%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP226-1 : 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 : 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 07:28:24 AM UTC 2026
% Result : Unsatisfiable 33.59s 5.22s
% Output : CNFRefutation 33.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 20
% Syntax : Number of formulae : 297 ( 36 unt; 0 def)
% Number of atoms : 787 ( 786 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 802 ( 312 ~; 490 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 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 : 117 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_15,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c3 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_19,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c5) = sk_c6
| 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_c6
| multiply(VAR_4,sk_c6) != sk_c7
| multiply(VAR_3,sk_c6) != sk_c7
| inverse(VAR_3) != sk_c7
| inverse(VAR_2) != sk_c7
| multiply(VAR_2,sk_c7) != VAR_1
| multiply(sk_c7,VAR_1) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(E) != sk_c6
| multiply(E,sk_c6) != sk_c7
| multiply(D,sk_c6) != sk_c7
| inverse(D) != sk_c7
| 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 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
cnf(c_25,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c7
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(A,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_12615,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c7
| multiply(A,sk_c6) != sk_c7
| 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 ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_26,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c7
| 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 ),
inference(copy,[status(thm)],[c_12615]) ).
cnf(c_12616,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(A,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_27,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c7
| multiply(A,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(copy,[status(thm)],[c_12616]) ).
cnf(c_28,plain,
( inverse(A) != sk_c6
| 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 ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_29,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_12617,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_12618,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_12617]) ).
cnf(c_30,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_12618]) ).
cnf(c_31,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_12619,plain,
( multiply(sk_c7,A) = multiply(sk_c4,multiply(sk_c6,A))
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_34,plain,
( multiply(sk_c4,multiply(sk_c6,A)) = multiply(sk_c7,A)
| inverse(sk_c1) = sk_c7 ),
inference(copy,[status(thm)],[c_12619]) ).
cnf(c_39,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_40,plain,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_12620,plain,
( multiply(multiply(A,sk_c4),sk_c6) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_13,c_3]) ).
cnf(c_61,plain,
( multiply(A,multiply(sk_c4,sk_c6)) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_12620]) ).
cnf(c_12621,plain,
( multiply(sk_c7,A) = multiply(sk_c5,multiply(sk_c6,A))
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_64,plain,
( multiply(sk_c5,multiply(sk_c6,A)) = multiply(sk_c7,A)
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(copy,[status(thm)],[c_12621]) ).
cnf(c_12622,plain,
( multiply(multiply(A,sk_c2),sk_c7) = multiply(A,sk_c3)
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_71,plain,
( multiply(A,multiply(sk_c2,sk_c7)) = multiply(A,sk_c3)
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_12622]) ).
cnf(c_12623,plain,
( multiply(multiply(A,sk_c2),sk_c7) = multiply(A,sk_c3)
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_3]) ).
cnf(c_77,plain,
( multiply(A,multiply(sk_c2,sk_c7)) = multiply(A,sk_c3)
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_12623]) ).
cnf(c_12624,plain,
( multiply(multiply(A,sk_c2),sk_c7) = multiply(A,sk_c3)
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_82,plain,
( multiply(A,multiply(sk_c2,sk_c7)) = multiply(A,sk_c3)
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_12624]) ).
cnf(c_83,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_91,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_92,plain,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_12625,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(identity,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_27]) ).
cnf(c_94,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_12625]) ).
cnf(c_99,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| inverse(sk_c1) != sk_c7 ),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_107,plain,
( inverse(identity) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_12626,plain,
( inverse(identity) != sk_c6
| multiply(identity,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(factor,[status(thm)],[c_107]) ).
cnf(c_120,plain,
( inverse(identity) != sk_c6
| sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_12626]) ).
cnf(c_165,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_30]) ).
cnf(c_166,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_30]) ).
cnf(c_178,plain,
( multiply(inverse(sk_c4),sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_9,c_30]) ).
cnf(c_188,plain,
( multiply(inverse(sk_c5),sk_c7) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_30]) ).
cnf(c_207,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_30,c_30]) ).
cnf(c_208,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_207,c_165]) ).
cnf(c_12627,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_31,c_30]) ).
cnf(c_214,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12627]) ).
