%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP347-1 : 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 : n011.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 07:28:41 AM UTC 2026
% Result : Unsatisfiable 112.47s 20.56s
% Output : CNFRefutation 112.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 20
% Syntax : Number of formulae : 177 ( 29 unt; 0 def)
% Number of atoms : 504 ( 503 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 549 ( 222 ~; 327 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 9 !; 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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_9,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_20,axiom,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_26,axiom,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c5
| inverse(VAR_2) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c5
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_37,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c5
| inverse(A) != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_14949,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_14950,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_14949]) ).
cnf(c_50,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_14950]) ).
cnf(c_62,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_64,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_77,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_83,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_637,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_50]) ).
cnf(c_669,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_50,c_50]) ).
cnf(c_670,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_669,c_637]) ).
cnf(c_671,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_670,c_2]) ).
cnf(c_1054,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_669,c_2]) ).
cnf(c_14951,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_669,c_670]) ).
cnf(c_14952,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_670,c_14951]) ).
cnf(c_1077,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_14952]) ).
cnf(c_14953,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c5
| inverse(inverse(sk_c7)) != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(resolve,[status(thm)],[c_1077,c_37]) ).
cnf(c_1109,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_1077,c_14953]) ).
cnf(c_1120,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_5,c_1077]) ).
cnf(c_14954,plain,
identity = multiply(A,multiply(B,inverse(multiply(A,B)))),
inference(paramod,[status(thm)],[c_1054,c_3]) ).
cnf(c_1184,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(copy,[status(thm)],[c_14954]) ).
cnf(c_1185,plain,
( multiply(sk_c6,sk_c5) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_5,c_1054]) ).
cnf(c_1191,plain,
( multiply(sk_c3,sk_c6) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_13,c_1054]) ).
cnf(c_1193,plain,
( multiply(sk_c4,sk_c7) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_1054]) ).
cnf(c_1195,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_19,c_1054]) ).
cnf(c_1196,plain,
( multiply(sk_c4,sk_c7) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_21,c_1054]) ).
cnf(c_1198,plain,
( multiply(sk_c2,sk_c6) = identity
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_23,c_1054]) ).
cnf(c_1200,plain,
( multiply(sk_c3,sk_c6) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_25,c_1054]) ).
cnf(c_1204,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_31,c_1054]) ).
cnf(c_3464,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_1191,c_2]) ).
cnf(c_3532,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_1193,c_2]) ).
cnf(c_3887,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_1200,c_2]) ).
cnf(c_8417,plain,
( multiply(sk_c2,multiply(sk_c5,inverse(sk_c6))) = identity
| multiply(sk_c5,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_83,c_1184]) ).
cnf(c_14955,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1185,c_4]) ).
cnf(c_9604,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_14955]) ).
cnf(c_9610,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9604,c_50]) ).
cnf(c_14956,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1195,c_18]) ).
cnf(c_10142,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_14956]) ).
cnf(c_10146,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10142,c_50]) ).
cnf(c_14957,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1196,c_20]) ).
cnf(c_10289,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_14957]) ).
cnf(c_10294,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_10289,c_50]) ).
cnf(c_14958,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_1204,c_30]) ).
cnf(c_10445,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_14958]) ).
cnf(c_14959,plain,
( B != sk_c7
| multiply(inverse(B),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_1077,c_1109]) ).
cnf(c_10507,plain,
( sk_c7 != B
| multiply(inverse(B),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(copy,[status(thm)],[c_14959]) ).
cnf(c_10529,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(factor,[status(thm)],[c_10507]) ).
cnf(c_14960,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_3464,c_62]) ).
cnf(c_11330,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_14960]) ).
cnf(c_14961,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11330,c_50]) ).
cnf(c_11333,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_670,c_14961]) ).
cnf(c_11418,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11333,c_1077]) ).
cnf(c_14962,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11418,c_10146]) ).
cnf(c_11507,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_14962]) ).
cnf(c_11511,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11507,c_50]) ).
cnf(c_14963,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c5
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_3532,c_64]) ).
cnf(c_11601,plain,
( identity = sk_c5
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_14963]) ).
cnf(c_14964,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11601,c_50]) ).
cnf(c_11604,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_670,c_14964]) ).
