%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP321-1 : 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 : n015.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 07:28:38 AM UTC 2026
% Result : Unsatisfiable 203.38s 27.39s
% Output : CNFRefutation 203.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 24
% Syntax : Number of formulae : 209 ( 27 unt; 0 def)
% Number of atoms : 580 ( 579 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 556 ( 185 ~; 371 |; 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 : 65 ( 0 sgn 10 !; 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,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_6,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_21,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_26,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(sk_c6,sk_c7) != sk_c8
| inverse(VAR_4) != sk_c7
| multiply(VAR_4,sk_c7) != sk_c6
| inverse(VAR_3) != sk_c8
| multiply(VAR_3,sk_c8) != sk_c7
| inverse(VAR_2) != sk_c8
| multiply(VAR_2,sk_c8) != VAR_1
| multiply(sk_c8,VAR_1) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| inverse(E) != sk_c7
| multiply(E,sk_c7) != sk_c6
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_30808,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_30809,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_30808]) ).
cnf(c_62,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_30809]) ).
cnf(c_73,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_76,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_100,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_101,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_140,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c6
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_34]) ).
cnf(c_301,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c6
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_140]) ).
cnf(c_30810,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c6
| multiply(inverse(sk_c8),sk_c8) != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_301]) ).
cnf(c_551,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c6
| identity != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_30810]) ).
cnf(c_970,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_62]) ).
cnf(c_1002,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_62,c_62]) ).
cnf(c_1003,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_1002,c_970]) ).
cnf(c_1012,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_1003,c_2]) ).
cnf(c_1307,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1002,c_2]) ).
cnf(c_30811,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1002,c_1003]) ).
cnf(c_30812,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1003,c_30811]) ).
cnf(c_1335,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_30812]) ).
cnf(c_30813,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c6
| identity != sk_c7
| sk_c8 != sk_c8
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_1335,c_551]) ).
cnf(c_1353,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c6
| identity != sk_c7
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_30813]) ).
cnf(c_1407,plain,
( inverse(sk_c8) = sk_c4
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(paramod,[status(thm)],[c_25,c_1335]) ).
cnf(c_1499,plain,
( multiply(sk_c4,sk_c8) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_1307]) ).
cnf(c_1500,plain,
( multiply(sk_c5,sk_c7) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_1307]) ).
cnf(c_1503,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_14,c_1307]) ).
cnf(c_1504,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_15,c_1307]) ).
cnf(c_1505,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_16,c_1307]) ).
cnf(c_1506,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_1307]) ).
cnf(c_1507,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_18,c_1307]) ).
cnf(c_1508,plain,
( multiply(sk_c4,sk_c8) = identity
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_20,c_1307]) ).
cnf(c_1512,plain,
( multiply(sk_c2,sk_c8) = identity
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_29,c_1307]) ).
cnf(c_1529,plain,
( multiply(sk_c4,sk_c8) = identity
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_101,c_1307]) ).
cnf(c_3378,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_1504,c_2]) ).
cnf(c_3563,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_1506,c_2]) ).
cnf(c_30814,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1499,c_4]) ).
cnf(c_6093,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_30814]) ).
cnf(c_30815,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1500,c_6]) ).
cnf(c_6259,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_30815]) ).
cnf(c_6272,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_6259,c_62]) ).
cnf(c_30816,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| identity = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1503,c_9]) ).
cnf(c_6494,plain,
( identity = sk_c8
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_30816]) ).
cnf(c_30817,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| identity = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1505,c_11]) ).
cnf(c_6791,plain,
( identity = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_30817]) ).
cnf(c_30818,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| identity = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_1507,c_13]) ).
cnf(c_7054,plain,
( identity = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_30818]) ).
cnf(c_7060,plain,
( multiply(inverse(sk_c6),sk_c8) = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_7054,c_62]) ).
cnf(c_30819,plain,
( identity = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_1508,c_19]) ).
cnf(c_7364,plain,
( identity = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_30819]) ).
cnf(c_7377,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_7364,c_62]) ).
cnf(c_30820,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| identity = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1512,c_24]) ).
cnf(c_7791,plain,
( identity = sk_c3
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_30820]) ).
cnf(c_30821,plain,
( multiply(sk_c8,sk_c2) = identity
| identity = sk_c7
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_1529,c_100]) ).
cnf(c_9173,plain,
( identity = sk_c7
| multiply(sk_c8,sk_c2) = identity ),
inference(copy,[status(thm)],[c_30821]) ).
cnf(c_30822,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9173,c_62]) ).
cnf(c_9342,plain,
( inverse(sk_c8) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1003,c_30822]) ).
cnf(c_30823,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_3378,c_73]) ).
cnf(c_10390,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(copy,[status(thm)],[c_30823]) ).
cnf(c_30824,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10390,c_62]) ).
cnf(c_10394,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1003,c_30824]) ).
cnf(c_10403,plain,
( multiply(sk_c4,sk_c8) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10394,c_2]) ).