cnf(c_307,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_208,c_2]) ).
cnf(c_12628,plain,
( inverse(A) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != identity
| sk_c7 != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_28]) ).
cnf(c_309,plain,
( inverse(A) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != identity
| sk_c6 != sk_c7
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(copy,[status(thm)],[c_12628]) ).
cnf(c_12629,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c7) != identity
| sk_c7 != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_29]) ).
cnf(c_310,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c7) != identity
| sk_c6 != sk_c7
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(copy,[status(thm)],[c_12629]) ).
cnf(c_12630,plain,
( inverse(identity) != sk_c6
| sk_c7 != identity
| sk_c7 != sk_c6
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_120]) ).
cnf(c_12631,plain,
( inverse(identity) != sk_c6
| sk_c7 != identity
| sk_c7 != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_307,c_12630]) ).
cnf(c_12632,plain,
( identity != sk_c6
| sk_c7 != identity
| sk_c7 != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_307,c_12631]) ).
cnf(c_12633,plain,
( identity != sk_c6
| sk_c7 != identity
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12632]) ).
cnf(c_12634,plain,
( identity != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12633]) ).
cnf(c_12635,plain,
( identity != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12634]) ).
cnf(c_311,plain,
( identity != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12635]) ).
cnf(c_382,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_307,c_94]) ).
cnf(c_386,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_214,c_2]) ).
cnf(c_12636,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_39,c_30]) ).
cnf(c_506,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_12636]) ).
cnf(c_12637,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_40,c_30]) ).
cnf(c_530,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12637]) ).
cnf(c_12638,plain,
( multiply(sk_c4,identity) = multiply(sk_c7,sk_c5)
| inverse(sk_c1) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_40,c_34]) ).
cnf(c_12639,plain,
( sk_c4 = multiply(sk_c7,sk_c5)
| inverse(sk_c1) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12638]) ).
cnf(c_12640,plain,
( multiply(sk_c7,sk_c5) = sk_c4
| inverse(sk_c1) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(copy,[status(thm)],[c_12639]) ).
cnf(c_531,plain,
( multiply(sk_c7,sk_c5) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(copy,[status(thm)],[c_12640]) ).
cnf(c_538,plain,
( multiply(sk_c5,sk_c6) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_530,c_2]) ).
cnf(c_12641,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| sk_c7 != identity
| sk_c7 != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_382]) ).
cnf(c_12642,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| sk_c7 != identity
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12641]) ).
cnf(c_12643,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12642]) ).
cnf(c_12644,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12643]) ).
cnf(c_608,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12644]) ).
cnf(c_642,plain,
( inverse(multiply(A,B)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_608]) ).
cnf(c_12645,plain,
( inverse(multiply(inverse(multiply(A,sk_c6)),A)) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_642]) ).
cnf(c_669,plain,
( inverse(multiply(inverse(multiply(A,sk_c6)),A)) != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_12645]) ).
cnf(c_12646,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_83,c_30]) ).
cnf(c_718,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12646]) ).
cnf(c_726,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_718,c_2]) ).
cnf(c_12647,plain,
( sk_c2 = sk_c1
| inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_718,c_214]) ).
cnf(c_732,plain,
( sk_c2 = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_12647]) ).
cnf(c_746,plain,
( multiply(sk_c7,sk_c4) = identity
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_732,c_2]) ).
cnf(c_12648,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_746,c_30]) ).
cnf(c_758,plain,
( inverse(sk_c7) = sk_c4
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_208,c_12648]) ).
cnf(c_12649,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_91,c_30]) ).
cnf(c_928,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_12649]) ).
cnf(c_936,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_928,c_2]) ).
cnf(c_12650,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_92,c_30]) ).
cnf(c_1292,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12650]) ).
cnf(c_1519,plain,
( multiply(sk_c5,sk_c6) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_1292,c_2]) ).
cnf(c_12651,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_538,c_6]) ).
cnf(c_1946,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(copy,[status(thm)],[c_12651]) ).
cnf(c_1976,plain,
( multiply(sk_c7,A) = A
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_1946,c_1]) ).
cnf(c_1977,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1946,c_2]) ).
