%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP234-1 : 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 : n019.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 07:28:25 AM UTC 2026
% Result : Unsatisfiable 15.58s 2.43s
% Output : CNFRefutation 15.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 19
% Syntax : Number of formulae : 294 ( 29 unt; 0 def)
% Number of atoms : 728 ( 727 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 641 ( 207 ~; 434 |; 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 122 ( 1 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,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c7
| multiply(VAR_4,sk_c7) != VAR_3
| multiply(sk_c7,VAR_3) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_2) != sk_c7
| inverse(VAR_1) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c6
| multiply(VAR_0,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(E) != sk_c7
| multiply(E,sk_c7) != D
| multiply(sk_c7,D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
cnf(c_25,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_30,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c7
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_32,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_37,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_42,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_37]) ).
cnf(c_9173,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_9174,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_9173]) ).
cnf(c_43,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_9174]) ).
cnf(c_45,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_9175,plain,
( multiply(sk_c7,A) = multiply(sk_c3,multiply(sk_c6,A))
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_47,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A)
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9175]) ).
cnf(c_9176,plain,
( multiply(multiply(A,sk_c4),sk_c7) = multiply(A,sk_c5)
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_54,plain,
( multiply(A,multiply(sk_c4,sk_c7)) = multiply(A,sk_c5)
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_9176]) ).
cnf(c_56,plain,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_9177,plain,
( multiply(sk_c6,A) = multiply(sk_c2,multiply(sk_c7,A))
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_78,plain,
( multiply(sk_c2,multiply(sk_c7,A)) = multiply(sk_c6,A)
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_9177]) ).
cnf(c_9178,plain,
( multiply(sk_c7,A) = multiply(sk_c3,multiply(sk_c6,A))
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_80,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A)
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9178]) ).
cnf(c_9179,plain,
( multiply(sk_c6,A) = multiply(sk_c7,multiply(sk_c5,A))
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_84,plain,
( multiply(sk_c7,multiply(sk_c5,A)) = multiply(sk_c6,A)
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9179]) ).
cnf(c_93,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_94,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_95,plain,
( multiply(sk_c7,sk_c2) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_9180,plain,
( multiply(sk_c7,A) = multiply(sk_c3,multiply(sk_c6,A))
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_20,c_3]) ).
cnf(c_96,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A)
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_9180]) ).
cnf(c_98,plain,
( multiply(sk_c7,sk_c2) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_104,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_105,plain,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_9181,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_32]) ).
cnf(c_9182,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9181]) ).
cnf(c_9183,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_9182]) ).
cnf(c_122,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_9183]) ).
cnf(c_9184,plain,
( multiply(identity,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_122]) ).
cnf(c_123,plain,
( sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9184]) ).
cnf(c_160,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_42,c_5]) ).
cnf(c_165,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_43]) ).
cnf(c_166,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_43]) ).
cnf(c_169,plain,
( multiply(sk_c6,multiply(sk_c7,A)) = A
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_43]) ).
cnf(c_171,plain,
( multiply(sk_c6,multiply(sk_c7,A)) = A
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_43]) ).
cnf(c_193,plain,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_17,c_43]) ).
cnf(c_207,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_43,c_43]) ).
cnf(c_208,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_207,c_165]) ).
cnf(c_252,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_208,c_2]) ).
cnf(c_9185,plain,
( sk_c7 != identity
| sk_c7 != sk_c6
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_123]) ).
cnf(c_9186,plain,
( sk_c7 != identity
| sk_c7 != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_252,c_9185]) ).
cnf(c_9187,plain,
( sk_c7 != identity
| sk_c6 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_9186]) ).
cnf(c_9188,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_9187]) ).
cnf(c_9189,plain,
( identity != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_9188]) ).
cnf(c_254,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_9189]) ).
cnf(c_9190,plain,
( multiply(multiply(A,sk_c7),sk_c3) = multiply(A,identity)
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_45,c_3]) ).
cnf(c_9191,plain,
( multiply(A,multiply(sk_c7,sk_c3)) = multiply(A,identity)
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_9190]) ).
cnf(c_285,plain,
( multiply(A,multiply(sk_c7,sk_c3)) = A
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9191]) ).
cnf(c_9192,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_45,c_43]) ).
cnf(c_287,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9192]) ).
