%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP363-1 : 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 : n014.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 07:28:43 AM UTC 2026
% Result : Unsatisfiable 132.32s 18.11s
% Output : CNFRefutation 132.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 19
% Syntax : Number of formulae : 198 ( 29 unt; 0 def)
% Number of atoms : 555 ( 554 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 588 ( 231 ~; 357 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 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 : 97 ( 14 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_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_7,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_16,axiom,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_22,axiom,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != VAR_2
| multiply(sk_c7,VAR_2) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(VAR_0) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
cnf(c_5196,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_5197,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_5196]) ).
cnf(c_32,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_5197]) ).
cnf(c_5198,plain,
( multiply(multiply(A,sk_c6),sk_c5) = multiply(A,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_34,plain,
( multiply(A,multiply(sk_c6,sk_c5)) = multiply(A,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3,c_5198]) ).
cnf(c_49,plain,
( multiply(sk_c6,sk_c2) = identity
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_54,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_76,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_97,plain,
( inverse(identity) != sk_c7
| sk_c7 != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_190,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_32]) ).
cnf(c_198,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_10,c_32]) ).
cnf(c_201,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c4
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_13,c_32]) ).
cnf(c_209,plain,
( multiply(inverse(sk_c1),sk_c5) = sk_c6
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_21,c_32]) ).
cnf(c_213,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_25,c_32]) ).
cnf(c_216,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_32,c_32]) ).
cnf(c_217,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_216,c_190]) ).
cnf(c_262,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_217,c_2]) ).
cnf(c_314,plain,
( identity != sk_c7
| sk_c7 != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_262,c_97]) ).
cnf(c_5199,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_49,c_32]) ).
cnf(c_319,plain,
( inverse(sk_c6) = sk_c2
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_217,c_5199]) ).
cnf(c_320,plain,
( multiply(sk_c2,sk_c6) = identity
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_319,c_2]) ).
cnf(c_5200,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_54,c_32]) ).
cnf(c_327,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_217,c_5200]) ).
cnf(c_5201,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_76,c_32]) ).
cnf(c_368,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_217,c_5201]) ).
cnf(c_375,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_368,c_2]) ).
cnf(c_5202,plain,
( identity = sk_c7
| inverse(sk_c6) = sk_c5
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_320,c_11]) ).
cnf(c_382,plain,
( identity = sk_c7
| inverse(sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_5202]) ).
cnf(c_388,plain,
( multiply(sk_c5,sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_382,c_2]) ).
cnf(c_402,plain,
( multiply(inverse(sk_c7),multiply(sk_c6,sk_c5)) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_34]) ).
cnf(c_5203,plain,
( multiply(inverse(sk_c5),identity) = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_388,c_32]) ).
cnf(c_426,plain,
( inverse(sk_c5) = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_217,c_5203]) ).
cnf(c_434,plain,
( multiply(sk_c6,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_426,c_2]) ).
cnf(c_5204,plain,
( inverse(sk_c2) = sk_c6
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_434,c_6]) ).
cnf(c_441,plain,
( inverse(sk_c2) = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_5204]) ).
cnf(c_449,plain,
( multiply(sk_c6,sk_c2) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_441,c_2]) ).
cnf(c_5205,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_449,c_32]) ).
cnf(c_548,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_217,c_5205]) ).
cnf(c_550,plain,
( multiply(sk_c2,sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_548,c_2]) ).
cnf(c_5206,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_550,c_5]) ).
cnf(c_725,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_5206]) ).
cnf(c_5207,plain,
( sk_c7 = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_725,c_434]) ).
cnf(c_5208,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_5207]) ).
cnf(c_5209,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_5208]) ).
cnf(c_993,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_5209]) ).
cnf(c_1226,plain,
( multiply(inverse(sk_c7),multiply(sk_c6,sk_c5)) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_993,c_402]) ).
cnf(c_1229,plain,
( multiply(sk_c6,sk_c1) = sk_c7
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_993,c_375]) ).
cnf(c_5210,plain,
( sk_c7 != sk_c7
| sk_c7 != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_993,c_314]) ).
cnf(c_1243,plain,
( sk_c7 != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_5210]) ).
cnf(c_5211,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_993,c_262]) ).
cnf(c_1264,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_993,c_5211]) ).
cnf(c_1265,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_993,c_217]) ).