cnf(c_30825,plain,
( identity = sk_c8
| identity = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10403,c_6494]) ).
cnf(c_10922,plain,
( identity = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_30825]) ).
cnf(c_10924,plain,
( multiply(A,sk_c8) = A
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10922,c_1003]) ).
cnf(c_10925,plain,
( inverse(sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10922,c_1012]) ).
cnf(c_30826,plain,
( multiply(identity,sk_c7) = sk_c3
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10925,c_7377]) ).
cnf(c_30827,plain,
( sk_c7 = sk_c3
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_30826]) ).
cnf(c_30828,plain,
( sk_c3 = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_30827]) ).
cnf(c_10957,plain,
( sk_c3 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_30828]) ).
cnf(c_30829,plain,
( identity = sk_c2
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10925,c_9342]) ).
cnf(c_10963,plain,
( identity = sk_c2
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_30829]) ).
cnf(c_10982,plain,
( multiply(A,sk_c7) = A
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_10957,c_1003]) ).
cnf(c_10983,plain,
( inverse(sk_c7) = identity
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_10957,c_1012]) ).
cnf(c_30830,plain,
( identity = sk_c7
| sk_c2 = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10963,c_10922]) ).
cnf(c_11357,plain,
( sk_c2 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_30830]) ).
cnf(c_30831,plain,
( multiply(identity,sk_c6) = sk_c8
| identity = sk_c6
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_10983,c_6272]) ).
cnf(c_11483,plain,
( sk_c6 = sk_c8
| identity = sk_c6
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_30831]) ).
cnf(c_30832,plain,
( identity = sk_c7
| sk_c7 = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10924,c_6093]) ).
cnf(c_30833,plain,
( identity = sk_c7
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_30832]) ).
cnf(c_12100,plain,
( sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_30833]) ).
cnf(c_12108,plain,
( identity = sk_c3
| sk_c4 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10924,c_7791]) ).
cnf(c_12832,plain,
( identity = sk_c8
| sk_c6 = sk_c8
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_10982,c_7054]) ).
cnf(c_30834,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c6
| sk_c3 = sk_c7
| sk_c6 = sk_c8
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_12832,c_11483]) ).
cnf(c_30835,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c3 = sk_c7
| sk_c6 = sk_c8
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_30834]) ).
cnf(c_30836,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_30835]) ).
cnf(c_30837,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_30836]) ).
cnf(c_14635,plain,
( sk_c6 = sk_c8
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_30837]) ).
cnf(c_30838,plain,
( identity = sk_c7
| sk_c4 = sk_c7
| identity = sk_c7
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_14635,c_12108]) ).
cnf(c_14655,plain,
( sk_c4 = sk_c7
| identity = sk_c7
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_30838]) ).
cnf(c_30839,plain,
( multiply(sk_c7,sk_c5) = identity
| identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_3563,c_76]) ).
cnf(c_16226,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(copy,[status(thm)],[c_30839]) ).
cnf(c_30840,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16226,c_62]) ).
cnf(c_16242,plain,
( inverse(sk_c7) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1003,c_30840]) ).
cnf(c_16292,plain,
( multiply(sk_c5,sk_c7) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16242,c_2]) ).
cnf(c_30841,plain,
( identity = sk_c8
| identity = sk_c6
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16292,c_6791]) ).
cnf(c_16360,plain,
( identity = sk_c6
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_30841]) ).
cnf(c_16373,plain,
( inverse(sk_c6) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16360,c_1012]) ).
cnf(c_30842,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16360,c_12100]) ).
cnf(c_16396,plain,
( sk_c6 = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_30842]) ).
cnf(c_16408,plain,
( multiply(A,sk_c8) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_16396,c_1003]) ).
cnf(c_30843,plain,
( multiply(identity,sk_c8) = sk_c7
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16373,c_7060]) ).
cnf(c_30844,plain,
( sk_c8 = sk_c7
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_30843]) ).
cnf(c_16584,plain,
( sk_c8 = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_30844]) ).
cnf(c_30845,plain,
( inverse(sk_c6) = sk_c6
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16360,c_16373]) ).
cnf(c_16644,plain,
( inverse(sk_c6) = sk_c6
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_30845]) ).
cnf(c_30846,plain,
( sk_c3 = sk_c7
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_16584,c_10957]) ).
cnf(c_16681,plain,
( sk_c3 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30846]) ).
cnf(c_30847,plain,
( sk_c2 = sk_c8
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_16584,c_11357]) ).
cnf(c_16682,plain,
( sk_c2 = sk_c8
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30847]) ).
cnf(c_30848,plain,
( sk_c4 = sk_c7
| sk_c8 = sk_c7
| sk_c6 = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_16584,c_14655]) ).
cnf(c_16685,plain,
( sk_c4 = sk_c7
| sk_c6 = sk_c8
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30848]) ).
cnf(c_30849,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16644,c_7060]) ).