cnf(c_310,plain,
( inverse(sk_c7) = sk_c3
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(resolve,[status(thm)],[c_254,c_287]) ).
cnf(c_9193,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_56,c_43]) ).
cnf(c_381,plain,
( inverse(sk_c7) = sk_c4
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9193]) ).
cnf(c_390,plain,
( multiply(sk_c4,sk_c7) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_381,c_2]) ).
cnf(c_9194,plain,
( sk_c4 = sk_c3
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_381,c_287]) ).
cnf(c_397,plain,
( sk_c4 = sk_c3
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9194]) ).
cnf(c_403,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| sk_c4 = sk_c3 ),
inference(resolve,[status(thm)],[c_397,c_254]) ).
cnf(c_410,plain,
( multiply(sk_c6,sk_c7) = identity
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_397,c_2]) ).
cnf(c_9195,plain,
( multiply(inverse(sk_c6),identity) = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_410,c_43]) ).
cnf(c_483,plain,
( inverse(sk_c6) = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_208,c_9195]) ).
cnf(c_9196,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_93,c_43]) ).
cnf(c_508,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_9196]) ).
cnf(c_528,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_508,c_2]) ).
cnf(c_9197,plain,
( inverse(sk_c3) = sk_c7
| sk_c2 = sk_c6
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_508,c_4]) ).
cnf(c_529,plain,
( sk_c2 = sk_c6
| inverse(sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_9197]) ).
cnf(c_544,plain,
( multiply(sk_c7,sk_c3) = identity
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_529,c_2]) ).
cnf(c_9198,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_544,c_43]) ).
cnf(c_552,plain,
( inverse(sk_c7) = sk_c3
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9198]) ).
cnf(c_553,plain,
( multiply(sk_c3,sk_c7) = identity
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_552,c_2]) ).
cnf(c_9199,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_94,c_43]) ).
cnf(c_624,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_9199]) ).
cnf(c_629,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_624,c_2]) ).
cnf(c_9200,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c6) = sk_c7
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_552,c_624]) ).
cnf(c_642,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c7) = sk_c3 ),
inference(copy,[status(thm)],[c_9200]) ).
cnf(c_9201,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_104,c_43]) ).
cnf(c_670,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_9201]) ).
cnf(c_696,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_670,c_2]) ).
cnf(c_9202,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_105,c_43]) ).
cnf(c_784,plain,
( inverse(sk_c7) = sk_c4
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_9202]) ).
cnf(c_9203,plain,
( sk_c4 = sk_c3
| inverse(sk_c2) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_784,c_624]) ).
cnf(c_801,plain,
( sk_c4 = sk_c3
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_9203]) ).
cnf(c_9204,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_801,c_22]) ).
cnf(c_813,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_9204]) ).
cnf(c_9205,plain,
( identity = sk_c5
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_390,c_7]) ).
cnf(c_996,plain,
( identity = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9205]) ).
cnf(c_9206,plain,
( multiply(A,identity) = multiply(A,sk_c5)
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_390,c_54]) ).
cnf(c_9207,plain,
( A = multiply(A,sk_c5)
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9206]) ).
cnf(c_9208,plain,
( multiply(A,sk_c5) = A
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9207]) ).
cnf(c_999,plain,
( multiply(A,sk_c5) = A
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9208]) ).
cnf(c_1004,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| identity = sk_c5 ),
inference(resolve,[status(thm)],[c_996,c_254]) ).
cnf(c_9209,plain,
( inverse(sk_c3) = sk_c7
| identity = sk_c6
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_528,c_14]) ).
cnf(c_1336,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_9209]) ).
cnf(c_1348,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1336,c_2]) ).
cnf(c_9210,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1348,c_43]) ).
cnf(c_1360,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9210]) ).
cnf(c_1411,plain,
( inverse(sk_c6) = identity
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_1360,c_252]) ).
cnf(c_9211,plain,
( identity = sk_c7
| inverse(sk_c7) = sk_c3
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_1411,c_642]) ).
cnf(c_1665,plain,
( identity = sk_c7
| inverse(sk_c7) = sk_c3 ),
inference(copy,[status(thm)],[c_9211]) ).
cnf(c_1678,plain,
( multiply(sk_c3,sk_c7) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1665,c_2]) ).