cnf(c_1276,plain,
multiply(inverse(A),A) = sk_c7,
inference(paramod,[status(thm)],[c_993,c_2]) ).
cnf(c_1277,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_993,c_1]) ).
cnf(c_5212,plain,
( multiply(sk_c6,sk_c1) = sk_c7
| sk_c7 = sk_c3 ),
inference(paramod,[status(thm)],[c_1264,c_1229]) ).
cnf(c_1295,plain,
( multiply(sk_c6,sk_c1) = sk_c7
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_5212]) ).
cnf(c_5213,plain,
( multiply(inverse(sk_c7),multiply(sk_c6,sk_c5)) = sk_c7
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1265,c_1226]) ).
cnf(c_5214,plain,
( multiply(sk_c7,multiply(sk_c6,sk_c5)) = sk_c7
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1264,c_5213]) ).
cnf(c_5215,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1277,c_5214]) ).
cnf(c_1296,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_5215]) ).
cnf(c_5216,plain,
( sk_c7 = sk_c3
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_1264,c_327]) ).
cnf(c_1313,plain,
( sk_c3 = sk_c7
| inverse(sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_5216]) ).
cnf(c_5217,plain,
( multiply(sk_c7,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_1264,c_213]) ).
cnf(c_5218,plain,
( sk_c6 = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_1277,c_5217]) ).
cnf(c_1315,plain,
( sk_c4 = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_5218]) ).
cnf(c_5219,plain,
( multiply(sk_c7,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_1264,c_201]) ).
cnf(c_5220,plain,
( sk_c6 = sk_c4
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_1277,c_5219]) ).
cnf(c_1316,plain,
( sk_c4 = sk_c6
| inverse(sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_5220]) ).
cnf(c_5221,plain,
( sk_c7 != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| sk_c6 != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1265,c_1243]) ).
cnf(c_5222,plain,
( sk_c7 != C
| C != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| sk_c6 != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1277,c_5221]) ).
cnf(c_5223,plain,
( sk_c7 != C
| C != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| sk_c5 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_5222]) ).
cnf(c_1318,plain,
( sk_c7 != C
| sk_c6 != C
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| sk_c5 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_5223]) ).
cnf(c_5224,plain,
( sk_c3 = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_1265,c_26]) ).
cnf(c_1498,plain,
( sk_c4 = sk_c3
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_5224]) ).
cnf(c_5225,plain,
( sk_c3 = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_1265,c_20]) ).
cnf(c_1500,plain,
( sk_c4 = sk_c3
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_5225]) ).
cnf(c_5226,plain,
( sk_c3 = sk_c4
| inverse(sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_1265,c_14]) ).
cnf(c_1502,plain,
( sk_c4 = sk_c3
| inverse(sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_5226]) ).
cnf(c_1546,plain,
( sk_c4 = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_1277,c_19]) ).
cnf(c_5227,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c1
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_1295,c_32]) ).
cnf(c_1839,plain,
( inverse(sk_c6) = sk_c1
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_1265,c_5227]) ).
cnf(c_5228,plain,
( sk_c3 = sk_c7
| sk_c1 = sk_c5
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_1839,c_1313]) ).
cnf(c_1844,plain,
( sk_c1 = sk_c5
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_5228]) ).
cnf(c_5229,plain,
multiply(inverse(inverse(A)),sk_c7) = A,
inference(paramod,[status(thm)],[c_1276,c_32]) ).
cnf(c_2991,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_1265,c_5229]) ).
cnf(c_2995,plain,
( multiply(sk_c6,sk_c1) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_1315,c_1276]) ).
cnf(c_2998,plain,
( multiply(sk_c6,sk_c1) = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_1498,c_1276]) ).
cnf(c_5230,plain,
( sk_c7 != B
| sk_c6 != B
| inverse(inverse(sk_c6)) != sk_c6
| sk_c7 != sk_c7
| sk_c5 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1276,c_1318]) ).
cnf(c_5231,plain,
( sk_c7 != B
| sk_c6 != B
| sk_c6 != sk_c6
| sk_c7 != sk_c7
| sk_c5 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_2991,c_5230]) ).
cnf(c_5232,plain,
( sk_c7 != B
| sk_c6 != B
| sk_c6 != sk_c6
| sk_c5 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_5231]) ).
cnf(c_3008,plain,
( sk_c7 != B
| sk_c6 != B
| sk_c5 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_5232]) ).
cnf(c_5233,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c1
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_2995,c_32]) ).
