%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP278-1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:32 AM UTC 2026
% Result : Unsatisfiable 182.33s 28.60s
% Output : CNFRefutation 182.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 18
% Syntax : Number of formulae : 204 ( 34 unt; 0 def)
% Number of atoms : 490 ( 489 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 422 ( 136 ~; 286 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 8 !; 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_c5,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c4) = sk_c5 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c4) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c3) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c3) = sk_c5
| inverse(sk_c4) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c4) = sk_c5 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c4) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c4) = sk_c5 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_21,axiom,
! [VAR_0,VAR_1,VAR_2] :
( multiply(VAR_2,sk_c4) != sk_c5
| inverse(VAR_2) != sk_c5
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| inverse(VAR_0) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c5 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(C,sk_c4) != sk_c5
| inverse(C) != sk_c5
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
cnf(c_25,plain,
( multiply(B,sk_c4) != sk_c5
| inverse(B) != sk_c5
| multiply(A,sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_29,plain,
( inverse(sk_c6) != sk_c5
| multiply(A,sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_24171,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_24172,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_24171]) ).
cnf(c_30,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_24172]) ).
cnf(c_24173,plain,
( multiply(multiply(A,sk_c1),sk_c6) = multiply(A,sk_c5)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_32,plain,
( multiply(A,multiply(sk_c1,sk_c6)) = multiply(A,sk_c5)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_3,c_24173]) ).
cnf(c_33,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_36,plain,
( multiply(sk_c5,sk_c3) = identity
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_40,plain,
( multiply(sk_c6,sk_c2) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_41,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_42,plain,
( multiply(sk_c5,sk_c3) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_43,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_48,plain,
( multiply(sk_c5,sk_c4) = identity
| multiply(sk_c3,sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_154,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_30]) ).
cnf(c_158,plain,
( multiply(inverse(sk_c2),sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_6,c_30]) ).
cnf(c_160,plain,
( multiply(inverse(sk_c3),sk_c5) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_8,c_30]) ).
cnf(c_171,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_19,c_30]) ).
cnf(c_176,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_30,c_30]) ).
cnf(c_177,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_176,c_154]) ).
cnf(c_178,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_177,c_2]) ).
cnf(c_276,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_176,c_2]) ).
cnf(c_291,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_176,c_30]) ).
cnf(c_24174,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_176,c_177]) ).
cnf(c_24175,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_177,c_24174]) ).
cnf(c_292,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_24175]) ).
cnf(c_24176,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| multiply(inverse(sk_c6),sk_c6) != sk_c5 ),
inference(resolve,[status(thm)],[c_292,c_29]) ).
cnf(c_298,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| identity != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_24176]) ).
cnf(c_312,plain,
( inverse(sk_c6) = sk_c2
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_292]) ).
cnf(c_314,plain,
( inverse(sk_c5) = sk_c3
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_12,c_292]) ).
cnf(c_319,plain,
( inverse(sk_c5) = sk_c3
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_17,c_292]) ).
cnf(c_24177,plain,
identity = multiply(A,multiply(B,inverse(multiply(A,B)))),
inference(paramod,[status(thm)],[c_276,c_3]) ).
cnf(c_372,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(copy,[status(thm)],[c_24177]) ).
cnf(c_375,plain,
( multiply(sk_c1,sk_c6) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_9,c_276]) ).
cnf(c_387,plain,
( multiply(sk_c1,sk_c6) = identity
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_40,c_276]) ).
cnf(c_388,plain,
( multiply(sk_c1,sk_c6) = identity
| multiply(sk_c5,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_42,c_276]) ).
cnf(c_423,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_312,c_2]) ).
cnf(c_441,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c5) = sk_c3 ),
inference(paramod,[status(thm)],[c_314,c_2]) ).
cnf(c_593,plain,
( inverse(sk_c5) = sk_c4
| inverse(sk_c5) = sk_c3 ),
inference(paramod,[status(thm)],[c_319,c_292]) ).
cnf(c_727,plain,
( multiply(sk_c5,multiply(sk_c3,A)) = A
| inverse(sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_593,c_291]) ).
cnf(c_1812,plain,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_423,c_292]) ).
cnf(c_1847,plain,
( multiply(inverse(sk_c2),sk_c6) = sk_c5
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_41,c_30]) ).
cnf(c_2124,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_441,c_292]) ).
cnf(c_2277,plain,
( multiply(inverse(sk_c3),sk_c5) = sk_c4
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_43,c_30]) ).
cnf(c_24178,plain,
multiply(inverse(A),identity) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_372,c_30]) ).
cnf(c_24179,plain,
inverse(A) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_177,c_24178]) ).
cnf(c_4055,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(copy,[status(thm)],[c_24179]) ).
cnf(c_24180,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_4055,c_30]) ).