cnf(c_9212,plain,
( multiply(sk_c7,B) = multiply(sk_c3,multiply(sk_c6,B))
| multiply(sk_c2,multiply(sk_c7,A)) = multiply(sk_c6,A) ),
inference(paramod,[status(thm)],[c_78,c_3]) ).
cnf(c_1729,plain,
( multiply(sk_c3,multiply(sk_c6,B)) = multiply(sk_c7,B)
| multiply(sk_c2,multiply(sk_c7,A)) = multiply(sk_c6,A) ),
inference(copy,[status(thm)],[c_9212]) ).
cnf(c_9213,plain,
( multiply(sk_c3,multiply(sk_c6,multiply(sk_c5,A))) = multiply(sk_c6,A)
| multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_84,c_80]) ).
cnf(c_2342,plain,
( multiply(sk_c3,multiply(sk_c6,multiply(sk_c5,A))) = multiply(sk_c6,A)
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9213]) ).
cnf(c_3358,plain,
( multiply(sk_c7,multiply(sk_c2,B)) = B
| multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_96,c_43]) ).
cnf(c_9214,plain,
( inverse(sk_c4) = sk_c7
| identity = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_696,c_18]) ).
cnf(c_3607,plain,
( identity = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_9214]) ).
cnf(c_3654,plain,
( multiply(sk_c7,sk_c4) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3607,c_2]) ).
cnf(c_9215,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3654,c_43]) ).
cnf(c_3677,plain,
( inverse(sk_c7) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9215]) ).
cnf(c_9216,plain,
( sk_c4 = sk_c3
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3677,c_1360]) ).
cnf(c_3747,plain,
( sk_c4 = sk_c3
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_9216]) ).
cnf(c_3769,plain,
( inverse(sk_c6) = identity
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3747,c_252]) ).
cnf(c_9217,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3747,c_403]) ).
cnf(c_9218,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_9217]) ).
cnf(c_3771,plain,
( sk_c6 != sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_9218]) ).
cnf(c_9219,plain,
( identity = sk_c7
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3769,c_483]) ).
cnf(c_3892,plain,
( identity = sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_9219]) ).
cnf(c_9220,plain,
( sk_c4 = sk_c3
| sk_c7 = sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3892,c_3747]) ).
cnf(c_9221,plain,
( sk_c4 = sk_c3
| sk_c6 = sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_9220]) ).
cnf(c_3946,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_9221]) ).
cnf(c_9222,plain,
( sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(resolve,[status(thm)],[c_3946,c_3771]) ).
cnf(c_3947,plain,
sk_c4 = sk_c3,
inference(copy,[status(thm)],[c_9222]) ).
cnf(c_4227,plain,
( multiply(inverse(sk_c2),sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3947,c_193]) ).
cnf(c_9223,plain,
( sk_c5 = identity
| inverse(sk_c2) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_813,c_629]) ).
cnf(c_9224,plain,
( identity = sk_c5
| inverse(sk_c2) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_9223]) ).
cnf(c_4330,plain,
( identity = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_9224]) ).
cnf(c_4339,plain,
( multiply(sk_c7,sk_c2) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4330,c_2]) ).
cnf(c_9225,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4339,c_43]) ).
cnf(c_4349,plain,
( inverse(sk_c7) = sk_c2
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_208,c_9225]) ).
cnf(c_9226,plain,
( identity = sk_c5
| sk_c2 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4349,c_996]) ).
cnf(c_4387,plain,
( sk_c2 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_9226]) ).
cnf(c_4445,plain,
( multiply(A,sk_c5) = A
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_4387,c_208]) ).
cnf(c_9227,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| sk_c6 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_160]) ).
cnf(c_5244,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| sk_c6 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_9227]) ).
cnf(c_5411,plain,
( multiply(inverse(multiply(A,sk_c2)),multiply(A,sk_c6)) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_16,c_166]) ).
cnf(c_9228,plain,
( sk_c7 = sk_c6
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_999,c_6]) ).
cnf(c_9229,plain,
( sk_c6 = sk_c7
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9228]) ).
cnf(c_5549,plain,
( sk_c6 = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9229]) ).
cnf(c_9230,plain,
( multiply(sk_c6,identity) = sk_c2
| multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_95,c_169]) ).
cnf(c_9231,plain,
( sk_c6 = sk_c2
| multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_9230]) ).
cnf(c_9232,plain,
( sk_c2 = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_9231]) ).