cnf(c_12652,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1977,c_30]) ).
cnf(c_2007,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12652]) ).
cnf(c_12653,plain,
( inverse(sk_c4) = sk_c7
| identity = sk_c3
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_726,c_16]) ).
cnf(c_2764,plain,
( identity = sk_c3
| inverse(sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_12653]) ).
cnf(c_2821,plain,
( multiply(sk_c7,sk_c4) = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_2764,c_2]) ).
cnf(c_12654,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_2821,c_30]) ).
cnf(c_2848,plain,
( inverse(sk_c7) = sk_c4
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_208,c_12654]) ).
cnf(c_12655,plain,
( sk_c4 = sk_c1
| identity = sk_c7
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_2848,c_2007]) ).
cnf(c_2924,plain,
( sk_c1 = sk_c4
| identity = sk_c7
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12655]) ).
cnf(c_12656,plain,
( multiply(sk_c5,multiply(sk_c6,sk_c7)) = multiply(sk_c7,multiply(sk_c4,sk_c6))
| multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_61,c_64]) ).
cnf(c_3242,plain,
( multiply(sk_c5,multiply(sk_c6,sk_c7)) = multiply(sk_c7,multiply(sk_c4,sk_c6))
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(copy,[status(thm)],[c_12656]) ).
cnf(c_12657,plain,
( inverse(sk_c5) = sk_c6
| identity = sk_c3
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_936,c_19]) ).
cnf(c_3466,plain,
( identity = sk_c3
| inverse(sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_12657]) ).
cnf(c_3489,plain,
( multiply(sk_c6,sk_c5) = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_3466,c_2]) ).
cnf(c_12658,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_3489,c_30]) ).
cnf(c_3518,plain,
( inverse(sk_c6) = sk_c5
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_208,c_12658]) ).
cnf(c_3551,plain,
( multiply(sk_c5,sk_c6) = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_3518,c_2]) ).
cnf(c_3637,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c7) = sk_c3
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_3551,c_18]) ).
cnf(c_12659,plain,
( identity = sk_c7
| inverse(sk_c2) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_1519,c_22]) ).
cnf(c_3886,plain,
( identity = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_12659]) ).
cnf(c_3921,plain,
( multiply(sk_c7,sk_c2) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3886,c_2]) ).
cnf(c_12660,plain,
( multiply(sk_c7,multiply(sk_c2,sk_c7)) = sk_c6
| inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_71]) ).
cnf(c_3948,plain,
( multiply(sk_c7,multiply(sk_c2,sk_c7)) = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_12660]) ).
cnf(c_12661,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3921,c_30]) ).
cnf(c_3998,plain,
( inverse(sk_c7) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12661]) ).
cnf(c_12662,plain,
( sk_c2 = sk_c1
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3998,c_2007]) ).
cnf(c_4073,plain,
( sk_c2 = sk_c1
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_12662]) ).
cnf(c_4098,plain,
( identity != sk_c6
| sk_c6 != sk_c7
| sk_c2 = sk_c1 ),
inference(resolve,[status(thm)],[c_4073,c_311]) ).
cnf(c_4103,plain,
( inverse(sk_c7) = identity
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_4073,c_307]) ).
cnf(c_12663,plain,
( sk_c7 != sk_c6
| sk_c6 != sk_c7
| sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_4073,c_4098]) ).
cnf(c_12664,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12663]) ).
cnf(c_12665,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12664]) ).
cnf(c_4175,plain,
( sk_c6 != sk_c7
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12665]) ).
cnf(c_12666,plain,
( identity = sk_c4
| sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_4103,c_758]) ).
cnf(c_4238,plain,
( identity = sk_c4
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12666]) ).
cnf(c_4255,plain,
( multiply(sk_c4,A) = A
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_4238,c_1]) ).
cnf(c_12667,plain,
( multiply(sk_c7,multiply(sk_c2,sk_c7)) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_14,c_77]) ).
cnf(c_4537,plain,
( multiply(sk_c7,multiply(sk_c2,sk_c7)) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_12667]) ).
cnf(c_12668,plain,
( multiply(sk_c7,multiply(sk_c2,sk_c7)) = sk_c6
| inverse(sk_c5) = sk_c6
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_82]) ).
