%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP289-1 : 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 : n011.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 07:28:33 AM UTC 2026
% Result : Unsatisfiable 94.40s 13.42s
% Output : CNFRefutation 94.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 117
% Number of leaves : 24
% Syntax : Number of formulae : 327 ( 35 unt; 0 def)
% Number of atoms : 997 ( 996 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1136 ( 466 ~; 670 |; 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 : 137 ( 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_c7,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
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,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c5) = 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,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c5) = 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_17,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_19,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c5) = 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_22,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c4,sk_c5) = 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] :
( 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
| 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_c7,sk_c6) != sk_c5 ),
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
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
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(sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_31,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| 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_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_33,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_19155,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_19156,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_19155]) ).
cnf(c_37,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_19156]) ).
cnf(c_51,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_54,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,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_56,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_57,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_58,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_61,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_64,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_67,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_68,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_69,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_26,c_2]) ).
cnf(c_70,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_71,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_105,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(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_29]) ).
cnf(c_201,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_105]) ).
cnf(c_457,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_55,c_2]) ).
cnf(c_480,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_57,c_2]) ).
cnf(c_501,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_68,c_2]) ).
cnf(c_524,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_70,c_2]) ).
cnf(c_829,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_37]) ).
cnf(c_860,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_54,c_37]) ).
cnf(c_865,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_67,c_37]) ).
cnf(c_868,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_457,c_37]) ).
cnf(c_869,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_480,c_37]) ).
cnf(c_870,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_501,c_37]) ).
cnf(c_871,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_524,c_37]) ).
cnf(c_872,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_37,c_37]) ).
cnf(c_873,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_872,c_829]) ).
cnf(c_874,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_873,c_871]) ).
cnf(c_875,plain,
( inverse(sk_c7) = sk_c3
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_873,c_870]) ).
cnf(c_876,plain,
( inverse(sk_c7) = sk_c1
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_873,c_869]) ).
cnf(c_877,plain,
( inverse(sk_c7) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_873,c_868]) ).
cnf(c_878,plain,
( inverse(sk_c6) = sk_c2
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_873,c_865]) ).
cnf(c_879,plain,
( inverse(sk_c7) = sk_c1
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_873,c_860]) ).
cnf(c_889,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_873,c_2]) ).
cnf(c_1130,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_875,c_2]) ).
cnf(c_1157,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_876,c_2]) ).
cnf(c_1184,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_877,c_2]) ).
cnf(c_1211,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_878,c_2]) ).
cnf(c_1213,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_879,c_2]) ).
cnf(c_19157,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_1157,c_51]) ).
cnf(c_1321,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(copy,[status(thm)],[c_19157]) ).
cnf(c_19158,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1321,c_37]) ).
cnf(c_1324,plain,
( inverse(sk_c6) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_873,c_19158]) ).
cnf(c_19159,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1211,c_19]) ).
cnf(c_1470,plain,
( identity = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_19159]) ).
cnf(c_1540,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1470,c_37]) ).
cnf(c_19160,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1213,c_9]) ).
cnf(c_1544,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_19160]) ).
cnf(c_1571,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1544,c_37]) ).
cnf(c_1579,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c5
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_874,c_1540]) ).
cnf(c_19161,plain,
( multiply(sk_c6,sk_c2) = identity
| sk_c7 = sk_c6
| identity = sk_c5
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_1579,c_71]) ).
cnf(c_1698,plain,
( sk_c7 = sk_c6
| identity = sk_c5
| multiply(sk_c6,sk_c2) = identity ),
inference(copy,[status(thm)],[c_19161]) ).
cnf(c_19162,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1698,c_37]) ).
cnf(c_1704,plain,
( inverse(sk_c6) = sk_c2
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_873,c_19162]) ).
cnf(c_1705,plain,
( multiply(sk_c2,sk_c6) = identity
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1704,c_2]) ).
cnf(c_19163,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1705,c_64]) ).
cnf(c_1773,plain,
( multiply(sk_c6,sk_c4) = identity
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19163]) ).
cnf(c_19164,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1773,c_37]) ).
cnf(c_1946,plain,
( inverse(sk_c6) = sk_c4
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_873,c_19164]) ).
cnf(c_19165,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1946,c_1540]) ).
cnf(c_1978,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19165]) ).
cnf(c_19166,plain,
( sk_c7 = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1978,c_23]) ).
cnf(c_2359,plain,
( multiply(sk_c2,sk_c6) = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19166]) ).
cnf(c_19167,plain,
( sk_c5 = identity
| sk_c7 = sk_c6
| identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_2359,c_1705]) ).