cnf(c_16895,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_30849]) ).
cnf(c_30850,plain,
( identity = sk_c6
| sk_c7 = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_16408,c_6259]) ).
cnf(c_30851,plain,
( identity = sk_c6
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_30850]) ).
cnf(c_17224,plain,
( identity = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_30851]) ).
cnf(c_30852,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_17224,c_12100]) ).
cnf(c_30853,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_30852]) ).
cnf(c_17340,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_30853]) ).
cnf(c_17534,plain,
( multiply(sk_c7,sk_c8) = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_17340,c_16895]) ).
cnf(c_30854,plain,
( sk_c4 = sk_c7
| sk_c7 = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_17340,c_16685]) ).
cnf(c_30855,plain,
( sk_c4 = sk_c7
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30854]) ).
cnf(c_17583,plain,
( sk_c4 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30855]) ).
cnf(c_30856,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c6
| identity != sk_c7
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_17340,c_1353]) ).
cnf(c_30857,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c7
| identity != sk_c7
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_17340,c_30856]) ).
cnf(c_24728,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c7
| identity != sk_c7
| identity != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_17340,c_30857]) ).
cnf(c_26918,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_17583,c_1407]) ).
cnf(c_30858,plain,
( multiply(inverse(sk_c7),sk_c7) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_17534,c_62]) ).
cnf(c_30859,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_30858]) ).
cnf(c_27143,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_30859]) ).
cnf(c_30860,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c7
| identity != sk_c7
| sk_c8 != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_27143,c_24728]) ).
cnf(c_27671,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c7
| sk_c8 != sk_c7
| sk_c8 != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_27143,c_30860]) ).
cnf(c_30861,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_27143,c_1012]) ).
cnf(c_29173,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_27143,c_30861]) ).
cnf(c_29174,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_27143,c_1003]) ).
cnf(c_29186,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_27143,c_1]) ).
cnf(c_30862,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_27671]) ).
cnf(c_30863,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_29174,c_30862]) ).
cnf(c_30864,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(sk_c8) != sk_c7
| sk_c7 != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_29186,c_30863]) ).
cnf(c_30865,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c7
| sk_c8 != sk_c7
| sk_c7 != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_29173,c_30864]) ).
cnf(c_30866,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c7 != sk_c7
| sk_c8 != sk_c7
| sk_c7 != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_29186,c_30865]) ).
cnf(c_30867,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c7 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_30866]) ).
cnf(c_30868,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c7 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_30867]) ).
cnf(c_30869,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_30868]) ).
cnf(c_30870,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_30869]) ).
cnf(c_30871,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_30870]) ).
cnf(c_29274,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_30871]) ).
cnf(c_30872,plain,
( inverse(sk_c8) = sk_c7
| sk_c2 = sk_c3
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_29174,c_26918]) ).
cnf(c_30873,plain,
( sk_c8 = sk_c7
| sk_c2 = sk_c3
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_29173,c_30872]) ).
cnf(c_30874,plain,
( sk_c8 = sk_c7
| sk_c3 = sk_c2
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30873]) ).
cnf(c_29422,plain,
( sk_c3 = sk_c2
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30874]) ).
cnf(c_30875,plain,
( sk_c2 = sk_c7
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_29422,c_16681]) ).
cnf(c_30090,plain,
( sk_c2 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30875]) ).
cnf(c_30876,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_30090,c_16682]) ).
cnf(c_30877,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30876]) ).
cnf(c_30878,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_30877]) ).
cnf(c_30406,plain,
sk_c8 = sk_c7,
inference(copy,[status(thm)],[c_30878]) ).
cnf(c_30879,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_30406,c_29274]) ).
cnf(c_30880,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_30406,c_30879]) ).
cnf(c_30805,plain,
multiply(sk_c7,sk_c7) != sk_c7,
inference(copy,[status(thm)],[c_30880]) ).
cnf(c_30806,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_30406,c_29186]) ).
cnf(c_30807,plain,
$false,
inference(resolve,[status(thm)],[c_30806,c_30805]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP321-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 14:48:57 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1637627 was started by sandbox2 on n015,
% 0.18/0.45 % Fri Sep 25 14:48:57 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 203.38/27.39
% 203.38/27.39 % given #500 (T,wt=8): 13547 identity = sk_c7 | multiply(sk_c6,sk_c1) = sk_c2. [para(10963(b,1),12256(b,2)),merge(b)].
% 203.38/27.39
% 203.38/27.39 % SZS status Unsatisfiable for theBenchmark
% 203.38/27.39
% 203.38/27.39 % Proof 1 at 22.70 (+ 2.97) seconds.
% 203.38/27.39 % Length of proof is 112.
% 203.38/27.39 % Level of proof is 23.
% 203.38/27.39 % Maximum clause weight is 51.000.
% 203.38/27.39 % Given clauses 806.
% 203.38/27.39
% 203.38/27.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
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