cnf(c_3392,plain,
( inverse(sk_c6) = sk_c1
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_1265,c_5233]) ).
cnf(c_5234,plain,
( sk_c4 = sk_c6
| sk_c1 = sk_c5
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_3392,c_1316]) ).
cnf(c_3397,plain,
( sk_c1 = sk_c5
| sk_c4 = sk_c6 ),
inference(copy,[status(thm)],[c_5234]) ).
cnf(c_3398,plain,
( multiply(sk_c1,sk_c6) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_3392,c_1276]) ).
cnf(c_3449,plain,
( sk_c7 != C
| sk_c6 != C
| sk_c5 != sk_c6
| inverse(multiply(A,B)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_3008]) ).
cnf(c_5235,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c1
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_2998,c_32]) ).
cnf(c_3530,plain,
( inverse(sk_c6) = sk_c1
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_1265,c_5235]) ).
cnf(c_5236,plain,
( sk_c4 = sk_c3
| sk_c1 = sk_c5
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3530,c_1502]) ).
cnf(c_3536,plain,
( sk_c1 = sk_c5
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_5236]) ).
cnf(c_3537,plain,
( multiply(sk_c1,sk_c6) = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3530,c_1276]) ).
cnf(c_5237,plain,
( sk_c1 = sk_c5
| sk_c4 = sk_c7
| sk_c1 = sk_c5 ),
inference(paramod,[status(thm)],[c_1844,c_3536]) ).
cnf(c_3539,plain,
( sk_c4 = sk_c7
| sk_c1 = sk_c5 ),
inference(copy,[status(thm)],[c_5237]) ).
cnf(c_5238,plain,
( sk_c1 = sk_c5
| sk_c7 = sk_c6
| sk_c1 = sk_c5 ),
inference(paramod,[status(thm)],[c_3539,c_3397]) ).
cnf(c_3543,plain,
( sk_c7 = sk_c6
| sk_c1 = sk_c5 ),
inference(copy,[status(thm)],[c_5238]) ).
cnf(c_5239,plain,
( multiply(inverse(sk_c5),sk_c5) = sk_c6
| inverse(sk_c3) = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3543,c_209]) ).
cnf(c_5240,plain,
( sk_c7 = sk_c6
| inverse(sk_c3) = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1276,c_5239]) ).
cnf(c_3809,plain,
( inverse(sk_c3) = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_5240]) ).
cnf(c_5241,plain,
( multiply(sk_c7,sk_c3) = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3809,c_1276]) ).
cnf(c_3921,plain,
( sk_c3 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1277,c_5241]) ).
cnf(c_5242,plain,
( sk_c4 = sk_c6
| sk_c7 = sk_c5
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_3398,c_1546]) ).
cnf(c_5243,plain,
( sk_c4 = sk_c6
| sk_c5 = sk_c7
| sk_c4 = sk_c6 ),
inference(copy,[status(thm)],[c_5242]) ).
cnf(c_3957,plain,
( sk_c5 = sk_c7
| sk_c4 = sk_c6 ),
inference(copy,[status(thm)],[c_5243]) ).
cnf(c_5244,plain,
( sk_c7 != B
| sk_c6 != B
| sk_c5 != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| multiply(A,sk_c7) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1276,c_3449]) ).
cnf(c_5245,plain,
( sk_c7 != B
| sk_c6 != B
| sk_c5 != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| A != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1265,c_5244]) ).
cnf(c_4045,plain,
( sk_c7 != B
| sk_c6 != B
| sk_c5 != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| sk_c5 != A
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_5245]) ).
cnf(c_5246,plain,
( sk_c4 = sk_c3
| sk_c7 = sk_c5
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3537,c_1500]) ).
cnf(c_5247,plain,
( sk_c4 = sk_c3
| sk_c5 = sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_5246]) ).
cnf(c_4207,plain,
( sk_c5 = sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_5247]) ).
cnf(c_5248,plain,
( sk_c5 = sk_c7
| sk_c3 = sk_c6
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4207,c_3957]) ).
cnf(c_4219,plain,
( sk_c3 = sk_c6
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_5248]) ).
cnf(c_5249,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4219,c_3921]) ).
cnf(c_5250,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_5249]) ).
cnf(c_4238,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_5250]) ).
cnf(c_5251,plain,
( multiply(sk_c6,sk_c7) = sk_c7
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_4238,c_1296]) ).
