%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP352-1 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:41 AM UTC 2026
% Result : Unsatisfiable 170.45s 27.77s
% Output : CNFRefutation 170.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 23
% Syntax : Number of formulae : 243 ( 27 unt; 0 def)
% Number of atoms : 682 ( 681 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 715 ( 276 ~; 439 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_19,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_24,axiom,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c6
| multiply(VAR_3,sk_c6) != sk_c7
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c5
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c7
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
cnf(c_30,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_33,plain,
( multiply(B,sk_c6) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_36,plain,
( multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(factor,[status(thm)],[c_33]) ).
cnf(c_31266,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_31267,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_31266]) ).
cnf(c_37,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_31267]) ).
cnf(c_31268,plain,
( multiply(sk_c7,A) = multiply(sk_c3,multiply(sk_c6,A))
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_41,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31268]) ).
cnf(c_31269,plain,
( multiply(sk_c7,A) = multiply(sk_c4,multiply(sk_c6,A))
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_43,plain,
( multiply(sk_c4,multiply(sk_c6,A)) = multiply(sk_c7,A)
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31269]) ).
cnf(c_45,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_48,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_53,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_55,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_57,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_58,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_70,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c4,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_361,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_37]) ).
cnf(c_388,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_37,c_37]) ).
cnf(c_389,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_388,c_361]) ).
cnf(c_390,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_389,c_2]) ).
cnf(c_31270,plain,
( multiply(A,sk_c6) != sk_c7
| multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_390,c_33]) ).
cnf(c_31271,plain,
( multiply(A,sk_c6) != sk_c7
| multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_31270]) ).
cnf(c_31272,plain,
( multiply(A,sk_c6) != sk_c7
| sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_31271]) ).
cnf(c_31273,plain,
( multiply(A,sk_c6) != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_31272]) ).
cnf(c_401,plain,
( multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_31273]) ).
cnf(c_31274,plain,
( multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(identity) != sk_c6
| multiply(identity,sk_c6) != sk_c5
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_390,c_36]) ).
cnf(c_31275,plain,
( multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(identity) != sk_c6
| multiply(identity,sk_c6) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_31274]) ).
cnf(c_31276,plain,
( multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(identity) != sk_c6
| sk_c6 != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_31275]) ).
cnf(c_31277,plain,
( multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c6 != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_390,c_31276]) ).
cnf(c_31278,plain,
( sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c6 != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_31277]) ).
cnf(c_31279,plain,
( sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c5 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_31278]) ).
cnf(c_31280,plain,
( sk_c7 != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c5 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_31279]) ).
cnf(c_406,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c5 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_31280]) ).
cnf(c_561,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_388,c_2]) ).
cnf(c_31281,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_388,c_389]) ).
cnf(c_31282,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_389,c_31281]) ).
cnf(c_579,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_31282]) ).
cnf(c_31283,plain,
( multiply(inverse(sk_c6),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(inverse(sk_c6),sk_c6) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(resolve,[status(thm)],[c_579,c_401]) ).
cnf(c_31284,plain,
( multiply(inverse(sk_c6),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_31283]) ).
cnf(c_31285,plain,
( identity != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_31284]) ).
cnf(c_586,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_31285]) ).
cnf(c_674,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_8,c_561]) ).
cnf(c_676,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_13,c_561]) ).
cnf(c_677,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,c_561]) ).
cnf(c_679,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_561]) ).
cnf(c_681,plain,
( multiply(sk_c4,sk_c6) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_561]) ).
cnf(c_683,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_23,c_561]) ).
cnf(c_684,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_24,c_561]) ).
cnf(c_688,plain,
( multiply(sk_c4,sk_c6) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_28,c_561]) ).
cnf(c_689,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_55,c_561]) ).
cnf(c_690,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_58,c_561]) ).
cnf(c_31286,plain,
( multiply(sk_c3,identity) = multiply(sk_c7,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_45,c_41]) ).
cnf(c_31287,plain,
( sk_c3 = multiply(sk_c7,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_389,c_31286]) ).
cnf(c_31288,plain,
( multiply(sk_c7,sk_c4) = sk_c3
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31287]) ).
cnf(c_1775,plain,
( multiply(sk_c7,sk_c4) = sk_c3
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31288]) ).
cnf(c_31289,plain,
( multiply(sk_c4,identity) = multiply(sk_c7,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_45,c_43]) ).