cnf(c_19168,plain,
( identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19167]) ).
cnf(c_19169,plain,
( identity = sk_c5
| sk_c7 = sk_c6
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19168]) ).
cnf(c_19170,plain,
( identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19169]) ).
cnf(c_2650,plain,
( sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19170]) ).
cnf(c_2652,plain,
( multiply(sk_c5,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2650,c_1]) ).
cnf(c_2662,plain,
( multiply(A,sk_c5) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2650,c_873]) ).
cnf(c_2770,plain,
( sk_c4 = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2662,c_13]) ).
cnf(c_2778,plain,
( multiply(sk_c7,sk_c1) = identity
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2662,c_58]) ).
cnf(c_19171,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2778,c_37]) ).
cnf(c_3470,plain,
( inverse(sk_c7) = sk_c1
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_873,c_19171]) ).
cnf(c_3476,plain,
( multiply(sk_c1,sk_c7) = identity
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3470,c_2]) ).
cnf(c_19172,plain,
( sk_c4 = sk_c6
| identity = sk_c6
| sk_c7 = sk_c6
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3476,c_2770]) ).
cnf(c_19173,plain,
( sk_c4 = sk_c6
| identity = sk_c6
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19172]) ).
cnf(c_3820,plain,
( identity = sk_c6
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19173]) ).
cnf(c_19174,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c5
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3820,c_2650]) ).
cnf(c_19175,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19174]) ).
cnf(c_3839,plain,
( sk_c5 = sk_c6
| sk_c4 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19175]) ).
cnf(c_6459,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c7
| multiply(inverse(sk_c6),sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_201]) ).
cnf(c_19176,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1324,c_1571]) ).
cnf(c_6836,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_19176]) ).
cnf(c_19177,plain,
( sk_c7 = sk_c4
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_6836,c_2662]) ).
cnf(c_6869,plain,
( sk_c4 = sk_c7
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_19177]) ).
cnf(c_19178,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c5
| sk_c4 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_6869,c_2650]) ).
cnf(c_19179,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c4 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19178]) ).
cnf(c_7662,plain,
( sk_c5 = sk_c6
| sk_c4 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19179]) ).
cnf(c_19180,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_7662,c_3839]) ).
cnf(c_19181,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19180]) ).
cnf(c_19182,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19181]) ).
cnf(c_7682,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19182]) ).
cnf(c_19183,plain,
( multiply(sk_c6,A) = A
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_7682,c_2652]) ).
cnf(c_7811,plain,
( multiply(sk_c6,A) = A
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19183]) ).
cnf(c_19184,plain,
( multiply(A,sk_c6) = A
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_7682,c_2662]) ).
cnf(c_7812,plain,
( multiply(A,sk_c6) = A
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19184]) ).
cnf(c_19185,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_7812,c_4]) ).
cnf(c_8524,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19185]) ).
cnf(c_19186,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6
| sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_8524,c_7811]) ).
cnf(c_19187,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19186]) ).
cnf(c_11518,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19187]) ).
cnf(c_19188,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_11518,c_7682]) ).
cnf(c_19189,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_19188]) ).
cnf(c_11662,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_19189]) ).
cnf(c_19190,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c7
| multiply(inverse(sk_c6),sk_c7) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_6459]) ).
cnf(c_19191,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c7
| multiply(inverse(sk_c6),sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19190]) ).
cnf(c_19192,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_19191]) ).
cnf(c_19193,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19192]) ).
cnf(c_19194,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19193]) ).
cnf(c_19195,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19194]) ).
cnf(c_19196,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_19195]) ).
cnf(c_19197,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_19196]) ).
cnf(c_12483,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_19197]) ).
cnf(c_19198,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_11662,c_1184]) ).
cnf(c_13797,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_11662,c_19198]) ).
cnf(c_13821,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_11662,c_1130]) ).
cnf(c_14241,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c3,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_11662,c_69]) ).
cnf(c_14246,plain,
( multiply(sk_c6,sk_c3) = identity
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_61]) ).
cnf(c_19199,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_11662,c_56]) ).
cnf(c_14251,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_11662,c_19199]) ).
cnf(c_19200,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_33]) ).
cnf(c_19201,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19200]) ).
cnf(c_19202,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19201]) ).
cnf(c_19203,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19202]) ).
cnf(c_19204,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19203]) ).
cnf(c_19205,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19204]) ).
cnf(c_19206,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_19205]) ).
cnf(c_14272,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_19206]) ).