cnf(c_5734,plain,
( sk_c2 = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_9232]) ).
cnf(c_9233,plain,
( multiply(sk_c6,identity) = sk_c2
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_98,c_171]) ).
cnf(c_9234,plain,
( sk_c6 = sk_c2
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_9233]) ).
cnf(c_9235,plain,
( sk_c2 = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9234]) ).
cnf(c_5946,plain,
( sk_c2 = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9235]) ).
cnf(c_9236,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_5946,c_4445]) ).
cnf(c_5958,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9236]) ).
cnf(c_9237,plain,
( sk_c2 = sk_c6
| multiply(sk_c3,sk_c7) = sk_c7
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_5958,c_5734]) ).
cnf(c_6000,plain,
( multiply(sk_c3,sk_c7) = sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9237]) ).
cnf(c_9238,plain,
( sk_c7 = identity
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_6000,c_553]) ).
cnf(c_9239,plain,
( identity = sk_c7
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9238]) ).
cnf(c_6010,plain,
( identity = sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9239]) ).
cnf(c_6031,plain,
( inverse(sk_c7) = identity
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_6010,c_252]) ).
cnf(c_9240,plain,
( inverse(sk_c7) = sk_c7
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_6010,c_6031]) ).
cnf(c_6126,plain,
( inverse(sk_c7) = sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9240]) ).
cnf(c_9241,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c6
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_6126,c_254]) ).
cnf(c_9242,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9241]) ).
cnf(c_6394,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9242]) ).
cnf(c_9243,plain,
( sk_c2 = sk_c6
| identity != sk_c7
| sk_c2 = sk_c6 ),
inference(resolve,[status(thm)],[c_6394,c_5958]) ).
cnf(c_6684,plain,
( identity != sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_9243]) ).
cnf(c_9244,plain,
( sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(resolve,[status(thm)],[c_6684,c_6010]) ).
cnf(c_6688,plain,
sk_c2 = sk_c6,
inference(copy,[status(thm)],[c_9244]) ).
cnf(c_9245,plain,
( multiply(inverse(multiply(A,sk_c6)),multiply(A,sk_c6)) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_6688,c_5411]) ).
cnf(c_6802,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_9245]) ).
cnf(c_9246,plain,
( multiply(inverse(sk_c6),sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6688,c_4227]) ).
cnf(c_6925,plain,
( identity = sk_c7
| multiply(sk_c3,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_9246]) ).
cnf(c_7048,plain,
( multiply(sk_c7,multiply(sk_c6,B)) = B
| multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_6688,c_3358]) ).
cnf(c_7084,plain,
( multiply(sk_c3,multiply(sk_c6,multiply(sk_c5,A))) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_6688,c_2342]) ).
cnf(c_7133,plain,
( multiply(sk_c3,multiply(sk_c6,B)) = multiply(sk_c7,B)
| multiply(sk_c6,multiply(sk_c7,A)) = multiply(sk_c6,A) ),
inference(paramod,[status(thm)],[c_6688,c_1729]) ).
cnf(c_7168,plain,
( inverse(sk_c7) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_6802,c_252]) ).
cnf(c_9247,plain,
( sk_c5 = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6925,c_1678]) ).
cnf(c_9248,plain,
( identity = sk_c5
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9247]) ).
cnf(c_7376,plain,
( identity = sk_c5
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9248]) ).
cnf(c_9249,plain,
( sk_c6 != sk_c7
| identity = sk_c5
| identity = sk_c5 ),
inference(resolve,[status(thm)],[c_7376,c_1004]) ).
cnf(c_7388,plain,
( sk_c6 != sk_c7
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_9249]) ).
cnf(c_7395,plain,
( inverse(sk_c7) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_7376,c_252]) ).
cnf(c_9250,plain,
( identity = sk_c5
| identity = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_7395,c_996]) ).
cnf(c_7425,plain,
( identity = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_9250]) ).
cnf(c_9251,plain,
( identity = sk_c5
| sk_c6 = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_7425,c_7376]) ).
cnf(c_7469,plain,
( sk_c6 = sk_c7
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_9251]) ).
cnf(c_9252,plain,
( identity = sk_c5
| identity = sk_c5 ),
inference(resolve,[status(thm)],[c_7469,c_7388]) ).
cnf(c_7482,plain,
identity = sk_c5,
inference(copy,[status(thm)],[c_9252]) ).