cnf(c_5017,plain,
( multiply(sk_c7,multiply(sk_c2,sk_c7)) = sk_c6
| inverse(sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_12668]) ).
cnf(c_12669,plain,
( sk_c5 = sk_c4
| inverse(sk_c1) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_1976,c_531]) ).
cnf(c_5847,plain,
( sk_c5 = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(copy,[status(thm)],[c_12669]) ).
cnf(c_5863,plain,
( multiply(sk_c7,sk_c1) = identity
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_5847,c_2]) ).
cnf(c_12670,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7
| inverse(sk_c1) != sk_c6
| inverse(sk_c1) != sk_c7
| multiply(sk_c7,identity) != sk_c6
| inverse(sk_c1) != sk_c7 ),
inference(resolve,[status(thm)],[c_99,c_386]) ).
cnf(c_12671,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7
| inverse(sk_c1) != sk_c6
| inverse(sk_c1) != sk_c7
| sk_c7 != sk_c6
| inverse(sk_c1) != sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12670]) ).
cnf(c_12672,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7
| inverse(sk_c1) != sk_c6
| inverse(sk_c1) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c1) != sk_c7 ),
inference(copy,[status(thm)],[c_12671]) ).
cnf(c_12673,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7
| inverse(sk_c1) != sk_c6
| sk_c6 != sk_c7
| inverse(sk_c1) != sk_c7 ),
inference(copy,[status(thm)],[c_12672]) ).
cnf(c_5961,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) != sk_c6
| sk_c6 != sk_c7
| inverse(sk_c1) != sk_c7 ),
inference(copy,[status(thm)],[c_12673]) ).
cnf(c_12674,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_5863,c_30]) ).
cnf(c_6031,plain,
( inverse(sk_c7) = sk_c1
| sk_c5 = sk_c4 ),
inference(paramod,[status(thm)],[c_208,c_12674]) ).
cnf(c_12675,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_6031,c_506]) ).
cnf(c_6095,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c1 ),
inference(copy,[status(thm)],[c_12675]) ).
cnf(c_12676,plain,
( inverse(sk_c7) = sk_c1
| sk_c6 = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_6095,c_214]) ).
cnf(c_7197,plain,
( sk_c6 = sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(copy,[status(thm)],[c_12676]) ).
cnf(c_7222,plain,
( sk_c2 = sk_c1
| inverse(sk_c7) = sk_c1 ),
inference(resolve,[status(thm)],[c_7197,c_4175]) ).
cnf(c_7227,plain,
( inverse(multiply(inverse(multiply(A,sk_c6)),A)) != sk_c6
| identity != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(resolve,[status(thm)],[c_7197,c_669]) ).
cnf(c_7280,plain,
( sk_c1 = sk_c4
| identity = sk_c3
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_7197,c_2848]) ).
cnf(c_12677,plain,
( sk_c1 = sk_c4
| sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_7222,c_758]) ).
cnf(c_7477,plain,
( sk_c1 = sk_c4
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12677]) ).
cnf(c_12678,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_7477,c_9]) ).
cnf(c_7482,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12678]) ).
cnf(c_7581,plain,
( inverse(multiply(inverse(multiply(A,sk_c6)),A)) != sk_c6
| identity != sk_c7
| sk_c1 = sk_c4
| identity = sk_c3 ),
inference(resolve,[status(thm)],[c_7280,c_669]) ).
cnf(c_12679,plain,
( sk_c7 = sk_c6
| sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_7482,c_4255]) ).
cnf(c_12680,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12679]) ).
cnf(c_9283,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_12680]) ).
cnf(c_12681,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),A)),identity) = B,
inference(paramod,[status(thm)],[c_2,c_166]) ).
cnf(c_9288,plain,
inverse(multiply(inverse(multiply(A,B)),A)) = B,
inference(paramod,[status(thm)],[c_208,c_12681]) ).
cnf(c_12682,plain,
( sk_c6 != sk_c6
| identity != sk_c7
| sk_c1 = sk_c4
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_9288,c_7581]) ).
cnf(c_9486,plain,
( identity != sk_c7
| sk_c1 = sk_c4
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12682]) ).
