%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP213-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 07:28:22 AM UTC 2026
% Result : Unsatisfiable 30.88s 4.39s
% Output : CNFRefutation 30.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 18
% Syntax : Number of formulae : 186 ( 30 unt; 0 def)
% Number of atoms : 449 ( 448 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 400 ( 137 ~; 263 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 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_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_19,axiom,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c8
| multiply(VAR_5,sk_c8) != VAR_4
| multiply(sk_c8,VAR_4) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_3) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(VAR_1) != VAR_2
| multiply(VAR_1,VAR_2) != sk_c8
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(D) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(B) != C
| multiply(B,C) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
cnf(c_31,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c8) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_50,plain,
( inverse(C) != sk_c8
| multiply(C,sk_c8) != B
| multiply(sk_c8,B) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| multiply(A,sk_c8) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_31]) ).
cnf(c_6347,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_6348,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_6347]) ).
cnf(c_86,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_6348]) ).
cnf(c_108,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_110,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_121,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_122,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_144,plain,
( multiply(sk_c3,sk_c2) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_6349,plain,
( inverse(B) != sk_c8
| multiply(B,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(identity,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c7 ),
inference(resolve,[status(thm)],[c_50,c_1]) ).
cnf(c_6350,plain,
( inverse(B) != sk_c8
| multiply(B,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(identity,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_6349]) ).
cnf(c_6351,plain,
( inverse(B) != sk_c8
| multiply(B,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| sk_c7 != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_6350]) ).
cnf(c_6352,plain,
( inverse(B) != sk_c8
| multiply(B,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| sk_c7 != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_6351]) ).
cnf(c_164,plain,
( inverse(B) != sk_c8
| multiply(B,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_6352]) ).
cnf(c_6353,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| sk_c7 != sk_c8 ),
inference(factor,[status(thm)],[c_164]) ).
cnf(c_165,plain,
( sk_c8 != A
| multiply(sk_c8,A) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_6353]) ).
cnf(c_191,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_86]) ).
cnf(c_197,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_6,c_86]) ).
cnf(c_199,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_86]) ).
cnf(c_241,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_86,c_86]) ).
cnf(c_242,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_241,c_191]) ).
cnf(c_285,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_242,c_2]) ).
cnf(c_6354,plain,
( sk_c8 != identity
| sk_c8 != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(identity) != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_242,c_165]) ).
cnf(c_6355,plain,
( sk_c8 != identity
| sk_c8 != sk_c7
| inverse(sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_6354]) ).
cnf(c_6356,plain,
( sk_c8 != identity
| sk_c7 != sk_c8
| inverse(sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_6355]) ).
cnf(c_6357,plain,
( identity != sk_c8
| sk_c7 != sk_c8
| inverse(sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_6356]) ).
cnf(c_6358,plain,
( identity != sk_c8
| inverse(sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_6357]) ).
cnf(c_287,plain,
( inverse(sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_6358]) ).
cnf(c_6359,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_108,c_86]) ).
cnf(c_313,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_242,c_6359]) ).
cnf(c_317,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_313,c_2]) ).
cnf(c_6360,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_110,c_86]) ).
cnf(c_389,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_242,c_6360]) ).
cnf(c_392,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_389,c_2]) ).
cnf(c_6361,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_121,c_86]) ).
cnf(c_571,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_242,c_6361]) ).
cnf(c_576,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_571,c_2]) ).
cnf(c_6362,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_122,c_86]) ).
cnf(c_589,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_242,c_6362]) ).
cnf(c_594,plain,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_589,c_2]) ).
cnf(c_6363,plain,
( multiply(inverse(sk_c3),identity) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_144,c_86]) ).
cnf(c_765,plain,
( inverse(sk_c3) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_242,c_6363]) ).
cnf(c_780,plain,
( multiply(sk_c2,sk_c3) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_765,c_2]) ).
cnf(c_6364,plain,
( inverse(sk_c8) = sk_c7
| identity = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_317,c_4]) ).
cnf(c_1145,plain,
( identity = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6364]) ).
cnf(c_1184,plain,
( inverse(sk_c7) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1145,c_285]) ).
cnf(c_6365,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1145,c_1184]) ).
cnf(c_1334,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6365]) ).
cnf(c_6366,plain,
( inverse(sk_c4) = sk_c8
| identity = sk_c7
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_392,c_5]) ).
cnf(c_1502,plain,
( identity = sk_c7
| inverse(sk_c4) = sk_c8 ),
inference(copy,[status(thm)],[c_6366]) ).
cnf(c_1513,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1502,c_2]) ).
cnf(c_6367,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1513,c_86]) ).
cnf(c_1524,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_242,c_6367]) ).
