%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP262-1 : 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 : n006.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 07:28:29 AM UTC 2026
% Result : Unsatisfiable 224.50s 29.90s
% Output : CNFRefutation 224.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 21
% Syntax : Number of formulae : 227 ( 34 unt; 0 def)
% Number of atoms : 619 ( 618 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 643 ( 251 ~; 392 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 5 ( 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 : 93 ( 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_1,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_19,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_26,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(VAR_3,sk_c5) != sk_c6
| inverse(VAR_3) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c5
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
cnf(c_30,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_33,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_30460,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_30461,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_30460]) ).
cnf(c_37,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_30461]) ).
cnf(c_40,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_43,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_47,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_48,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_49,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_50,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_30462,plain,
( multiply(multiply(A,sk_c2),sk_c6) = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_52,plain,
( multiply(A,multiply(sk_c2,sk_c6)) = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3,c_30462]) ).
cnf(c_63,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_30463,plain,
( multiply(sk_c6,A) = multiply(sk_c5,multiply(sk_c7,A))
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_24,c_3]) ).
cnf(c_64,plain,
( multiply(sk_c5,multiply(sk_c7,A)) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_30463]) ).
cnf(c_313,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_37]) ).
cnf(c_317,plain,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_37]) ).
cnf(c_319,plain,
( multiply(inverse(sk_c4),sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_37]) ).
cnf(c_329,plain,
( multiply(inverse(sk_c4),sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_18,c_37]) ).
cnf(c_340,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_37,c_37]) ).
cnf(c_341,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_340,c_313]) ).
cnf(c_342,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_341,c_2]) ).
cnf(c_485,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_340,c_2]) ).
cnf(c_502,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_340,c_37]) ).
cnf(c_30464,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_340,c_341]) ).
cnf(c_30465,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_341,c_30464]) ).
cnf(c_503,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_30465]) ).
cnf(c_533,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_503]) ).
cnf(c_535,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_503]) ).
cnf(c_542,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_22,c_503]) ).
cnf(c_30466,plain,
( multiply(inverse(B),sk_c5) != sk_c6
| B != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_503,c_33]) ).
cnf(c_560,plain,
( multiply(inverse(B),sk_c5) != sk_c6
| sk_c6 != B
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_30466]) ).
cnf(c_30467,plain,
identity = multiply(A,multiply(B,inverse(multiply(A,B)))),
inference(paramod,[status(thm)],[c_485,c_3]) ).
cnf(c_578,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(copy,[status(thm)],[c_30467]) ).
cnf(c_581,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9,c_485]) ).
cnf(c_588,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_19,c_485]) ).
cnf(c_595,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_47,c_485]) ).
cnf(c_596,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_49,c_485]) ).
cnf(c_633,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c7) = sk_c3 ),
inference(paramod,[status(thm)],[c_533,c_2]) ).
cnf(c_660,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_535,c_2]) ).
cnf(c_793,plain,
( inverse(sk_c6) = sk_c2
| inverse(sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_542,c_503]) ).
cnf(c_1003,plain,
( multiply(sk_c6,multiply(sk_c4,A)) = A
| inverse(sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_793,c_502]) ).
cnf(c_2190,plain,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_48,c_37]) ).
cnf(c_2428,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_633,c_503]) ).
cnf(c_2542,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_660,c_503]) ).
cnf(c_2575,plain,
( multiply(inverse(sk_c4),sk_c6) = sk_c5
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_50,c_37]) ).
cnf(c_30468,plain,
multiply(inverse(A),identity) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_578,c_37]) ).
cnf(c_30469,plain,
inverse(A) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_341,c_30468]) ).
cnf(c_5204,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(copy,[status(thm)],[c_30469]) ).
cnf(c_30470,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_5204,c_37]) ).
cnf(c_5458,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_30470]) ).
cnf(c_30471,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_581,c_4]) ).
cnf(c_5491,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_30471]) ).
cnf(c_5736,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5491,c_37]) ).
cnf(c_30472,plain,
( multiply(A,identity) = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_588,c_52]) ).
cnf(c_30473,plain,
( A = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_341,c_30472]) ).
cnf(c_30474,plain,
( multiply(A,sk_c5) = A
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_30473]) ).
cnf(c_6168,plain,
( multiply(A,sk_c5) = A
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_30474]) ).
cnf(c_30475,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_595,c_40]) ).
cnf(c_6828,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(copy,[status(thm)],[c_30475]) ).