cnf(c_4080,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_24180]) ).
cnf(c_24181,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| identity = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_375,c_4]) ).
cnf(c_4112,plain,
( identity = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_24181]) ).
cnf(c_24182,plain,
( multiply(A,identity) = multiply(A,sk_c5)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_375,c_32]) ).
cnf(c_24183,plain,
( A = multiply(A,sk_c5)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_177,c_24182]) ).
cnf(c_24184,plain,
( multiply(A,sk_c5) = A
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_24183]) ).
cnf(c_4113,plain,
( multiply(A,sk_c5) = A
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_24184]) ).
cnf(c_4116,plain,
( multiply(inverse(sk_c5),sk_c4) = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4112,c_30]) ).
cnf(c_24185,plain,
( multiply(sk_c6,sk_c2) = identity
| identity = sk_c5
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_387,c_33]) ).
cnf(c_4183,plain,
( identity = sk_c5
| multiply(sk_c6,sk_c2) = identity ),
inference(copy,[status(thm)],[c_24185]) ).
cnf(c_24186,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4183,c_30]) ).
cnf(c_4195,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_177,c_24186]) ).
cnf(c_24187,plain,
( multiply(sk_c5,sk_c3) = identity
| identity = sk_c5
| multiply(sk_c5,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_388,c_36]) ).
cnf(c_4330,plain,
( identity = sk_c5
| multiply(sk_c5,sk_c3) = identity ),
inference(copy,[status(thm)],[c_24187]) ).
cnf(c_24188,plain,
( multiply(inverse(sk_c5),identity) = sk_c3
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4330,c_30]) ).
cnf(c_4333,plain,
( inverse(sk_c5) = sk_c3
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_177,c_24188]) ).
cnf(c_4350,plain,
( multiply(sk_c3,multiply(sk_c5,A)) = A
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4333,c_30]) ).
cnf(c_24189,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),inverse(inverse(sk_c5)))
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4116,c_4080]) ).
cnf(c_24190,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),sk_c5)
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_292,c_24189]) ).
cnf(c_4956,plain,
( multiply(inverse(sk_c4),sk_c5) = inverse(sk_c6)
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24190]) ).
cnf(c_24191,plain,
( multiply(inverse(sk_c4),sk_c5) = sk_c2
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4195,c_4956]) ).
cnf(c_6275,plain,
( multiply(inverse(sk_c4),sk_c5) = sk_c2
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24191]) ).
cnf(c_24192,plain,
( inverse(sk_c2) = multiply(inverse(sk_c5),inverse(inverse(sk_c4)))
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_6275,c_4080]) ).
cnf(c_6318,plain,
( inverse(sk_c2) = multiply(inverse(sk_c5),sk_c4)
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_292,c_24192]) ).
cnf(c_24193,plain,
( inverse(sk_c2) = multiply(sk_c3,sk_c4)
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4333,c_6318]) ).
cnf(c_8243,plain,
( inverse(sk_c2) = multiply(sk_c3,sk_c4)
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24193]) ).
cnf(c_24194,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_5,c_158]) ).
cnf(c_9084,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_24194]) ).
cnf(c_24195,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_7,c_160]) ).
cnf(c_9206,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_24195]) ).
cnf(c_24196,plain,
( sk_c4 = inverse(sk_c6)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_171,c_4113]) ).
cnf(c_24197,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_24196]) ).
cnf(c_9707,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_24197]) ).
cnf(c_9790,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_9707,c_292]) ).
cnf(c_24198,plain,
( multiply(sk_c5,sk_c6) = sk_c4
| sk_c6 = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_9790,c_14]) ).
cnf(c_9817,plain,
( sk_c6 = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_24198]) ).
cnf(c_9822,plain,
( multiply(inverse(sk_c5),sk_c4) = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_9817,c_30]) ).
cnf(c_24199,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),inverse(inverse(sk_c5)))
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_9822,c_4080]) ).
cnf(c_24200,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),sk_c5)
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_292,c_24199]) ).
cnf(c_10060,plain,
( multiply(inverse(sk_c4),sk_c5) = inverse(sk_c6)
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_24200]) ).
cnf(c_24201,plain,
( multiply(inverse(inverse(sk_c4)),inverse(sk_c6)) = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_10060,c_30]) ).
cnf(c_10246,plain,
( multiply(sk_c4,inverse(sk_c6)) = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_292,c_24201]) ).
cnf(c_24202,plain,
( inverse(sk_c5) = multiply(inverse(inverse(sk_c6)),inverse(sk_c4))
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_10246,c_4080]) ).
cnf(c_24203,plain,
( inverse(sk_c5) = multiply(sk_c6,inverse(sk_c4))
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_292,c_24202]) ).
cnf(c_10371,plain,
( multiply(sk_c6,inverse(sk_c4)) = inverse(sk_c5)
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_24203]) ).