cnf(c_6368,plain,
( identity = sk_c7
| sk_c4 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1524,c_1145]) ).
cnf(c_1575,plain,
( sk_c4 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_6368]) ).
cnf(c_1605,plain,
( inverse(sk_c7) = identity
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_1575,c_285]) ).
cnf(c_6369,plain,
( inverse(sk_c8) != sk_c7
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_1575,c_287]) ).
cnf(c_1606,plain,
( inverse(sk_c8) != sk_c7
| sk_c7 != sk_c8
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_6369]) ).
cnf(c_6370,plain,
( inverse(sk_c7) = sk_c7
| sk_c4 = sk_c7
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_1575,c_1605]) ).
cnf(c_1681,plain,
( inverse(sk_c7) = sk_c7
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_6370]) ).
cnf(c_6371,plain,
( inverse(sk_c5) = sk_c8
| identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_576,c_9]) ).
cnf(c_2233,plain,
( identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_6371]) ).
cnf(c_2248,plain,
( multiply(sk_c8,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2233,c_2]) ).
cnf(c_6372,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2248,c_86]) ).
cnf(c_2258,plain,
( inverse(sk_c8) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_242,c_6372]) ).
cnf(c_6373,plain,
( sk_c5 = sk_c4
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2258,c_1524]) ).
cnf(c_2302,plain,
( sk_c5 = sk_c4
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_6373]) ).
cnf(c_2367,plain,
( inverse(sk_c7) = identity
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_2302,c_285]) ).
cnf(c_6374,plain,
( inverse(sk_c8) != sk_c7
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_2302,c_287]) ).
cnf(c_2368,plain,
( inverse(sk_c8) != sk_c7
| sk_c7 != sk_c8
| sk_c5 = sk_c4 ),
inference(copy,[status(thm)],[c_6374]) ).
cnf(c_6375,plain,
( inverse(sk_c7) = sk_c7
| sk_c5 = sk_c4
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_2302,c_2367]) ).
cnf(c_2409,plain,
( inverse(sk_c7) = sk_c7
| sk_c5 = sk_c4 ),
inference(copy,[status(thm)],[c_6375]) ).
cnf(c_6376,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_594,c_14]) ).
cnf(c_3157,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_6376]) ).
cnf(c_3172,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3157,c_2]) ).
cnf(c_6377,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3172,c_86]) ).
cnf(c_3184,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_242,c_6377]) ).
cnf(c_3214,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3184,c_2]) ).
cnf(c_3410,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3214,c_8]) ).
cnf(c_6378,plain,
( inverse(sk_c8) = sk_c7
| identity = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_780,c_16]) ).
cnf(c_3617,plain,
( identity = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6378]) ).
cnf(c_6379,plain,
( sk_c8 = sk_c7
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3617,c_1145]) ).
cnf(c_6380,plain,
( sk_c7 = sk_c8
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6379]) ).
cnf(c_3656,plain,
( sk_c7 = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6380]) ).
cnf(c_6381,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3656,c_1334]) ).
cnf(c_6382,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6381]) ).
cnf(c_3818,plain,
inverse(sk_c8) = sk_c7,
inference(copy,[status(thm)],[c_6382]) ).
cnf(c_6383,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c8
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_3818,c_2368]) ).
cnf(c_3978,plain,
( sk_c7 != sk_c8
| sk_c5 = sk_c4 ),
inference(copy,[status(thm)],[c_6383]) ).
cnf(c_6384,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c8
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_3818,c_1606]) ).
cnf(c_4067,plain,
( sk_c7 != sk_c8
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_6384]) ).
cnf(c_6385,plain,
( sk_c7 != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_3818,c_287]) ).
cnf(c_4269,plain,
( identity != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_6385]) ).
cnf(c_4301,plain,
multiply(sk_c7,sk_c8) = identity,
inference(paramod,[status(thm)],[c_3818,c_2]) ).
cnf(c_6386,plain,
multiply(inverse(sk_c7),identity) = sk_c8,
inference(paramod,[status(thm)],[c_4301,c_86]) ).
cnf(c_4680,plain,
inverse(sk_c7) = sk_c8,
inference(paramod,[status(thm)],[c_242,c_6386]) ).
cnf(c_6387,plain,
( sk_c8 = sk_c7
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_4680,c_2409]) ).
cnf(c_4793,plain,
( sk_c7 = sk_c8
| sk_c5 = sk_c4 ),
inference(copy,[status(thm)],[c_6387]) ).
cnf(c_6388,plain,
( sk_c8 = sk_c7
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_4680,c_1681]) ).
cnf(c_4821,plain,
( sk_c7 = sk_c8
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_6388]) ).
cnf(c_6389,plain,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_197]) ).
cnf(c_4851,plain,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_6389]) ).