cnf(c_30476,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_6828,c_37]) ).
cnf(c_6831,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_341,c_30476]) ).
cnf(c_30477,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_596,c_43]) ).
cnf(c_7229,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(copy,[status(thm)],[c_30477]) ).
cnf(c_30478,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_7229,c_37]) ).
cnf(c_7232,plain,
( inverse(sk_c6) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_341,c_30478]) ).
cnf(c_7483,plain,
( multiply(sk_c4,multiply(sk_c6,A)) = A
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_7232,c_37]) ).
cnf(c_30479,plain,
( multiply(multiply(inverse(C),inverse(B)),sk_c5) != sk_c6
| sk_c6 != multiply(B,C)
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_5458,c_560]) ).
cnf(c_30480,plain,
( multiply(inverse(C),multiply(inverse(B),sk_c5)) != sk_c6
| sk_c6 != multiply(B,C)
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_30479]) ).
cnf(c_8744,plain,
( multiply(inverse(C),multiply(inverse(B),sk_c5)) != sk_c6
| multiply(B,C) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_30480]) ).
cnf(c_30481,plain,
( inverse(sk_c7) = multiply(inverse(sk_c5),inverse(inverse(sk_c6)))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5736,c_5458]) ).
cnf(c_30482,plain,
( inverse(sk_c7) = multiply(inverse(sk_c5),sk_c6)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_503,c_30481]) ).
cnf(c_8787,plain,
( multiply(inverse(sk_c5),sk_c6) = inverse(sk_c7)
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30482]) ).
cnf(c_30483,plain,
( multiply(inverse(sk_c7),multiply(inverse(sk_c5),sk_c5)) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_8744]) ).
cnf(c_30484,plain,
( multiply(inverse(sk_c7),identity) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_30483]) ).
cnf(c_8973,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_341,c_30484]) ).
cnf(c_30485,plain,
( multiply(sk_c5,multiply(sk_c7,sk_c5)) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6168,c_64]) ).
cnf(c_9310,plain,
( multiply(sk_c5,multiply(sk_c7,sk_c5)) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_30485]) ).
cnf(c_30486,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c3
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_6831,c_8787]) ).
cnf(c_10785,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c3
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30486]) ).
cnf(c_30487,plain,
( inverse(sk_c3) = multiply(inverse(sk_c6),inverse(inverse(sk_c5)))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10785,c_5458]) ).
cnf(c_11052,plain,
( inverse(sk_c3) = multiply(inverse(sk_c6),sk_c5)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_503,c_30487]) ).
cnf(c_30488,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(inverse(B),inverse(A)) != sk_c6
| multiply(multiply(A,B),sk_c6) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_5458,c_8973]) ).
cnf(c_11197,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(inverse(B),inverse(A)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_30488]) ).
cnf(c_30489,plain,
( inverse(sk_c3) = multiply(sk_c4,sk_c5)
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_7232,c_11052]) ).
cnf(c_13380,plain,
( inverse(sk_c3) = multiply(sk_c4,sk_c5)
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30489]) ).
cnf(c_30490,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_317]) ).
cnf(c_14807,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_30490]) ).
cnf(c_30491,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_319]) ).
cnf(c_14839,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_30491]) ).
cnf(c_30492,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_17,c_329]) ).
cnf(c_15086,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_30492]) ).
cnf(c_16875,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c2
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_63,c_1003]) ).
cnf(c_30493,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2428,c_2190]) ).
cnf(c_16980,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_30493]) ).
cnf(c_30494,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_16980,c_37]) ).
cnf(c_17035,plain,
( inverse(sk_c7) = sk_c1
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_341,c_30494]) ).
cnf(c_17046,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_17035,c_2]) ).
cnf(c_30495,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_17046,c_14807]) ).
cnf(c_17133,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_30495]) ).
cnf(c_17174,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_17133,c_37]) ).
cnf(c_30496,plain,
( inverse(sk_c7) = multiply(inverse(sk_c6),inverse(inverse(sk_c7)))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_17174,c_5458]) ).
cnf(c_17215,plain,
( inverse(sk_c7) = multiply(inverse(sk_c6),sk_c7)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_503,c_30496]) ).
cnf(c_30497,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c3
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_17215,c_6831]) ).
cnf(c_17275,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c3
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30497]) ).