cnf(c_7636,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_7482,c_7168]) ).
cnf(c_7708,plain,
( sk_c5 = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_7482,c_6802]) ).
cnf(c_7980,plain,
( sk_c5 = sk_c7
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_7482,c_1665]) ).
cnf(c_8129,plain,
( inverse(sk_c7) = sk_c3
| sk_c5 != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_7482,c_310]) ).
cnf(c_8143,plain,
multiply(A,sk_c5) = A,
inference(paramod,[status(thm)],[c_7482,c_208]) ).
cnf(c_8148,plain,
multiply(sk_c5,A) = A,
inference(paramod,[status(thm)],[c_7482,c_1]) ).
cnf(c_9253,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_8143,c_7708]) ).
cnf(c_8181,plain,
( sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9253]) ).
cnf(c_9254,plain,
( inverse(sk_c7) = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_8143,c_7636]) ).
cnf(c_8192,plain,
( inverse(sk_c7) = sk_c5
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9254]) ).
cnf(c_8340,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_8148,c_7084]) ).
cnf(c_9255,plain,
( multiply(sk_c3,sk_c6) = multiply(sk_c7,multiply(sk_c7,sk_c3))
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_285,c_47]) ).
cnf(c_8437,plain,
( multiply(sk_c3,sk_c6) = multiply(sk_c7,multiply(sk_c7,sk_c3))
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9255]) ).
cnf(c_9256,plain,
( sk_c6 = sk_c7
| sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_8192,c_5549]) ).
cnf(c_8481,plain,
( sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9256]) ).
cnf(c_9257,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_8481,c_8181]) ).
cnf(c_9258,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9257]) ).
cnf(c_8587,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_9258]) ).
cnf(c_9259,plain,
( multiply(sk_c3,sk_c6) = multiply(sk_c7,multiply(sk_c7,sk_c3))
| inverse(sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_8437]) ).
cnf(c_8639,plain,
( multiply(sk_c3,sk_c7) = multiply(sk_c7,multiply(sk_c7,sk_c3))
| inverse(sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9259]) ).
cnf(c_9260,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_8587,c_8340]) ).
cnf(c_9261,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9260]) ).
cnf(c_9262,plain,
( multiply(sk_c3,multiply(sk_c7,A)) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9261]) ).
cnf(c_8673,plain,
( multiply(sk_c3,multiply(sk_c7,A)) = multiply(sk_c7,A)
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9262]) ).
cnf(c_9263,plain,
( inverse(sk_c7) = sk_c3
| sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_8129]) ).
cnf(c_8706,plain,
( inverse(sk_c7) = sk_c3
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_9263]) ).
cnf(c_9264,plain,
( multiply(sk_c3,multiply(sk_c6,B)) = multiply(sk_c7,B)
| multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c6,A) ),
inference(paramod,[status(thm)],[c_8587,c_7133]) ).
cnf(c_9265,plain,
( multiply(sk_c3,multiply(sk_c6,B)) = multiply(sk_c7,B)
| multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_8587,c_9264]) ).
cnf(c_8827,plain,
( multiply(sk_c3,multiply(sk_c7,B)) = multiply(sk_c7,B)
| multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_8587,c_9265]) ).
cnf(c_9266,plain,
( multiply(sk_c7,multiply(sk_c6,B)) = B
| multiply(sk_c3,multiply(sk_c7,A)) = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_8587,c_7048]) ).
cnf(c_8844,plain,
( multiply(sk_c7,multiply(sk_c7,B)) = B
| multiply(sk_c3,multiply(sk_c7,A)) = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_8587,c_9266]) ).
cnf(c_9267,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| sk_c6 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_5244]) ).
cnf(c_9268,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| sk_c6 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9267]) ).
cnf(c_9269,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9268]) ).
cnf(c_9270,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9269]) ).
cnf(c_9271,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(copy,[status(thm)],[c_9270]) ).
cnf(c_9272,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(copy,[status(thm)],[c_9271]) ).
cnf(c_8957,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(copy,[status(thm)],[c_9272]) ).
cnf(c_9273,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_42]) ).
cnf(c_9274,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9273]) ).
cnf(c_9275,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_8587,c_9274]) ).
cnf(c_9276,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(copy,[status(thm)],[c_9275]) ).