cnf(c_31290,plain,
( sk_c4 = multiply(sk_c7,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_389,c_31289]) ).
cnf(c_31291,plain,
( multiply(sk_c7,sk_c4) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31290]) ).
cnf(c_1776,plain,
( multiply(sk_c7,sk_c4) = sk_c4
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31291]) ).
cnf(c_2216,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_681,c_2]) ).
cnf(c_2422,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c4,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_688,c_2]) ).
cnf(c_31292,plain,
( multiply(multiply(A,sk_c1),sk_c7) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_53,c_3]) ).
cnf(c_4709,plain,
( multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_3,c_31292]) ).
cnf(c_31293,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_674,c_7]) ).
cnf(c_5801,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31293]) ).
cnf(c_31294,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_676,c_12]) ).
cnf(c_6093,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_31294]) ).
cnf(c_31295,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_677,c_9]) ).
cnf(c_6129,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_31295]) ).
cnf(c_31296,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_683,c_22]) ).
cnf(c_6830,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_31296]) ).
cnf(c_31297,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_684,c_19]) ).
cnf(c_7326,plain,
( identity = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_31297]) ).
cnf(c_31298,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_689,c_48]) ).
cnf(c_7522,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(copy,[status(thm)],[c_31298]) ).
cnf(c_31299,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_7522,c_37]) ).
cnf(c_7525,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_389,c_31299]) ).
cnf(c_31300,plain,
( multiply(multiply(A,sk_c1),sk_c7) = multiply(A,identity)
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_690,c_3]) ).
cnf(c_31301,plain,
( multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,identity)
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_3,c_31300]) ).
cnf(c_7782,plain,
( multiply(A,multiply(sk_c1,sk_c7)) = A
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_389,c_31301]) ).
cnf(c_31302,plain,
( sk_c4 = sk_c3
| multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_1776,c_1775]) ).
cnf(c_8898,plain,
( sk_c4 = sk_c3
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_31302]) ).
cnf(c_8900,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c5 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(resolve,[status(thm)],[c_8898,c_406]) ).
cnf(c_31303,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2216,c_57]) ).
cnf(c_9053,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_31303]) ).
cnf(c_31304,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9053,c_37]) ).
cnf(c_9205,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_389,c_31304]) ).
cnf(c_9206,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9205,c_2]) ).
cnf(c_31305,plain,
( identity = sk_c7
| identity = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9206,c_6093]) ).
cnf(c_9336,plain,
( identity = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31305]) ).
cnf(c_9608,plain,
( multiply(A,sk_c7) = A
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9336,c_389]) ).
cnf(c_9609,plain,
( inverse(sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9336,c_390]) ).
cnf(c_31306,plain,
( identity = sk_c3
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9609,c_7525]) ).
cnf(c_9669,plain,
( identity = sk_c3
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_31306]) ).
cnf(c_9675,plain,
( multiply(sk_c3,A) = A
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9669,c_1]) ).
cnf(c_31307,plain,
( identity = sk_c6
| sk_c3 = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9669,c_9336]) ).
cnf(c_9685,plain,
( sk_c3 = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_31307]) ).
cnf(c_9687,plain,
( multiply(A,sk_c6) = A
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9685,c_389]) ).
cnf(c_31308,plain,
( identity = sk_c6
| sk_c6 = sk_c5
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9608,c_6129]) ).
cnf(c_31309,plain,
( identity = sk_c6
| sk_c5 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_31308]) ).
cnf(c_10100,plain,
( sk_c5 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_31309]) ).
cnf(c_31310,plain,
( sk_c6 = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9675,c_11]) ).
cnf(c_10348,plain,
( sk_c7 = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_31310]) ).
cnf(c_31311,plain,
( multiply(sk_c1,sk_c7) = identity
| sk_c6 = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9675,c_679]) ).
cnf(c_10366,plain,
( multiply(sk_c1,sk_c7) = identity
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_31311]) ).
cnf(c_31312,plain,
( sk_c3 = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9687,c_6]) ).
cnf(c_10456,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_31312]) ).
cnf(c_10742,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c5 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(resolve,[status(thm)],[c_10456,c_406]) ).
cnf(c_31313,plain,
( multiply(sk_c6,sk_c2) = identity
| identity = sk_c7
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_2422,c_70]) ).
cnf(c_16704,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c2) = identity ),
inference(copy,[status(thm)],[c_31313]) ).
