%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:28:28 AM UTC 2026
% Result : Unsatisfiable 44.47s 6.90s
% Output : CNFRefutation 44.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 19
% Syntax : Number of formulae : 196 ( 32 unt; 0 def)
% Number of atoms : 576 ( 575 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 674 ( 294 ~; 380 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_7,axiom,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_10,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_13,axiom,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_19,axiom,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_26,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_32,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_33,axiom,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_37,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( multiply(VAR_5,sk_c7) != sk_c8
| inverse(VAR_4) != VAR_5
| multiply(VAR_4,VAR_5) != sk_c8
| multiply(VAR_3,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(VAR_2,sk_c7) != sk_c9
| inverse(VAR_2) != sk_c9
| inverse(VAR_1) != sk_c8
| multiply(VAR_1,sk_c8) != sk_c7
| inverse(VAR_0) != sk_c9
| multiply(VAR_0,sk_c9) != sk_c8 ),
file('theBenchmark.p',prove_this_37) ).
cnf(c_40,plain,
( multiply(F,sk_c7) != sk_c8
| inverse(E) != F
| multiply(E,F) != sk_c8
| multiply(D,sk_c8) != sk_c9
| inverse(D) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(C,sk_c7) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_37]) ).
cnf(c_42,plain,
( multiply(E,sk_c7) != sk_c8
| inverse(D) != E
| multiply(D,E) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_51,plain,
( multiply(D,sk_c7) != sk_c8
| inverse(C) != D
| multiply(C,D) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_64,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_51]) ).
cnf(c_6069,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_6070,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_6069]) ).
cnf(c_65,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_6070]) ).
cnf(c_6071,plain,
( multiply(sk_c8,A) = multiply(sk_c1,multiply(sk_c9,A))
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_72,plain,
( multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c8,A)
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_6071]) ).
cnf(c_87,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_89,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_94,plain,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_97,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_123,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_140,plain,
( multiply(sk_c9,sk_c3) = identity
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_142,plain,
( multiply(sk_c9,sk_c3) = identity
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_175,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_65]) ).
cnf(c_176,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_65]) ).
cnf(c_249,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_65,c_65]) ).
cnf(c_250,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_249,c_175]) ).
cnf(c_256,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_250,c_2]) ).
cnf(c_6072,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_87,c_65]) ).
cnf(c_260,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_250,c_6072]) ).
cnf(c_262,plain,
( multiply(sk_c1,sk_c9) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_260,c_2]) ).
cnf(c_6073,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_89,c_65]) ).
cnf(c_284,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_250,c_6073]) ).
cnf(c_6074,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_97,c_65]) ).
cnf(c_307,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_250,c_6074]) ).
cnf(c_309,plain,
( multiply(sk_c1,sk_c9) = identity
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_307,c_2]) ).
cnf(c_6075,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_123,c_65]) ).
cnf(c_322,plain,
( inverse(sk_c8) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_250,c_6075]) ).
cnf(c_6076,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_140,c_65]) ).
cnf(c_471,plain,
( inverse(sk_c9) = sk_c3
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_250,c_6076]) ).
cnf(c_6077,plain,
( sk_c3 = sk_c1
| inverse(sk_c4) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_471,c_284]) ).
cnf(c_492,plain,
( sk_c3 = sk_c1
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_6077]) ).
cnf(c_6078,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_492,c_35]) ).
cnf(c_494,plain,
( multiply(sk_c1,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_6078]) ).
cnf(c_6079,plain,
( inverse(sk_c8) = sk_c7
| identity = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_262,c_4]) ).
cnf(c_636,plain,
( identity = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6079]) ).
cnf(c_642,plain,
( inverse(sk_c8) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_636,c_256]) ).
cnf(c_6080,plain,
( identity = sk_c2
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_642,c_322]) ).
cnf(c_688,plain,
( identity = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6080]) ).
cnf(c_6081,plain,
( sk_c2 = sk_c8
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_688,c_636]) ).
cnf(c_702,plain,
( sk_c2 = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6081]) ).
cnf(c_6082,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_702,c_16]) ).
cnf(c_704,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6082]) ).
cnf(c_6083,plain,
( inverse(sk_c5) = sk_c6
| identity = sk_c8
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_309,c_8]) ).
cnf(c_1430,plain,
( identity = sk_c8
| inverse(sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_6083]) ).
cnf(c_1442,plain,
( multiply(sk_c6,sk_c5) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1430,c_2]) ).
cnf(c_6084,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1442,c_65]) ).
cnf(c_1458,plain,
( inverse(sk_c6) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_250,c_6084]) ).
cnf(c_1474,plain,
( multiply(sk_c5,sk_c6) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1458,c_2]) ).
cnf(c_6085,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1474,c_7]) ).
cnf(c_1558,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_6085]) ).
cnf(c_6086,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1474,c_94]) ).
cnf(c_1573,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_6086]) ).
cnf(c_6087,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1573,c_65]) ).
cnf(c_1886,plain,
( inverse(sk_c9) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_250,c_6087]) ).
cnf(c_1908,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1886,c_2]) ).
cnf(c_6088,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_142,c_65]) ).