cnf(c_12238,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| inverse(sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_48,c_727]) ).
cnf(c_24204,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c6,sk_c1) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_1812,c_1847]) ).
cnf(c_12435,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_24204]) ).
cnf(c_24205,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_12435,c_30]) ).
cnf(c_12445,plain,
( inverse(sk_c6) = sk_c1
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_177,c_24205]) ).
cnf(c_12518,plain,
( multiply(sk_c1,sk_c6) = identity
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_12445,c_2]) ).
cnf(c_24206,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| identity = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_12518,c_9084]) ).
cnf(c_12593,plain,
( identity = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_24206]) ).
cnf(c_12598,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_12593,c_30]) ).
cnf(c_24207,plain,
( inverse(sk_c6) = multiply(inverse(sk_c5),inverse(inverse(sk_c6)))
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_12598,c_4080]) ).
cnf(c_12670,plain,
( inverse(sk_c6) = multiply(inverse(sk_c5),sk_c6)
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_292,c_24207]) ).
cnf(c_24208,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c2
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_12670,c_4195]) ).
cnf(c_12721,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c2
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24208]) ).
cnf(c_24209,plain,
( inverse(sk_c2) = multiply(inverse(sk_c6),inverse(inverse(sk_c5)))
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_12721,c_4080]) ).
cnf(c_12777,plain,
( inverse(sk_c2) = multiply(inverse(sk_c6),sk_c5)
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_292,c_24209]) ).
cnf(c_24210,plain,
( inverse(sk_c2) = multiply(sk_c2,sk_c5)
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4195,c_12777]) ).
cnf(c_12947,plain,
( inverse(sk_c2) = multiply(sk_c2,sk_c5)
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24210]) ).
cnf(c_24211,plain,
( inverse(multiply(sk_c2,sk_c5)) = sk_c2
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_12947,c_292]) ).
cnf(c_12966,plain,
( multiply(inverse(sk_c5),inverse(sk_c2)) = sk_c2
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4080,c_24211]) ).
cnf(c_24212,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c6,sk_c1) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2124,c_2277]) ).
cnf(c_15636,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_24212]) ).
cnf(c_24213,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_15636,c_30]) ).
cnf(c_15648,plain,
( inverse(sk_c6) = sk_c1
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_177,c_24213]) ).
cnf(c_15665,plain,
( multiply(sk_c1,sk_c6) = identity
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_15648,c_2]) ).
cnf(c_24214,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| identity = sk_c5
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_15665,c_9206]) ).
cnf(c_15751,plain,
( identity = sk_c5
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(copy,[status(thm)],[c_24214]) ).
cnf(c_24215,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15751,c_4350]) ).
cnf(c_15758,plain,
( multiply(sk_c3,sk_c4) = sk_c5
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24215]) ).
cnf(c_24216,plain,
( inverse(sk_c2) = sk_c5
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15758,c_8243]) ).
cnf(c_15776,plain,
( inverse(sk_c2) = sk_c5
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24216]) ).
cnf(c_24217,plain,
( multiply(inverse(sk_c5),sk_c5) = sk_c2
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15776,c_12966]) ).
cnf(c_24218,plain,
( identity = sk_c2
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_24217]) ).
cnf(c_15830,plain,
( identity = sk_c2
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24218]) ).
cnf(c_15839,plain,
( inverse(sk_c2) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15830,c_178]) ).
cnf(c_24219,plain,
( identity = sk_c5
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15839,c_15776]) ).
cnf(c_24220,plain,
( identity = sk_c5
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_24219]) ).
cnf(c_16134,plain,
identity = sk_c5,
inference(copy,[status(thm)],[c_24220]) ).
cnf(c_17406,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| inverse(sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_16134,c_12238]) ).
cnf(c_24221,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_16134,c_298]) ).
cnf(c_23505,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c4) != sk_c5 ),
inference(copy,[status(thm)],[c_24221]) ).
cnf(c_24222,plain,
inverse(sk_c5) = identity,
inference(paramod,[status(thm)],[c_16134,c_178]) ).
cnf(c_23546,plain,
inverse(sk_c5) = sk_c5,
inference(paramod,[status(thm)],[c_16134,c_24222]) ).
cnf(c_23547,plain,
multiply(A,sk_c5) = A,
inference(paramod,[status(thm)],[c_16134,c_177]) ).
cnf(c_23559,plain,
multiply(sk_c5,A) = A,
inference(paramod,[status(thm)],[c_16134,c_1]) ).
cnf(c_24223,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| inverse(sk_c5) = sk_c4
| sk_c4 = sk_c5 ),
inference(paramod,[status(thm)],[c_23559,c_17406]) ).
cnf(c_24224,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| sk_c5 = sk_c4
| sk_c4 = sk_c5 ),
inference(paramod,[status(thm)],[c_23546,c_24223]) ).