cnf(c_19207,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| 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_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_31]) ).
cnf(c_19208,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| 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_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19207]) ).
cnf(c_19209,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| 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_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19208]) ).
cnf(c_19210,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19209]) ).
cnf(c_19211,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19210]) ).
cnf(c_19212,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(A,sk_c6) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_19211]) ).
cnf(c_14273,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_19212]) ).
cnf(c_19213,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_11662,c_11]) ).
cnf(c_14287,plain,
( multiply(sk_c3,sk_c6) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_11662,c_19213]) ).
cnf(c_19214,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_11662,c_10]) ).
cnf(c_14288,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_11662,c_19214]) ).
cnf(c_19215,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_4]) ).
cnf(c_19216,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_11662,c_19215]) ).
cnf(c_14294,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(copy,[status(thm)],[c_19216]) ).
cnf(c_19217,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_12483]) ).
cnf(c_19218,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_14294,c_19217]) ).
cnf(c_14804,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19218]) ).
cnf(c_19219,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_14272]) ).
cnf(c_19220,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_14294,c_19219]) ).
cnf(c_15620,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6 ),
inference(copy,[status(thm)],[c_19220]) ).
cnf(c_19221,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_14273]) ).
cnf(c_19222,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_14294,c_19221]) ).
cnf(c_15621,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6 ),
inference(copy,[status(thm)],[c_19222]) ).
cnf(c_19223,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_14273]) ).
cnf(c_19224,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_14294,c_19223]) ).
cnf(c_15623,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6 ),
inference(copy,[status(thm)],[c_19224]) ).
cnf(c_16454,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c6,
inference(paramod,[status(thm)],[c_14294,c_37]) ).
cnf(c_19225,plain,
( sk_c6 != sk_c6
| identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_16454,c_14804]) ).
cnf(c_16597,plain,
( identity != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19225]) ).
cnf(c_19226,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_15620]) ).
cnf(c_19227,plain,
( sk_c6 != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_16454,c_19226]) ).
cnf(c_16622,plain,
( inverse(sk_c6) != sk_c6
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19227]) ).
cnf(c_19228,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_15623]) ).
cnf(c_19229,plain,
( sk_c6 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_16454,c_19228]) ).
cnf(c_16767,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19229]) ).
cnf(c_16924,plain,
( inverse(multiply(A,B)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c5
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_16767]) ).
cnf(c_19230,plain,
( sk_c6 = identity
| multiply(sk_c6,sk_c2) = identity
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_14241,c_13821]) ).
cnf(c_19231,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c2) = identity
| multiply(sk_c6,sk_c2) = identity ),
inference(copy,[status(thm)],[c_19230]) ).
cnf(c_17033,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c2) = identity ),
inference(copy,[status(thm)],[c_19231]) ).
cnf(c_19232,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_17033,c_37]) ).
cnf(c_17036,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_873,c_19232]) ).
cnf(c_19233,plain,
( sk_c2 = sk_c4
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_17036,c_1324]) ).
cnf(c_19234,plain,
( sk_c4 = sk_c2
| identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_19233]) ).
cnf(c_17039,plain,
( sk_c4 = sk_c2
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_19234]) ).
cnf(c_17120,plain,
( inverse(sk_c6) = identity
| sk_c4 = sk_c2 ),
inference(paramod,[status(thm)],[c_17039,c_889]) ).
cnf(c_19235,plain,
( identity != sk_c5
| inverse(identity) != sk_c6
| identity != sk_c6
| sk_c4 = sk_c2 ),
inference(paramod,[status(thm)],[c_17120,c_16597]) ).
cnf(c_19236,plain,
( identity != sk_c5
| identity != sk_c6
| identity != sk_c6
| sk_c4 = sk_c2 ),
inference(paramod,[status(thm)],[c_889,c_19235]) ).
cnf(c_17128,plain,
( identity != sk_c5
| identity != sk_c6
| sk_c4 = sk_c2 ),
inference(copy,[status(thm)],[c_19236]) ).
cnf(c_19237,plain,
( inverse(sk_c6) = sk_c6
| sk_c4 = sk_c2
| sk_c4 = sk_c2 ),
inference(paramod,[status(thm)],[c_17039,c_17120]) ).
cnf(c_17144,plain,
( inverse(sk_c6) = sk_c6
| sk_c4 = sk_c2 ),
inference(copy,[status(thm)],[c_19237]) ).
cnf(c_19238,plain,
( sk_c4 = sk_c2
| identity != sk_c5
| sk_c4 = sk_c2 ),
inference(resolve,[status(thm)],[c_17128,c_17039]) ).