cnf(c_31314,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16704,c_37]) ).
cnf(c_16708,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_389,c_31314]) ).
cnf(c_16716,plain,
( multiply(sk_c2,sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16708,c_2]) ).
cnf(c_31315,plain,
( identity = sk_c7
| identity = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16716,c_6830]) ).
cnf(c_16910,plain,
( identity = sk_c5
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31315]) ).
cnf(c_16916,plain,
( inverse(sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16910,c_390]) ).
cnf(c_31316,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16910,c_10100]) ).
cnf(c_16925,plain,
( sk_c5 = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31316]) ).
cnf(c_16928,plain,
( multiply(A,sk_c7) = A
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_16925,c_389]) ).
cnf(c_31317,plain,
( inverse(sk_c5) = sk_c5
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16910,c_16916]) ).
cnf(c_17103,plain,
( inverse(sk_c5) = sk_c5
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31317]) ).
cnf(c_17311,plain,
( multiply(sk_c5,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_17103,c_2]) ).
cnf(c_31318,plain,
( identity = sk_c5
| sk_c6 = sk_c5
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_16928,c_7326]) ).
cnf(c_31319,plain,
( identity = sk_c5
| sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_31318]) ).
cnf(c_17745,plain,
( identity = sk_c5
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_31319]) ).
cnf(c_31320,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_17745,c_10100]) ).
cnf(c_31321,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_31320]) ).
cnf(c_17787,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_31321]) ).
cnf(c_31322,plain,
( multiply(sk_c6,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_17311]) ).
cnf(c_17932,plain,
( multiply(sk_c6,sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_31322]) ).
cnf(c_31323,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c6 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_10742]) ).
cnf(c_31324,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c6 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_31323]) ).
cnf(c_19982,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_31324]) ).
cnf(c_31325,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c6 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_17787,c_8900]) ).
cnf(c_31326,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c6 != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_17787,c_31325]) ).
cnf(c_20740,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_31326]) ).
cnf(c_22492,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_5801]) ).
cnf(c_31327,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_586]) ).
cnf(c_31328,plain,
( multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_31327]) ).
cnf(c_24853,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_17787,c_31328]) ).
cnf(c_31329,plain,
( sk_c7 = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_22492,c_17932]) ).
cnf(c_31330,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31329]) ).
cnf(c_31331,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31330]) ).
cnf(c_27408,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_31331]) ).
cnf(c_31332,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_27408,c_24853]) ).
cnf(c_31333,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_27408,c_31332]) ).
cnf(c_31334,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_31333]) ).
cnf(c_27879,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_31334]) ).
cnf(c_31335,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_27408,c_20740]) ).
cnf(c_31336,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_27408,c_31335]) ).
cnf(c_31337,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_31336]) ).
cnf(c_28767,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_31337]) ).
cnf(c_31338,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_27408,c_19982]) ).
cnf(c_31339,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_27408,c_31338]) ).
cnf(c_31340,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_31339]) ).
cnf(c_28827,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_31340]) ).
cnf(c_31341,plain,
( multiply(sk_c1,sk_c7) = identity
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_27408,c_10366]) ).
cnf(c_31342,plain,
( multiply(sk_c1,sk_c7) = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_27408,c_31341]) ).
cnf(c_29169,plain,
( multiply(sk_c1,sk_c7) = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_31342]) ).
cnf(c_31343,plain,
( sk_c7 = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_27408,c_10348]) ).
cnf(c_29178,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_31343]) ).
cnf(c_29207,plain,
( multiply(A,multiply(sk_c1,sk_c7)) = A
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_27408,c_7782]) ).
cnf(c_29270,plain,
( multiply(A,multiply(sk_c1,sk_c7)) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_27408,c_4709]) ).
cnf(c_29356,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_27408,c_389]) ).
cnf(c_30030,plain,
( multiply(A,sk_c1) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_29356,c_29270]) ).
cnf(c_30047,plain,
( multiply(A,sk_c1) = A
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_29356,c_29207]) ).
cnf(c_30049,plain,
( sk_c1 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_29356,c_29178]) ).
cnf(c_30050,plain,
( sk_c1 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_29356,c_29169]) ).
cnf(c_31344,plain,
( sk_c6 != sk_c6
| sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_29356,c_28827]) ).
cnf(c_30109,plain,
( sk_c7 != sk_c6
| sk_c3 = sk_c7 ),
inference(copy,[status(thm)],[c_31344]) ).