cnf(c_9277,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(copy,[status(thm)],[c_9276]) ).
cnf(c_9006,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(copy,[status(thm)],[c_9277]) ).
cnf(c_9278,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c7) = sk_c3 ),
inference(resolve,[status(thm)],[c_8706,c_7980]) ).
cnf(c_9030,plain,
inverse(sk_c7) = sk_c3,
inference(copy,[status(thm)],[c_9278]) ).
cnf(c_9038,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| sk_c3 != sk_c7 ),
inference(paramod,[status(thm)],[c_9030,c_9006]) ).
cnf(c_9104,plain,
( multiply(sk_c3,sk_c7) = multiply(sk_c7,multiply(sk_c7,sk_c3))
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9030,c_8639]) ).
cnf(c_9120,plain,
multiply(sk_c3,multiply(sk_c7,A)) = A,
inference(paramod,[status(thm)],[c_9030,c_43]) ).
cnf(c_9279,plain,
( multiply(sk_c7,multiply(sk_c7,B)) = B
| A = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_9120,c_8844]) ).
cnf(c_9135,plain,
( multiply(sk_c7,multiply(sk_c7,B)) = B
| multiply(sk_c7,A) = A ),
inference(copy,[status(thm)],[c_9279]) ).
cnf(c_9280,plain,
( B = multiply(sk_c7,B)
| multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c7,A) ),
inference(paramod,[status(thm)],[c_9120,c_8827]) ).
cnf(c_9137,plain,
( multiply(sk_c7,B) = B
| multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c7,A) ),
inference(copy,[status(thm)],[c_9280]) ).
cnf(c_9281,plain,
( A = multiply(sk_c7,A)
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_9120,c_8673]) ).
cnf(c_9143,plain,
( multiply(sk_c7,A) = A
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(copy,[status(thm)],[c_9281]) ).
cnf(c_9145,plain,
multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c7,A),
inference(factor,[status(thm)],[c_9137]) ).
cnf(c_9146,plain,
multiply(sk_c7,sk_c7) = sk_c7,
inference(factor,[status(thm)],[c_9143]) ).
cnf(c_9151,plain,
( multiply(sk_c7,B) = B
| multiply(sk_c7,A) = A ),
inference(paramod,[status(thm)],[c_9145,c_9135]) ).
cnf(c_9152,plain,
( multiply(sk_c3,sk_c7) = multiply(sk_c7,sk_c3)
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9145,c_9104]) ).
cnf(c_9282,plain,
( sk_c7 != sk_c7
| sk_c3 != sk_c7 ),
inference(paramod,[status(thm)],[c_9146,c_9038]) ).
cnf(c_9158,plain,
sk_c3 != sk_c7,
inference(copy,[status(thm)],[c_9282]) ).
cnf(c_9283,plain,
( sk_c7 != sk_c7
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_9146,c_8957]) ).
cnf(c_9164,plain,
multiply(sk_c3,sk_c7) = sk_c7,
inference(copy,[status(thm)],[c_9283]) ).
cnf(c_9171,plain,
multiply(sk_c7,A) = A,
inference(factor,[status(thm)],[c_9151]) ).
cnf(c_9284,plain,
( sk_c7 = multiply(sk_c7,sk_c3)
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9164,c_9152]) ).
cnf(c_9285,plain,
( sk_c7 = sk_c3
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9171,c_9284]) ).
cnf(c_9286,plain,
( sk_c3 = sk_c7
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_9285]) ).
cnf(c_9287,plain,
sk_c3 = sk_c7,
inference(copy,[status(thm)],[c_9286]) ).
cnf(c_9172,plain,
$false,
inference(resolve,[status(thm)],[c_9158,c_9287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP234-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n019.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:40:18 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2996684 was started by sandbox2 on n019,
% 0.17/0.43 % Fri Sep 25 14:40:18 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 15.58/2.43
% 15.58/2.43 % SZS status Unsatisfiable for theBenchmark
% 15.58/2.43
% 15.58/2.43 % Proof 1 at 1.50 (+ 0.47) seconds.
% 15.58/2.43 % Length of proof is 160.
% 15.58/2.43 % Level of proof is 37.
% 15.58/2.43 % Maximum clause weight is 45.000.
% 15.58/2.43 % Given clauses 375.
% 15.58/2.43
% 15.58/2.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------