cnf(c_11673,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11604,c_1077]) ).
cnf(c_14965,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11673,c_10294]) ).
cnf(c_11766,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_14965]) ).
cnf(c_11770,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11766,c_50]) ).
cnf(c_14966,plain,
( multiply(sk_c6,sk_c2) = identity
| identity = sk_c7
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_3887,c_77]) ).
cnf(c_11974,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c2) = identity ),
inference(copy,[status(thm)],[c_14966]) ).
cnf(c_14967,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11974,c_50]) ).
cnf(c_11977,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_670,c_14967]) ).
cnf(c_14968,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11977,c_9610]) ).
cnf(c_12049,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_14968]) ).
cnf(c_14969,plain,
( identity = sk_c7
| sk_c7 = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12049,c_10445]) ).
cnf(c_12093,plain,
( sk_c7 = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_14969]) ).
cnf(c_12118,plain,
( multiply(A,sk_c7) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12093,c_670]) ).
cnf(c_12119,plain,
( inverse(sk_c7) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12093,c_671]) ).
cnf(c_14970,plain,
( multiply(identity,sk_c6) = sk_c7
| identity = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12119,c_11770]) ).
cnf(c_14971,plain,
( sk_c6 = sk_c7
| identity = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_14970]) ).
cnf(c_14972,plain,
( sk_c7 = sk_c6
| identity = sk_c5
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14971]) ).
cnf(c_12199,plain,
( identity = sk_c5
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14972]) ).
cnf(c_12205,plain,
( inverse(sk_c5) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12199,c_671]) ).
cnf(c_14973,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12199,c_12093]) ).
cnf(c_12236,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14973]) ).
cnf(c_14974,plain,
( inverse(sk_c5) = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12093,c_12205]) ).
cnf(c_12480,plain,
( inverse(sk_c5) = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14974]) ).
cnf(c_14975,plain,
( sk_c7 = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12480,c_1120]) ).
cnf(c_12548,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14975]) ).
cnf(c_14976,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12548,c_12118]) ).
cnf(c_12695,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14976]) ).
cnf(c_14977,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12695,c_12236]) ).
cnf(c_14978,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14977]) ).
cnf(c_14979,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14978]) ).
cnf(c_12734,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_14979]) ).
cnf(c_14980,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12734,c_11511]) ).
cnf(c_14981,plain,
( multiply(inverse(sk_c6),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12734,c_14980]) ).
cnf(c_14982,plain,
( identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_14981]) ).
cnf(c_14983,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12734,c_14982]) ).
cnf(c_13095,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_14983]) ).
cnf(c_14984,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_12734,c_10529]) ).
cnf(c_14985,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c6),sk_c6) != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_12734,c_14984]) ).
cnf(c_14986,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_14985]) ).
cnf(c_14987,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_13095,c_14986]) ).
cnf(c_14988,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_12734,c_14987]) ).
cnf(c_14989,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_12734,c_14988]) ).
cnf(c_14990,plain,
( multiply(inverse(sk_c6),sk_c7) != sk_c5
| sk_c6 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_12734,c_14989]) ).
cnf(c_14991,plain,
( multiply(inverse(sk_c6),sk_c6) != sk_c5
| sk_c6 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_12734,c_14990]) ).
cnf(c_14992,plain,
( identity != sk_c5
| sk_c6 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_14991]) ).
cnf(c_14993,plain,
( sk_c6 != sk_c5
| sk_c6 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_13095,c_14992]) ).
cnf(c_14994,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_14993]) ).
cnf(c_14995,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_14994]) ).
cnf(c_13447,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_14995]) ).
cnf(c_14996,plain,
( multiply(sk_c2,multiply(sk_c5,inverse(sk_c6))) = identity
| multiply(sk_c5,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_13095,c_8417]) ).
cnf(c_14867,plain,
( multiply(sk_c2,multiply(sk_c5,inverse(sk_c6))) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_13095,c_14996]) ).
cnf(c_14893,plain,
( multiply(sk_c2,sk_c6) = sk_c6
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_13095,c_1198]) ).
cnf(c_14997,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_13095,c_671]) ).
cnf(c_14903,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_13095,c_14997]) ).