cnf(c_2955,plain,
( inverse(sk_c9) = sk_c3
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_250,c_6088]) ).
cnf(c_6089,plain,
( multiply(sk_c1,identity) = multiply(sk_c8,sk_c3)
| multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_142,c_72]) ).
cnf(c_6090,plain,
( sk_c1 = multiply(sk_c8,sk_c3)
| multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_250,c_6089]) ).
cnf(c_6091,plain,
( multiply(sk_c8,sk_c3) = sk_c1
| multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_6090]) ).
cnf(c_2956,plain,
( multiply(sk_c8,sk_c3) = sk_c1
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_6091]) ).
cnf(c_6092,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1908,c_1558]) ).
cnf(c_6093,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_6092]) ).
cnf(c_4057,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_6093]) ).
cnf(c_6094,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_4057,c_256]) ).
cnf(c_4511,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_4057,c_6094]) ).
cnf(c_4515,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_4057,c_250]) ).
cnf(c_4528,plain,
multiply(inverse(A),A) = sk_c8,
inference(paramod,[status(thm)],[c_4057,c_2]) ).
cnf(c_4529,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_4057,c_1]) ).
cnf(c_6095,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_4511,c_704]) ).
cnf(c_6096,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_4515,c_6095]) ).
cnf(c_6097,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_6096]) ).
cnf(c_6098,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_6097]) ).
cnf(c_4573,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_6098]) ).
cnf(c_6099,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| B != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4515,c_64]) ).
cnf(c_6100,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6099]) ).
cnf(c_6101,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c8) != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6100]) ).
cnf(c_6102,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4515,c_6101]) ).
cnf(c_6103,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c8) != sk_c9
| sk_c8 != sk_c7
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4511,c_6102]) ).
cnf(c_6104,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c8) != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6103]) ).
cnf(c_6105,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4515,c_6104]) ).
cnf(c_6106,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6105]) ).
cnf(c_6107,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6106]) ).
cnf(c_6108,plain,
( inverse(sk_c7) != sk_c7
| sk_c8 != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4515,c_6107]) ).
cnf(c_6109,plain,
( inverse(sk_c8) != sk_c7
| sk_c8 != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6108]) ).
cnf(c_6110,plain,
( sk_c8 != sk_c7
| sk_c8 != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4511,c_6109]) ).
cnf(c_6111,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| B != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6110]) ).
cnf(c_6112,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| A != sk_c9
| inverse(B) != sk_c8
| sk_c8 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6111]) ).
cnf(c_6113,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| A != sk_c9
| sk_c8 != sk_c8
| sk_c9 != A
| inverse(B) != sk_c8
| sk_c8 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6112]) ).
cnf(c_6114,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c9 != A
| sk_c8 != sk_c8
| sk_c9 != A
| inverse(B) != sk_c8
| sk_c8 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6113]) ).
cnf(c_6115,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c9 != A
| sk_c9 != A
| inverse(B) != sk_c8
| sk_c8 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6114]) ).
cnf(c_6116,plain,
( sk_c8 != sk_c8
| sk_c9 != A
| sk_c9 != A
| inverse(B) != sk_c8
| sk_c8 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6115]) ).
cnf(c_6117,plain,
( sk_c9 != A
| sk_c9 != A
| inverse(B) != sk_c8
| sk_c8 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6116]) ).
cnf(c_4574,plain,
( sk_c9 != A
| inverse(B) != sk_c8
| sk_c8 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6117]) ).
cnf(c_6118,plain,
( multiply(sk_c8,sk_c3) = sk_c1
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4515,c_2956]) ).
cnf(c_4668,plain,
( sk_c3 = sk_c1
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4529,c_6118]) ).
cnf(c_4669,plain,
( inverse(sk_c9) = sk_c3
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4515,c_2955]) ).
cnf(c_6119,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_4573,c_36]) ).
cnf(c_6120,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_4515,c_6119]) ).
cnf(c_4829,plain,
( sk_c4 = sk_c9
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_4515,c_6120]) ).
cnf(c_6121,plain,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_4573,c_494]) ).
cnf(c_4928,plain,
( sk_c1 = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_4515,c_6121]) ).
cnf(c_6122,plain,
sk_c8 = sk_c7,
inference(copy,[status(thm)],[c_4573]) ).
cnf(c_6123,plain,
( sk_c9 != A
| inverse(sk_c7) != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_4574,c_6122]) ).
cnf(c_6124,plain,
( sk_c9 != A
| inverse(sk_c8) != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4573,c_6123]) ).
cnf(c_6125,plain,
( sk_c9 != A
| sk_c8 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4511,c_6124]) ).
cnf(c_4997,plain,
( sk_c9 != A
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6125]) ).
cnf(c_6126,plain,
C = multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))),
inference(copy,[status(thm)],[c_176]) ).
cnf(c_6127,plain,
( inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c9)))) != sk_c9
| multiply(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c9))),sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_4997,c_6126]) ).
cnf(c_6128,plain,
( inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c9)))) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_176,c_6127]) ).
cnf(c_5089,plain,
( inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_176,c_6128]) ).