cnf(c_12683,plain,
( sk_c6 != sk_c6
| identity != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(paramod,[status(thm)],[c_9288,c_7227]) ).
cnf(c_9487,plain,
( identity != sk_c7
| inverse(sk_c7) = sk_c1 ),
inference(copy,[status(thm)],[c_12683]) ).
cnf(c_12684,plain,
( sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(resolve,[status(thm)],[c_9283,c_4175]) ).
cnf(c_9538,plain,
sk_c2 = sk_c1,
inference(copy,[status(thm)],[c_12684]) ).
cnf(c_9685,plain,
( multiply(sk_c7,multiply(sk_c1,sk_c7)) = sk_c6
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_9538,c_5017]) ).
cnf(c_9737,plain,
( multiply(sk_c7,multiply(sk_c1,sk_c7)) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_9538,c_4537]) ).
cnf(c_9798,plain,
( multiply(sk_c7,multiply(sk_c1,sk_c7)) = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_9538,c_3948]) ).
cnf(c_9821,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c7) = sk_c3
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_9538,c_3637]) ).
cnf(c_12685,plain,
( sk_c1 = sk_c4
| identity = sk_c3
| sk_c1 = sk_c4
| identity = sk_c3 ),
inference(resolve,[status(thm)],[c_9486,c_2924]) ).
cnf(c_12686,plain,
( sk_c1 = sk_c4
| sk_c1 = sk_c4
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12685]) ).
cnf(c_9857,plain,
( sk_c1 = sk_c4
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12686]) ).
cnf(c_12687,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c7) = sk_c1 ),
inference(resolve,[status(thm)],[c_9487,c_2007]) ).
cnf(c_9913,plain,
inverse(sk_c7) = sk_c1,
inference(copy,[status(thm)],[c_12687]) ).
cnf(c_10538,plain,
multiply(sk_c1,sk_c7) = identity,
inference(paramod,[status(thm)],[c_9913,c_2]) ).
cnf(c_12688,plain,
( identity = sk_c7
| identity = sk_c3
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_10538,c_9821]) ).
cnf(c_10613,plain,
( identity = sk_c7
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12688]) ).
cnf(c_12689,plain,
( multiply(sk_c7,identity) = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_10538,c_9798]) ).
cnf(c_12690,plain,
( sk_c7 = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12689]) ).
cnf(c_10614,plain,
( sk_c6 = sk_c7
| inverse(sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_12690]) ).
cnf(c_12691,plain,
( multiply(sk_c7,identity) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_10538,c_9737]) ).
cnf(c_12692,plain,
( sk_c7 = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_208,c_12691]) ).
cnf(c_10640,plain,
( sk_c6 = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_12692]) ).
cnf(c_12693,plain,
( multiply(sk_c7,identity) = sk_c6
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_10538,c_9685]) ).
cnf(c_12694,plain,
( sk_c7 = sk_c6
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_208,c_12693]) ).
cnf(c_10660,plain,
( sk_c6 = sk_c7
| inverse(sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_12694]) ).
cnf(c_12695,plain,
( inverse(sk_c7) = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_10613,c_307]) ).
cnf(c_12696,plain,
( sk_c1 = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_9913,c_12695]) ).
cnf(c_10869,plain,
( identity = sk_c1
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12696]) ).
cnf(c_12697,plain,
( identity = sk_c4
| identity = sk_c3
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_9857,c_10869]) ).
cnf(c_10930,plain,
( identity = sk_c4
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12697]) ).
cnf(c_12698,plain,
( sk_c4 = sk_c7
| identity = sk_c3
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_10930,c_10613]) ).
cnf(c_10960,plain,
( sk_c4 = sk_c7
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12698]) ).
cnf(c_12699,plain,
( multiply(sk_c7,sk_c7) = identity
| identity = sk_c3
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_10960,c_2821]) ).
cnf(c_11113,plain,
( multiply(sk_c7,sk_c7) = identity
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12699]) ).
cnf(c_12700,plain,
multiply(inverse(sk_c1),identity) = sk_c7,
inference(paramod,[status(thm)],[c_10538,c_30]) ).