cnf(c_5016,plain,
multiply(sk_c8,sk_c7) = identity,
inference(paramod,[status(thm)],[c_4680,c_2]) ).
cnf(c_5072,plain,
( identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_5016,c_4851]) ).
cnf(c_6390,plain,
( sk_c5 = sk_c4
| sk_c5 = sk_c4 ),
inference(resolve,[status(thm)],[c_4793,c_3978]) ).
cnf(c_5240,plain,
sk_c5 = sk_c4,
inference(copy,[status(thm)],[c_6390]) ).
cnf(c_5321,plain,
( multiply(sk_c4,sk_c8) = sk_c6
| identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5240,c_3410]) ).
cnf(c_6391,plain,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_13,c_199]) ).
cnf(c_6392,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_5016,c_6391]) ).
cnf(c_5447,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_6392]) ).
cnf(c_6393,plain,
( sk_c4 = sk_c7
| sk_c4 = sk_c7 ),
inference(resolve,[status(thm)],[c_4821,c_4067]) ).
cnf(c_5555,plain,
sk_c4 = sk_c7,
inference(copy,[status(thm)],[c_6393]) ).
cnf(c_6394,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5555,c_5321]) ).
cnf(c_6395,plain,
( identity = sk_c6
| identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_4301,c_6394]) ).
cnf(c_5651,plain,
( identity = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_6395]) ).
cnf(c_5720,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_5555,c_5072]) ).
cnf(c_6396,plain,
( inverse(sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5651,c_285]) ).
cnf(c_6397,plain,
( sk_c8 = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_4680,c_6396]) ).
cnf(c_5876,plain,
( identity = sk_c8
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_6397]) ).
cnf(c_6398,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5651,c_4269]) ).
cnf(c_5883,plain,
( sk_c7 != sk_c8
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_6398]) ).
cnf(c_6399,plain,
( sk_c8 = sk_c7
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5876,c_5651]) ).
cnf(c_6400,plain,
( sk_c7 = sk_c8
| identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_6399]) ).
cnf(c_5950,plain,
( sk_c7 = sk_c8
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_6400]) ).
cnf(c_6401,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(resolve,[status(thm)],[c_5950,c_5883]) ).
cnf(c_5953,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_6401]) ).
cnf(c_6016,plain,
( sk_c6 = sk_c8
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_5953,c_5720]) ).
cnf(c_6071,plain,
( sk_c6 = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_5953,c_5447]) ).
cnf(c_6101,plain,
multiply(sk_c7,sk_c8) = sk_c6,
inference(paramod,[status(thm)],[c_5953,c_4301]) ).
cnf(c_6102,plain,
( sk_c6 != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_5953,c_4269]) ).
cnf(c_6402,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_5953,c_285]) ).
cnf(c_6138,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_5953,c_6402]) ).
cnf(c_6139,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_5953,c_242]) ).
cnf(c_6403,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_6139,c_6071]) ).
cnf(c_6166,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_6403]) ).
cnf(c_6404,plain,
( inverse(sk_c8) = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_6166,c_6138]) ).
cnf(c_6405,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3818,c_6404]) ).
cnf(c_6294,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_6405]) ).
cnf(c_6406,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_6294,c_6166]) ).
cnf(c_6407,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_6406]) ).
cnf(c_6318,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_6407]) ).
cnf(c_6408,plain,
( sk_c6 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6318,c_6102]) ).
cnf(c_6342,plain,
sk_c6 != sk_c8,
inference(copy,[status(thm)],[c_6408]) ).
cnf(c_6343,plain,
multiply(sk_c8,sk_c8) = sk_c6,
inference(paramod,[status(thm)],[c_6318,c_6101]) ).
cnf(c_6409,plain,
( sk_c6 = sk_c8
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_6318,c_6016]) ).
cnf(c_6410,plain,
( sk_c6 = sk_c8
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_6318,c_6409]) ).
cnf(c_6411,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_6343,c_6410]) ).
cnf(c_6412,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_6411]) ).
cnf(c_6346,plain,
$false,
inference(resolve,[status(thm)],[c_6342,c_6412]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP213-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:39:04 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 3146947 was started by sandbox2 on n020,
% 0.14/0.37 % Fri Sep 25 14:39:04 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 30.88/4.39
% 30.88/4.39 % SZS status Unsatisfiable for theBenchmark
% 30.88/4.39
% 30.88/4.39 % Proof 1 at 3.05 (+ 0.92) seconds.
% 30.88/4.39 % Length of proof is 102.
% 30.88/4.39 % Level of proof is 24.
% 30.88/4.39 % Maximum clause weight is 49.000.
% 30.88/4.39 % Given clauses 360.
% 30.88/4.39
% 30.88/4.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------