cnf(c_30498,plain,
( inverse(sk_c3) = multiply(inverse(sk_c7),inverse(inverse(sk_c6)))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_17275,c_5458]) ).
cnf(c_17305,plain,
( inverse(sk_c3) = multiply(inverse(sk_c7),sk_c6)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_503,c_30498]) ).
cnf(c_30499,plain,
( inverse(sk_c3) = multiply(sk_c3,sk_c6)
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_6831,c_17305]) ).
cnf(c_17498,plain,
( inverse(sk_c3) = multiply(sk_c3,sk_c6)
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30499]) ).
cnf(c_30500,plain,
( inverse(multiply(sk_c3,sk_c6)) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_17498,c_503]) ).
cnf(c_17517,plain,
( multiply(inverse(sk_c6),inverse(sk_c3)) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5458,c_30500]) ).
cnf(c_30501,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(inverse(inverse(sk_c6)),inverse(A)) != sk_c6
| multiply(A,identity) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_11197]) ).
cnf(c_30502,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(inverse(inverse(sk_c6)),inverse(A)) != sk_c6
| A != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_341,c_30501]) ).
cnf(c_30503,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c6,inverse(A)) != sk_c6
| A != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_503,c_30502]) ).
cnf(c_18088,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c6,inverse(A)) != sk_c6
| sk_c5 != A
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_30503]) ).
cnf(c_30504,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c6,multiply(inverse(B),inverse(A))) != sk_c6
| sk_c5 != multiply(A,B)
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_5458,c_18088]) ).
cnf(c_18093,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c6,multiply(inverse(B),inverse(A))) != sk_c6
| multiply(A,B) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_30504]) ).
cnf(c_18094,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,multiply(inverse(sk_c7),inverse(sk_c6))) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_18093]) ).
cnf(c_30505,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c7,sk_c1) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2542,c_2575]) ).
cnf(c_18865,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_30505]) ).
cnf(c_30506,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_18865,c_37]) ).
cnf(c_18879,plain,
( inverse(sk_c7) = sk_c1
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_341,c_30506]) ).
cnf(c_18887,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_18879,c_2]) ).
cnf(c_30507,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| identity = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_18887,c_14839]) ).
cnf(c_18999,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_30507]) ).
cnf(c_30508,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_18999,c_7483]) ).
cnf(c_19008,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30508]) ).
cnf(c_30509,plain,
( inverse(sk_c3) = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19008,c_13380]) ).
cnf(c_19019,plain,
( inverse(sk_c3) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30509]) ).
cnf(c_30510,plain,
( multiply(inverse(sk_c6),sk_c6) = sk_c3
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19019,c_17517]) ).
cnf(c_30511,plain,
( identity = sk_c3
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_30510]) ).
cnf(c_19098,plain,
( identity = sk_c3
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30511]) ).
cnf(c_19107,plain,
( inverse(sk_c3) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19098,c_342]) ).
cnf(c_30512,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19107,c_19019]) ).
cnf(c_30513,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_30512]) ).
cnf(c_19347,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_30513]) ).
cnf(c_20025,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c2
| multiply(sk_c6,sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_19347,c_16875]) ).
cnf(c_30514,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_19347,c_342]) ).
cnf(c_28094,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_19347,c_30514]) ).
cnf(c_28095,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_19347,c_341]) ).
cnf(c_28111,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_19347,c_1]) ).
cnf(c_30515,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| inverse(sk_c6) = sk_c2
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_28111,c_20025]) ).
cnf(c_30516,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| sk_c6 = sk_c2
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_28094,c_30515]) ).
cnf(c_30517,plain,
( sk_c6 = sk_c5
| sk_c6 = sk_c2
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_28095,c_30516]) ).
cnf(c_30518,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_30517]) ).
cnf(c_30519,plain,
( sk_c5 = sk_c6
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_30518]) ).
cnf(c_28564,plain,
( sk_c5 = sk_c6
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_30519]) ).
cnf(c_30520,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,multiply(inverse(sk_c7),inverse(sk_c6))) != sk_c6
| sk_c7 != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_28111,c_18094]) ).
cnf(c_30521,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,multiply(inverse(sk_c7),sk_c6)) != sk_c6
| sk_c7 != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_28094,c_30520]) ).
cnf(c_30522,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,inverse(sk_c7)) != sk_c6
| sk_c7 != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_28095,c_30521]) ).
cnf(c_30523,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| sk_c7 != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_28111,c_30522]) ).