cnf(c_5252,plain,
( sk_c6 = sk_c7
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1265,c_5251]) ).
cnf(c_5253,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_5252]) ).
cnf(c_4245,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_5253]) ).
cnf(c_5254,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_4245,c_4238]) ).
cnf(c_5255,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_5254]) ).
cnf(c_5256,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_5255]) ).
cnf(c_4496,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_5256]) ).
cnf(c_5257,plain,
( sk_c7 != B
| sk_c6 != B
| sk_c5 != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| sk_c5 != A
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6 ),
inference(paramod,[status(thm)],[c_4496,c_4045]) ).
cnf(c_5258,plain,
( sk_c6 != B
| sk_c6 != B
| sk_c5 != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| sk_c5 != A
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6 ),
inference(paramod,[status(thm)],[c_4496,c_5257]) ).
cnf(c_4709,plain,
( sk_c6 != B
| sk_c5 != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| sk_c5 != A
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6 ),
inference(copy,[status(thm)],[c_5258]) ).
cnf(c_5158,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_4496,c_1277]) ).
cnf(c_5162,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_4496,c_1265]) ).
cnf(c_5259,plain,
inverse(sk_c6) = sk_c7,
inference(paramod,[status(thm)],[c_4496,c_1264]) ).
cnf(c_5163,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_4496,c_5259]) ).
cnf(c_5260,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_5163,c_198]) ).
cnf(c_5261,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_5163,c_5260]) ).
cnf(c_5262,plain,
( sk_c5 = sk_c7
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_5158,c_5261]) ).
cnf(c_5263,plain,
( sk_c5 = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_4496,c_5262]) ).
cnf(c_5264,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_5263]) ).
cnf(c_5175,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_5264]) ).
cnf(c_5265,plain,
( sk_c6 != A
| inverse(multiply(sk_c6,inverse(sk_c6))) != sk_c6
| sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6 ),
inference(factor,[status(thm)],[c_4709]) ).
cnf(c_5266,plain,
( sk_c6 != A
| inverse(multiply(sk_c6,inverse(sk_c6))) != sk_c6
| sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_5175,c_5265]) ).
cnf(c_5267,plain,
( sk_c6 != A
| inverse(multiply(sk_c6,inverse(sk_c6))) != sk_c6
| sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_5162,c_5266]) ).
cnf(c_5268,plain,
( sk_c6 != A
| inverse(multiply(sk_c6,inverse(sk_c6))) != sk_c6
| sk_c5 != sk_c6
| sk_c6 != sk_c5
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_5163,c_5267]) ).
cnf(c_5269,plain,
( sk_c6 != A
| inverse(multiply(sk_c6,inverse(sk_c6))) != sk_c6
| sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_5175,c_5268]) ).
cnf(c_5270,plain,
( sk_c6 != A
| inverse(multiply(sk_c6,inverse(sk_c6))) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_5175,c_5269]) ).
cnf(c_5271,plain,
( sk_c6 != A
| inverse(multiply(sk_c6,sk_c6)) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_5163,c_5270]) ).
cnf(c_5272,plain,
( sk_c6 != A
| inverse(sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_5162,c_5271]) ).
cnf(c_5273,plain,
( sk_c6 != A
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_5163,c_5272]) ).
cnf(c_5274,plain,
( sk_c6 != A
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_5273]) ).
cnf(c_5275,plain,
( sk_c6 != A
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_5274]) ).
cnf(c_5276,plain,
( sk_c6 != A
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_5275]) ).
cnf(c_5277,plain,
sk_c6 != A,
inference(copy,[status(thm)],[c_5276]) ).
cnf(c_5195,plain,
$false,
inference(copy,[status(thm)],[c_5277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP363-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:48:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 479697 was started by sandbox on n014,
% 0.08/0.36 % Fri Sep 25 14:48:20 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 132.32/18.11
% 132.32/18.11 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 132.32/18.11
% 132.32/18.11 % SZS status Unsatisfiable for theBenchmark
% 132.32/18.11
% 132.32/18.11 % Proof 1 at 1.41 (+ 0.24) seconds.
% 132.32/18.11 % Length of proof is 97.
% 132.32/18.11 % Level of proof is 30.
% 132.32/18.11 % Maximum clause weight is 56.000.
% 132.32/18.11 % Given clauses 246.
% 132.32/18.11
% 132.32/18.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------