cnf(c_11126,plain,
inverse(sk_c1) = sk_c7,
inference(paramod,[status(thm)],[c_208,c_12700]) ).
cnf(c_12701,plain,
( inverse(sk_c1) != sk_c6
| identity != identity
| sk_c6 != sk_c7
| multiply(sk_c1,sk_c6) != sk_c7
| inverse(sk_c1) != sk_c7 ),
inference(paramod,[status(thm)],[c_10538,c_310]) ).
cnf(c_12702,plain,
( inverse(sk_c1) != sk_c6
| identity != identity
| sk_c6 != sk_c7
| multiply(sk_c1,sk_c6) != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_11126,c_12701]) ).
cnf(c_12703,plain,
( sk_c7 != sk_c6
| identity != identity
| sk_c6 != sk_c7
| multiply(sk_c1,sk_c6) != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_11126,c_12702]) ).
cnf(c_12704,plain,
( sk_c6 != sk_c7
| identity != identity
| sk_c6 != sk_c7
| multiply(sk_c1,sk_c6) != sk_c7
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_12703]) ).
cnf(c_12705,plain,
( sk_c6 != sk_c7
| identity != identity
| sk_c6 != sk_c7
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_12704]) ).
cnf(c_12706,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_12705]) ).
cnf(c_11127,plain,
( sk_c6 != sk_c7
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_12706]) ).
cnf(c_12707,plain,
( inverse(A) != sk_c6
| inverse(sk_c1) != sk_c7
| identity != identity
| sk_c6 != sk_c7
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(paramod,[status(thm)],[c_10538,c_309]) ).
cnf(c_12708,plain,
( inverse(A) != sk_c6
| sk_c7 != sk_c7
| identity != identity
| sk_c6 != sk_c7
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(paramod,[status(thm)],[c_11126,c_12707]) ).
cnf(c_12709,plain,
( inverse(A) != sk_c6
| sk_c7 != sk_c7
| sk_c6 != sk_c7
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(copy,[status(thm)],[c_12708]) ).
cnf(c_11128,plain,
( inverse(A) != sk_c6
| sk_c6 != sk_c7
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(copy,[status(thm)],[c_12709]) ).
cnf(c_12710,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) != sk_c6
| sk_c6 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_11126,c_5961]) ).
cnf(c_12711,plain,
( inverse(sk_c4) = sk_c7
| sk_c7 != sk_c6
| sk_c6 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_11126,c_12710]) ).
cnf(c_12712,plain,
( inverse(sk_c4) = sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_12711]) ).
cnf(c_12713,plain,
( inverse(sk_c4) = sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_12712]) ).
cnf(c_11212,plain,
( inverse(sk_c4) = sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_12713]) ).
cnf(c_12714,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c6
| multiply(inverse(sk_c4),sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_178,c_30]) ).
cnf(c_11257,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(inverse(sk_c4),sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_11126,c_12714]) ).
cnf(c_11363,plain,
( multiply(sk_c1,sk_c6) != sk_c7
| inverse(sk_c5) = sk_c6 ),
inference(resolve,[status(thm)],[c_10660,c_11127]) ).
cnf(c_12715,plain,
( multiply(multiply(A,inverse(sk_c5)),sk_c7) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_188,c_3]) ).
cnf(c_11967,plain,
( multiply(A,multiply(inverse(sk_c5),sk_c7)) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_12715]) ).
cnf(c_12716,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c4) = sk_c7 ),
inference(resolve,[status(thm)],[c_11212,c_10614]) ).
cnf(c_12105,plain,
inverse(sk_c4) = sk_c7,
inference(copy,[status(thm)],[c_12716]) ).
cnf(c_12717,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_12105,c_11257]) ).
cnf(c_12152,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(copy,[status(thm)],[c_12717]) ).
cnf(c_12718,plain,
( sk_c6 = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_12152,c_11113]) ).
cnf(c_12194,plain,
( identity = sk_c6
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12718]) ).
cnf(c_12719,plain,
( inverse(sk_c4) != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c4,sk_c6) != sk_c7 ),
inference(resolve,[status(thm)],[c_12105,c_11128]) ).