cnf(c_17145,plain,
( identity != sk_c5
| sk_c4 = sk_c2 ),
inference(copy,[status(thm)],[c_19238]) ).
cnf(c_19239,plain,
( multiply(sk_c6,sk_c6) = identity
| sk_c4 = sk_c2 ),
inference(paramod,[status(thm)],[c_17144,c_2]) ).
cnf(c_19240,plain,
( sk_c5 = identity
| sk_c4 = sk_c2 ),
inference(paramod,[status(thm)],[c_14294,c_19239]) ).
cnf(c_17214,plain,
( identity = sk_c5
| sk_c4 = sk_c2 ),
inference(copy,[status(thm)],[c_19240]) ).
cnf(c_19241,plain,
( sk_c4 = sk_c2
| sk_c4 = sk_c2 ),
inference(resolve,[status(thm)],[c_17214,c_17145]) ).
cnf(c_17302,plain,
sk_c4 = sk_c2,
inference(copy,[status(thm)],[c_19241]) ).
cnf(c_19242,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_17302,c_524]) ).
cnf(c_18208,plain,
multiply(sk_c6,sk_c2) = identity,
inference(copy,[status(thm)],[c_19242]) ).
cnf(c_19243,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_17302,c_27]) ).
cnf(c_18211,plain,
inverse(sk_c2) = sk_c6,
inference(copy,[status(thm)],[c_19243]) ).
cnf(c_18302,plain,
( multiply(sk_c2,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6 ),
inference(resolve,[status(thm)],[c_18211,c_15621]) ).
cnf(c_19244,plain,
multiply(inverse(sk_c6),identity) = sk_c2,
inference(paramod,[status(thm)],[c_18208,c_37]) ).
cnf(c_18311,plain,
inverse(sk_c6) = sk_c2,
inference(paramod,[status(thm)],[c_873,c_19244]) ).
cnf(c_18318,plain,
( multiply(sk_c2,sk_c5) != sk_c6
| sk_c2 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_18311,c_18302]) ).
cnf(c_19245,plain,
( inverse(multiply(A,B)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c5
| inverse(sk_c2) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_18311,c_16924]) ).
cnf(c_19246,plain,
( inverse(multiply(A,B)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c5
| sk_c6 != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_18211,c_19245]) ).
cnf(c_18416,plain,
( inverse(multiply(A,B)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c5
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19246]) ).
cnf(c_19247,plain,
( inverse(sk_c6) != sk_c6
| inverse(sk_c2) != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_18311,c_16622]) ).
cnf(c_19248,plain,
( inverse(sk_c6) != sk_c6
| sk_c6 != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_18211,c_19247]) ).
cnf(c_19249,plain,
( sk_c2 != sk_c6
| sk_c6 != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_18311,c_19248]) ).
cnf(c_18430,plain,
( sk_c2 != sk_c6
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19249]) ).
cnf(c_18446,plain,
multiply(sk_c2,sk_c5) = sk_c6,
inference(paramod,[status(thm)],[c_18311,c_16454]) ).
cnf(c_19250,plain,
( sk_c6 != sk_c6
| sk_c2 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_18446,c_18318]) ).
cnf(c_18548,plain,
( sk_c2 != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c6 ),
inference(copy,[status(thm)],[c_19250]) ).
cnf(c_18560,plain,
multiply(sk_c2,sk_c6) = identity,
inference(paramod,[status(thm)],[c_18311,c_2]) ).
cnf(c_18597,plain,
( multiply(sk_c6,sk_c3) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_18560,c_14246]) ).
cnf(c_18605,plain,
( multiply(sk_c1,sk_c6) = sk_c6
| sk_c2 != sk_c6
| multiply(sk_c3,sk_c6) != sk_c6 ),
inference(resolve,[status(thm)],[c_18548,c_14288]) ).
cnf(c_19251,plain,
( multiply(inverse(sk_c6),identity) = sk_c3
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_18597,c_37]) ).
cnf(c_19252,plain,
( multiply(sk_c2,identity) = sk_c3
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_18311,c_19251]) ).
cnf(c_19253,plain,
( sk_c2 = sk_c3
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_873,c_19252]) ).
cnf(c_18651,plain,
( sk_c3 = sk_c2
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_19253]) ).
cnf(c_18656,plain,
( multiply(A,sk_c5) = A
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_18651,c_873]) ).
cnf(c_19254,plain,
( inverse(multiply(A,inverse(sk_c6))) != sk_c6
| multiply(A,identity) != sk_c5
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_18416]) ).