cnf(c_6129,plain,
( inverse(sk_c4) = sk_c9
| sk_c9 = inverse(sk_c1) ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_5098,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c1)) != sk_c9
| multiply(inverse(sk_c1),sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_4997,c_6129]) ).
cnf(c_6130,plain,
( sk_c9 = inverse(sk_c4)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_5099,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c4)) != sk_c9
| multiply(inverse(sk_c4),sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_4997,c_6130]) ).
cnf(c_6131,plain,
( sk_c9 = sk_c1
| sk_c4 = sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4829,c_4668]) ).
cnf(c_6132,plain,
( sk_c1 = sk_c9
| sk_c4 = sk_c9
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_6131]) ).
cnf(c_5165,plain,
( sk_c1 = sk_c9
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_6132]) ).
cnf(c_6133,plain,
( inverse(sk_c9) = sk_c9
| sk_c4 = sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4829,c_4669]) ).
cnf(c_5615,plain,
( inverse(sk_c9) = sk_c9
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_6133]) ).
cnf(c_6134,plain,
( sk_c1 = sk_c9
| inverse(sk_c9) = sk_c9
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_5165,c_4928]) ).
cnf(c_5792,plain,
( inverse(sk_c9) = sk_c9
| sk_c1 = sk_c9 ),
inference(copy,[status(thm)],[c_6134]) ).
cnf(c_6135,plain,
( A != sk_c9
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_4997]) ).
cnf(c_6136,plain,
( inverse(inverse(sk_c9)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8
| sk_c4 = sk_c9 ),
inference(resolve,[status(thm)],[c_5615,c_6135]) ).
cnf(c_6137,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4528,c_6136]) ).
cnf(c_5882,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_6137]) ).
cnf(c_6138,plain,
( A != sk_c9
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_4997]) ).
cnf(c_6139,plain,
( inverse(inverse(sk_c9)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8
| sk_c1 = sk_c9 ),
inference(resolve,[status(thm)],[c_5792,c_6138]) ).
cnf(c_6140,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_4528,c_6139]) ).
cnf(c_5961,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c1 = sk_c9 ),
inference(copy,[status(thm)],[c_6140]) ).
cnf(c_6141,plain,
multiply(A,sk_c8) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_249,c_4515]) ).
cnf(c_6142,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_4515,c_6141]) ).
cnf(c_6020,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_6142]) ).
cnf(c_6143,plain,
( sk_c9 != sk_c9
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_6020,c_5961]) ).
cnf(c_6053,plain,
sk_c1 = sk_c9,
inference(copy,[status(thm)],[c_6143]) ).
cnf(c_6144,plain,
( sk_c9 != sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_6020,c_5882]) ).
cnf(c_6055,plain,
sk_c4 = sk_c9,
inference(copy,[status(thm)],[c_6144]) ).
cnf(c_6145,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c4)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_6055,c_5099]) ).
cnf(c_6146,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c4)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_4528,c_6145]) ).
cnf(c_6147,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6055,c_6146]) ).
cnf(c_6148,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6020,c_6147]) ).
cnf(c_6149,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6053,c_6148]) ).
cnf(c_6150,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c9 != sk_c9 ),
inference(copy,[status(thm)],[c_6149]) ).
cnf(c_6066,plain,
multiply(sk_c9,sk_c9) = sk_c8,
inference(copy,[status(thm)],[c_6150]) ).
cnf(c_6151,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c1)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_6053,c_5098]) ).
cnf(c_6152,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c1)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_4528,c_6151]) ).
cnf(c_6153,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6053,c_6152]) ).
cnf(c_6154,plain,
( inverse(sk_c4) = sk_c9
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6020,c_6153]) ).
cnf(c_6155,plain,
( inverse(sk_c9) = sk_c9
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6055,c_6154]) ).
cnf(c_6156,plain,
( inverse(sk_c9) = sk_c9
| sk_c9 != sk_c9 ),
inference(copy,[status(thm)],[c_6155]) ).
cnf(c_6067,plain,
inverse(sk_c9) = sk_c9,
inference(copy,[status(thm)],[c_6156]) ).
cnf(c_6157,plain,
( inverse(sk_c9) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6066,c_5089]) ).
cnf(c_6158,plain,
( sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6067,c_6157]) ).
cnf(c_6159,plain,
sk_c9 != sk_c9,
inference(copy,[status(thm)],[c_6158]) ).
cnf(c_6068,plain,
$false,
inference(copy,[status(thm)],[c_6159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n009.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 14:41:28 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 1843447 was started by sandbox on n009,
% 0.16/0.45 % Fri Sep 25 14:41:28 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 44.47/6.90
% 44.47/6.90 % SZS status Unsatisfiable for theBenchmark
% 44.47/6.90
% 44.47/6.90 % Proof 1 at 4.87 (+ 1.52) seconds.
% 44.47/6.90 % Length of proof is 86.
% 44.47/6.90 % Level of proof is 22.
% 44.47/6.90 % Maximum clause weight is 58.000.
% 44.47/6.90 % Given clauses 399.
% 44.47/6.90
% 44.47/6.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------