cnf(c_31345,plain,
( sk_c6 != sk_c6
| sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_29356,c_28767]) ).
cnf(c_30125,plain,
( sk_c7 != sk_c6
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_31345]) ).
cnf(c_31346,plain,
( sk_c6 != sk_c6
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_29356,c_27879]) ).
cnf(c_30328,plain,
( sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_31346]) ).
cnf(c_31347,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_30050,c_30049]) ).
cnf(c_31348,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_31347]) ).
cnf(c_30951,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_31348]) ).
cnf(c_31349,plain,
( sk_c7 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_30951,c_30328]) ).
cnf(c_31350,plain,
( sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_30951,c_31349]) ).
cnf(c_31250,plain,
multiply(sk_c6,sk_c6) != sk_c6,
inference(copy,[status(thm)],[c_31350]) ).
cnf(c_31351,plain,
( sk_c6 != sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_30951,c_30125]) ).
cnf(c_31253,plain,
sk_c4 = sk_c3,
inference(copy,[status(thm)],[c_31351]) ).
cnf(c_31352,plain,
( sk_c7 != sk_c6
| sk_c3 = sk_c6 ),
inference(paramod,[status(thm)],[c_30951,c_30109]) ).
cnf(c_31353,plain,
( sk_c6 != sk_c6
| sk_c3 = sk_c6 ),
inference(paramod,[status(thm)],[c_30951,c_31352]) ).
cnf(c_31254,plain,
sk_c3 = sk_c6,
inference(copy,[status(thm)],[c_31353]) ).
cnf(c_31354,plain,
( multiply(A,sk_c1) = A
| multiply(sk_c6,sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_31253,c_30047]) ).
cnf(c_31355,plain,
( multiply(A,sk_c1) = A
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_31254,c_31354]) ).
cnf(c_31356,plain,
( multiply(A,sk_c1) = A
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_30951,c_31355]) ).
cnf(c_31257,plain,
multiply(A,sk_c1) = A,
inference(resolve,[status(thm)],[c_31250,c_31356]) ).
cnf(c_31357,plain,
( multiply(A,sk_c1) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_31253,c_30030]) ).
cnf(c_31358,plain,
( multiply(A,sk_c1) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_31254,c_31357]) ).
cnf(c_31359,plain,
( multiply(A,sk_c1) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_30951,c_31358]) ).
cnf(c_31360,plain,
( A = multiply(A,sk_c6)
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_31257,c_31359]) ).
cnf(c_31361,plain,
( multiply(A,sk_c6) = A
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(copy,[status(thm)],[c_31360]) ).
cnf(c_31264,plain,
multiply(A,sk_c6) = A,
inference(resolve,[status(thm)],[c_31250,c_31361]) ).
cnf(c_31265,plain,
$false,
inference(resolve,[status(thm)],[c_31264,c_31250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP352-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.36 % Computer : n004.cluster.edu
% 0.11/5.36 % Model : x86_64 x86_64
% 0.11/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.36 % Memory : 8046.5625MB
% 0.11/5.36 % OS : Linux 6.8.0-71-generic
% 0.11/5.36 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 14:47:42 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.37 % Process 3438576 was started by sandbox on n004,
% 0.11/5.37 % Fri Sep 25 14:47:42 2026
% 0.11/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.37
% 0.11/5.37 % From the command line: assign(max_seconds, 300).
% 170.45/27.77
% 170.45/27.77 % given #500 (A,wt=50): 102 multiply(sk_c3,sk_c6) = sk_c7 | multiply(sk_c6,sk_c5) != sk_c7 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(sk_c1,sk_c6) != sk_c5 | sk_c7 != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | inverse(B) != sk_c7 | multiply(B,sk_c6) != sk_c7 | multiply(C,sk_c6) != sk_c7 | inverse(C) != sk_c6. [para(16(a,1),29(e,1))].
% 170.45/27.77
% 170.45/27.77 % SZS status Unsatisfiable for theBenchmark
% 170.45/27.77
% 170.45/27.77 % Proof 1 at 19.48 (+ 2.79) seconds.
% 170.45/27.77 % Length of proof is 124.
% 170.45/27.77 % Level of proof is 24.
% 170.45/27.77 % Maximum clause weight is 46.000.
% 170.45/27.77 % Given clauses 892.
% 170.45/27.77
% 170.45/27.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------