cnf(c_24225,plain,
( sk_c5 = sk_c4
| sk_c5 = sk_c4
| sk_c4 = sk_c5 ),
inference(paramod,[status(thm)],[c_23547,c_24224]) ).
cnf(c_24226,plain,
( sk_c5 = sk_c4
| sk_c4 = sk_c5
| sk_c4 = sk_c5 ),
inference(copy,[status(thm)],[c_24225]) ).
cnf(c_24227,plain,
( sk_c4 = sk_c5
| sk_c4 = sk_c5
| sk_c4 = sk_c5 ),
inference(copy,[status(thm)],[c_24226]) ).
cnf(c_24228,plain,
( sk_c4 = sk_c5
| sk_c4 = sk_c5 ),
inference(copy,[status(thm)],[c_24227]) ).
cnf(c_24060,plain,
sk_c4 = sk_c5,
inference(copy,[status(thm)],[c_24228]) ).
cnf(c_24229,plain,
( multiply(sk_c6,inverse(sk_c5)) = inverse(sk_c5)
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_24060,c_10371]) ).
cnf(c_24230,plain,
( multiply(sk_c6,sk_c5) = inverse(sk_c5)
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_23546,c_24229]) ).
cnf(c_24231,plain,
( sk_c6 = inverse(sk_c5)
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_23547,c_24230]) ).
cnf(c_24232,plain,
( sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_23546,c_24231]) ).
cnf(c_24152,plain,
sk_c6 = sk_c5,
inference(copy,[status(thm)],[c_24232]) ).
cnf(c_24233,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| inverse(sk_c5) != sk_c5 ),
inference(paramod,[status(thm)],[c_24060,c_23505]) ).
cnf(c_24234,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c6,sk_c4) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_23546,c_24233]) ).
cnf(c_24235,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_24152,c_24234]) ).
cnf(c_24236,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| multiply(sk_c5,sk_c5) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_24060,c_24235]) ).
cnf(c_24237,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_23547,c_24236]) ).
cnf(c_24238,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c5,sk_c5) != sk_c4
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_24152,c_24237]) ).
cnf(c_24239,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| sk_c5 != sk_c4
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_23547,c_24238]) ).
cnf(c_24240,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c6),sk_c5) != sk_c6
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_24060,c_24239]) ).
cnf(c_24241,plain,
( inverse(sk_c6) != sk_c5
| multiply(inverse(sk_c5),sk_c5) != sk_c6
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_24152,c_24240]) ).
cnf(c_24242,plain,
( inverse(sk_c6) != sk_c5
| multiply(sk_c5,sk_c5) != sk_c6
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_23546,c_24241]) ).
cnf(c_24243,plain,
( inverse(sk_c6) != sk_c5
| sk_c5 != sk_c6
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_23547,c_24242]) ).
cnf(c_24244,plain,
( inverse(sk_c6) != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_24152,c_24243]) ).
cnf(c_24245,plain,
( inverse(sk_c5) != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_24152,c_24244]) ).
cnf(c_24246,plain,
( sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_23546,c_24245]) ).
cnf(c_24247,plain,
( sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(copy,[status(thm)],[c_24246]) ).
cnf(c_24248,plain,
( sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(copy,[status(thm)],[c_24247]) ).
cnf(c_24249,plain,
( sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(copy,[status(thm)],[c_24248]) ).
cnf(c_24250,plain,
sk_c5 != sk_c5,
inference(copy,[status(thm)],[c_24249]) ).
cnf(c_24170,plain,
$false,
inference(copy,[status(thm)],[c_24250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP278-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n009.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Fri Sep 25 14:43:19 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 1850591 was started by sandbox2 on n009,
% 0.18/5.45 % Fri Sep 25 14:43:19 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 182.33/28.60
% 182.33/28.60 % given #500 (F,wt=39): 6072 identity != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c6,sk_c4) != sk_c5 | multiply(sk_c5,sk_c6) != sk_c4 | multiply(A,multiply(B,C)) != sk_c6 | multiply(inverse(C),multiply(inverse(B),multiply(inverse(A),sk_c5))) != sk_c6 | sk_c4 != sk_c5. [para(3(a,1),4814(e,1)),rewrite([4080(24),3(27)])].
% 182.33/28.60
% 182.33/28.60 % SZS status Unsatisfiable for theBenchmark
% 182.33/28.60
% 182.33/28.60 % Proof 1 at 19.06 (+ 3.94) seconds.
% 182.33/28.60 % Length of proof is 106.
% 182.33/28.60 % Level of proof is 24.
% 182.33/28.60 % Maximum clause weight is 41.000.
% 182.33/28.60 % Given clauses 818.
% 182.33/28.60
% 182.33/28.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------