cnf(c_14904,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_13095,c_670]) ).
cnf(c_14909,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_13095,c_1]) ).
cnf(c_14998,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_13447]) ).
cnf(c_14999,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| sk_c6 != sk_c5 ),
inference(paramod,[status(thm)],[c_14904,c_14998]) ).
cnf(c_15000,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c5 ),
inference(paramod,[status(thm)],[c_14903,c_14999]) ).
cnf(c_15001,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c5 ),
inference(paramod,[status(thm)],[c_14909,c_15000]) ).
cnf(c_15002,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c5 ),
inference(paramod,[status(thm)],[c_14903,c_15001]) ).
cnf(c_15003,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_15002]) ).
cnf(c_15004,plain,
( sk_c5 != sk_c6
| sk_c5 != sk_c6
| sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_15003]) ).
cnf(c_15005,plain,
( sk_c5 != sk_c6
| sk_c5 != sk_c6
| sk_c5 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_15004]) ).
cnf(c_15006,plain,
( sk_c5 != sk_c6
| sk_c5 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_15005]) ).
cnf(c_15007,plain,
( sk_c5 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_15006]) ).
cnf(c_14944,plain,
sk_c5 != sk_c6,
inference(copy,[status(thm)],[c_15007]) ).
cnf(c_15008,plain,
( multiply(sk_c2,sk_c6) = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_14903,c_14893]) ).
cnf(c_15009,plain,
( sk_c2 = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_14904,c_15008]) ).
cnf(c_15010,plain,
( sk_c2 = sk_c6
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_15009]) ).
cnf(c_14947,plain,
sk_c2 = sk_c6,
inference(resolve,[status(thm)],[c_14944,c_15010]) ).
cnf(c_15011,plain,
( multiply(sk_c2,multiply(sk_c5,inverse(sk_c6))) = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_14904,c_14867]) ).
cnf(c_15012,plain,
( multiply(sk_c6,multiply(sk_c5,inverse(sk_c6))) = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_14947,c_15011]) ).
cnf(c_15013,plain,
( multiply(sk_c6,multiply(sk_c5,sk_c6)) = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_14903,c_15012]) ).
cnf(c_15014,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_14904,c_15013]) ).
cnf(c_15015,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_14909,c_15014]) ).
cnf(c_15016,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_15015]) ).
cnf(c_14948,plain,
$false,
inference(resolve,[status(thm)],[c_14944,c_15016]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP347-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.43 % Computer : n011.cluster.edu
% 0.18/5.43 % Model : x86_64 x86_64
% 0.18/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.43 % Memory : 8046.5625MB
% 0.18/5.43 % OS : Linux 6.8.0-71-generic
% 0.18/5.43 % CPULimit : 300
% 0.18/5.43 % WCLimit : 300
% 0.18/5.43 % DateTime : Fri Sep 25 14:47:34 UTC 2026
% 0.18/5.43 % CPUTime :
% 0.18/5.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.43 % Process 2265511 was started by sandbox2 on n011,
% 0.18/5.43 % Fri Sep 25 14:47:34 2026
% 0.18/5.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.44
% 0.18/5.44 % From the command line: assign(max_seconds, 300).
% 112.47/20.56
% 112.47/20.56 % given #500 (F,wt=41): 12324 multiply(sk_c6,sk_c7) != sk_c5 | sk_c7 != A | multiply(inverse(A),sk_c6) != sk_c7 | identity != sk_c6 | sk_c5 != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | inverse(sk_c6) != sk_c5 | sk_c6 != A | multiply(B,sk_c7) != sk_c5 | inverse(B) != sk_c7. [para(1077(a,1),683(b,1)),rewrite([1077(29)]),flip(b),flip(h)].
% 112.47/20.56
% 112.47/20.56 % SZS status Unsatisfiable for theBenchmark
% 112.47/20.56
% 112.47/20.56 % Proof 1 at 13.09 (+ 1.91) seconds.
% 112.47/20.56 % Length of proof is 89.
% 112.47/20.56 % Level of proof is 21.
% 112.47/20.56 % Maximum clause weight is 50.000.
% 112.47/20.56 % Given clauses 531.
% 112.47/20.56
% 112.47/20.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------