cnf(c_12720,plain,
( sk_c7 != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c4,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_12105,c_12719]) ).
cnf(c_12721,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| multiply(sk_c4,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_12720]) ).
cnf(c_12241,plain,
( sk_c6 != sk_c7
| multiply(sk_c4,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_12721]) ).
cnf(c_12246,plain,
multiply(sk_c7,multiply(sk_c4,A)) = A,
inference(paramod,[status(thm)],[c_12105,c_30]) ).
cnf(c_12249,plain,
( multiply(sk_c5,multiply(sk_c6,sk_c7)) = sk_c6
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_12246,c_3242]) ).
cnf(c_12722,plain,
( multiply(inverse(inverse(sk_c4)),sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_9,c_207]) ).
cnf(c_12723,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_12105,c_12722]) ).
cnf(c_12724,plain,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_9913,c_12723]) ).
cnf(c_12254,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(copy,[status(thm)],[c_12724]) ).
cnf(c_12725,plain,
multiply(inverse(sk_c7),A) = multiply(sk_c4,A),
inference(paramod,[status(thm)],[c_12105,c_207]) ).
cnf(c_12272,plain,
multiply(sk_c1,A) = multiply(sk_c4,A),
inference(paramod,[status(thm)],[c_9913,c_12725]) ).
cnf(c_12278,plain,
( multiply(sk_c4,sk_c6) != sk_c7
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_12272,c_11363]) ).
cnf(c_12334,plain,
multiply(sk_c4,sk_c6) = sk_c7,
inference(paramod,[status(thm)],[c_12272,c_12254]) ).
cnf(c_12726,plain,
( sk_c7 != sk_c7
| inverse(sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_12334,c_12278]) ).
cnf(c_12385,plain,
inverse(sk_c5) = sk_c6,
inference(copy,[status(thm)],[c_12726]) ).
cnf(c_12727,plain,
( sk_c6 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_12334,c_12241]) ).
cnf(c_12388,plain,
sk_c6 != sk_c7,
inference(copy,[status(thm)],[c_12727]) ).
cnf(c_12400,plain,
( multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_12385,c_11967]) ).
cnf(c_12415,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(resolve,[status(thm)],[c_12388,c_10640]) ).
cnf(c_12728,plain,
( sk_c6 = sk_c7
| identity = sk_c3
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_12194,c_10613]) ).
cnf(c_12729,plain,
( sk_c6 = sk_c7
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_12728]) ).
cnf(c_12460,plain,
identity = sk_c3,
inference(resolve,[status(thm)],[c_12388,c_12729]) ).
cnf(c_12599,plain,
multiply(A,sk_c3) = A,
inference(paramod,[status(thm)],[c_12460,c_208]) ).
cnf(c_12730,plain,
( multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c6)
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12599,c_12400]) ).
cnf(c_12731,plain,
( multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c6)
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_12730]) ).
cnf(c_12610,plain,
multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c6),
inference(resolve,[status(thm)],[c_12388,c_12731]) ).
cnf(c_12732,plain,
( multiply(sk_c5,multiply(sk_c6,sk_c7)) = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12599,c_12249]) ).
cnf(c_12733,plain,
( multiply(sk_c5,sk_c6) = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12610,c_12732]) ).
cnf(c_12734,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12415,c_12733]) ).
cnf(c_12735,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_12734]) ).
cnf(c_12736,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_12735]) ).
cnf(c_12737,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_12736]) ).
cnf(c_12614,plain,
$false,
inference(resolve,[status(thm)],[c_12388,c_12737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP226-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:39:28 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1837810 was started by sandbox on n009,
% 0.11/0.36 % Fri Sep 25 14:39:28 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 33.59/5.22
% 33.59/5.22 % SZS status Unsatisfiable for theBenchmark
% 33.59/5.22
% 33.59/5.22 % Proof 1 at 3.65 (+ 1.04) seconds.
% 33.59/5.22 % Length of proof is 154.
% 33.59/5.22 % Level of proof is 28.
% 33.59/5.22 % Maximum clause weight is 45.000.
% 33.59/5.22 % Given clauses 427.
% 33.59/5.22
% 33.59/5.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------