,additive_inverse(add(additive_identity,A))),additive_inverse(multiply(add(additive_identity,A),additive_inverse(add(additive_identity,A)))))),
inference(paramod,[status(thm)],[c_121,c_10705]) ).
cnf(c_10707,plain,
sum(additive_inverse(A),additive_identity,multiply(multiply(A,additive_inverse(A)),additive_inverse(multiply(add(additive_identity,A),additive_inverse(add(additive_identity,A)))))),
inference(paramod,[status(thm)],[c_121,c_10706]) ).
cnf(c_10708,plain,
sum(additive_inverse(A),additive_identity,multiply(A,additive_inverse(multiply(add(additive_identity,A),additive_inverse(add(additive_identity,A)))))),
inference(paramod,[status(thm)],[c_9898,c_10707]) ).
cnf(c_10709,plain,
sum(additive_inverse(A),additive_identity,multiply(A,additive_inverse(multiply(A,additive_inverse(add(additive_identity,A)))))),
inference(paramod,[status(thm)],[c_121,c_10708]) ).
cnf(c_10710,plain,
sum(additive_inverse(A),additive_identity,multiply(A,additive_inverse(multiply(A,additive_inverse(A))))),
inference(paramod,[status(thm)],[c_121,c_10709]) ).
cnf(c_10711,plain,
sum(additive_inverse(A),additive_identity,multiply(A,additive_inverse(A))),
inference(paramod,[status(thm)],[c_9898,c_10710]) ).
cnf(c_9916,plain,
sum(additive_inverse(A),additive_identity,A),
inference(paramod,[status(thm)],[c_9898,c_10711]) ).
cnf(c_10712,plain,
product(A,add(A,additive_inverse(B)),add(multiply(B,A),add(additive_inverse(B),add(B,A)))),
inference(paramod,[status(thm)],[c_9898,c_8644]) ).
cnf(c_10713,plain,
product(A,add(A,additive_inverse(B)),add(multiply(B,A),A)),
inference(paramod,[status(thm)],[c_461,c_10712]) ).
cnf(c_10026,plain,
product(A,add(A,additive_inverse(B)),add(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_657,c_10713]) ).
cnf(c_10714,plain,
( add(B,A) = C
| ~ sum(A,B,C) ),
inference(resolve,[status(thm)],[c_16,c_94]) ).
cnf(c_10715,plain,
add(additive_identity,additive_inverse(A)) = A,
inference(resolve,[status(thm)],[c_10714,c_9916]) ).
cnf(c_10558,plain,
additive_inverse(A) = A,
inference(paramod,[status(thm)],[c_121,c_10715]) ).
cnf(c_10631,plain,
product(A,add(A,B),add(A,multiply(B,A))),
inference(paramod,[status(thm)],[c_10558,c_10026]) ).
cnf(c_10632,plain,
$false,
inference(resolve,[status(thm)],[c_10631,c_5461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n010.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 05:45:29 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2611718 was started by sandbox2 on n010,
% 0.17/0.43 % Sat Sep 26 05:45:29 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 54.45/7.34
% 54.45/7.34 % SZS status Unsatisfiable for theBenchmark
% 54.45/7.34
% 54.45/7.34 % Proof 1 at 5.39 (+ 1.48) seconds.
% 54.45/7.34 % Length of proof is 51.
% 54.45/7.34 % Level of proof is 8.
% 54.45/7.34 % Maximum clause weight is 20.000.
% 54.45/7.34 % Given clauses 129.
% 54.45/7.34
% 54.45/7.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------