cnf(c_30524,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c7) != sk_c6
| sk_c7 != sk_c5
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_28095,c_30523]) ).
cnf(c_30525,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_30524]) ).
cnf(c_30526,plain,
( inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_30525]) ).
cnf(c_28577,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_30526]) ).
cnf(c_30527,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| sk_c2 = sk_c5 ),
inference(paramod,[status(thm)],[c_28095,c_15086]) ).
cnf(c_30528,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c5 ),
inference(paramod,[status(thm)],[c_28095,c_30527]) ).
cnf(c_29777,plain,
( sk_c5 = sk_c6
| sk_c2 = sk_c5 ),
inference(copy,[status(thm)],[c_30528]) ).
cnf(c_30529,plain,
( multiply(sk_c5,multiply(sk_c7,sk_c5)) = sk_c6
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_28111,c_9310]) ).
cnf(c_30279,plain,
( multiply(sk_c5,multiply(sk_c7,sk_c5)) = sk_c6
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_30529]) ).
cnf(c_30530,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_29777,c_28564]) ).
cnf(c_30531,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_30530]) ).
cnf(c_30384,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_30531]) ).
cnf(c_30532,plain,
( multiply(sk_c5,multiply(sk_c7,sk_c5)) = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_30384,c_30279]) ).
cnf(c_30533,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c5)) = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_30384,c_30532]) ).
cnf(c_30534,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c6)) = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_30384,c_30533]) ).
cnf(c_30535,plain,
( multiply(sk_c6,sk_c7) = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_28095,c_30534]) ).
cnf(c_30536,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_28111,c_30535]) ).
cnf(c_30537,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_30536]) ).
cnf(c_30432,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_30537]) ).
cnf(c_30538,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_30384,c_28577]) ).
cnf(c_30539,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_30432,c_30538]) ).
cnf(c_30540,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c5) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_28095,c_30539]) ).
cnf(c_30541,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| inverse(sk_c6) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_30384,c_30540]) ).
cnf(c_30542,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_28094,c_30541]) ).
cnf(c_30543,plain,
( inverse(sk_c7) != sk_c6
| sk_c5 != sk_c7
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_30432,c_30542]) ).
cnf(c_30544,plain,
( inverse(sk_c7) != sk_c6
| sk_c6 != sk_c7
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_30384,c_30543]) ).
cnf(c_30545,plain,
( inverse(sk_c7) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_30432,c_30544]) ).
cnf(c_30546,plain,
( inverse(sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_30432,c_30545]) ).
cnf(c_30547,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_28094,c_30546]) ).
cnf(c_30548,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_30547]) ).
cnf(c_30549,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_30548]) ).
cnf(c_30550,plain,
sk_c6 != sk_c6,
inference(copy,[status(thm)],[c_30549]) ).
cnf(c_30459,plain,
$false,
inference(copy,[status(thm)],[c_30550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP262-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n006.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Fri Sep 25 14:41:25 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.41 % Process 3137247 was started by sandbox on n006,
% 0.17/0.41 % Fri Sep 25 14:41:25 2026
% 0.17/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.42
% 0.17/0.42 % From the command line: assign(max_seconds, 300).
% 224.50/29.90
% 224.50/29.90 % given #500 (T,wt=9): 13922 identity = sk_c5 | multiply(sk_c6,inverse(sk_c3)) = sk_c5. [para(8277(b,1),12109(b,1,1)),merge(b)].
% 224.50/29.90
% 224.50/29.90 % given #1000 (F,wt=38): 12593 multiply(sk_c5,sk_c7) != sk_c6 | inverse(sk_c5) != sk_c7 | multiply(inverse(A),multiply(inverse(B),sk_c6)) != sk_c5 | multiply(B,A) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(inverse(sk_c7),sk_c6) != sk_c7 | inverse(sk_c7) != sk_c6. [para(5458(a,1),9002(c,1,1)),rewrite([3(14)]),flip(d)].
% 224.50/29.90
% 224.50/29.90 % SZS status Unsatisfiable for theBenchmark
% 224.50/29.90
% 224.50/29.90 % Proof 1 at 24.14 (+ 5.13) seconds.
% 224.50/29.90 % Length of proof is 115.
% 224.50/29.90 % Level of proof is 25.
% 224.50/29.90 % Maximum clause weight is 46.000.
% 224.50/29.90 % Given clauses 1048.
% 224.50/29.90
% 224.50/29.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------