cnf(c_19255,plain,
( inverse(multiply(A,inverse(sk_c6))) != sk_c6
| A != sk_c5
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_873,c_19254]) ).
cnf(c_19256,plain,
( inverse(multiply(A,sk_c2)) != sk_c6
| A != sk_c5
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_18311,c_19255]) ).
cnf(c_18662,plain,
( inverse(multiply(A,sk_c2)) != sk_c6
| sk_c5 != A
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19256]) ).
cnf(c_19257,plain,
( inverse(multiply(A,multiply(B,sk_c2))) != sk_c6
| sk_c5 != multiply(A,B)
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_18662]) ).
cnf(c_18671,plain,
( inverse(multiply(A,multiply(B,sk_c2))) != sk_c6
| multiply(A,B) != sk_c5
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19257]) ).
cnf(c_18678,plain,
( sk_c2 = sk_c6
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_18656,c_18446]) ).
cnf(c_19258,plain,
( sk_c6 = identity
| multiply(sk_c6,sk_c1) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_14251,c_13797]) ).
cnf(c_19259,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c1) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_19258]) ).
cnf(c_18735,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_19259]) ).
cnf(c_19260,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_18735,c_37]) ).
cnf(c_19261,plain,
( multiply(sk_c2,identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_18311,c_19260]) ).
cnf(c_18743,plain,
( sk_c2 = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_873,c_19261]) ).
cnf(c_18782,plain,
( multiply(sk_c6,A) = A
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_18743,c_1]) ).
cnf(c_19262,plain,
( inverse(sk_c6) = identity
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_18743,c_889]) ).
cnf(c_19263,plain,
( sk_c2 = identity
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_18311,c_19262]) ).
cnf(c_18784,plain,
( identity = sk_c2
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_19263]) ).
cnf(c_19264,plain,
( sk_c2 = sk_c1
| sk_c2 = sk_c6
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_18784,c_18743]) ).
cnf(c_18798,plain,
( sk_c2 = sk_c6
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_19264]) ).
cnf(c_19265,plain,
( sk_c2 = sk_c6
| sk_c3 = sk_c1
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_18798,c_18678]) ).
cnf(c_18812,plain,
( sk_c3 = sk_c1
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_19265]) ).
cnf(c_19266,plain,
( inverse(identity) != sk_c6
| multiply(inverse(multiply(A,sk_c2)),A) != sk_c5
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_18671]) ).
cnf(c_19267,plain,
( identity != sk_c6
| multiply(inverse(multiply(A,sk_c2)),A) != sk_c5
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_889,c_19266]) ).
cnf(c_18818,plain,
( multiply(inverse(multiply(A,sk_c2)),A) != sk_c5
| identity != sk_c6 ),
inference(copy,[status(thm)],[c_19267]) ).
cnf(c_19268,plain,
( multiply(inverse(sk_c2),sk_c6) != sk_c5
| identity != sk_c6
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_18782,c_18818]) ).
cnf(c_19269,plain,
( multiply(sk_c6,sk_c6) != sk_c5
| identity != sk_c6
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_18211,c_19268]) ).
cnf(c_19270,plain,
( sk_c5 != sk_c5
| identity != sk_c6
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_14294,c_19269]) ).
cnf(c_18886,plain,
( identity != sk_c6
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_19270]) ).
cnf(c_19271,plain,
( sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(resolve,[status(thm)],[c_18886,c_18743]) ).
cnf(c_18914,plain,
sk_c2 = sk_c1,
inference(copy,[status(thm)],[c_19271]) ).
cnf(c_18955,plain,
( sk_c3 = sk_c1
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_18914,c_18812]) ).
cnf(c_19029,plain,
( multiply(sk_c1,sk_c6) = sk_c6
| sk_c1 != sk_c6
| multiply(sk_c3,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_18914,c_18605]) ).
cnf(c_19032,plain,
multiply(sk_c1,sk_c6) = identity,
inference(paramod,[status(thm)],[c_18914,c_18560]) ).
cnf(c_19041,plain,
( sk_c1 != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_18914,c_18430]) ).
cnf(c_19047,plain,
inverse(sk_c6) = sk_c1,
inference(paramod,[status(thm)],[c_18914,c_18311]) ).
cnf(c_19050,plain,
multiply(sk_c6,sk_c1) = identity,
inference(paramod,[status(thm)],[c_18914,c_18208]) ).
cnf(c_19053,plain,
( identity = sk_c6
| sk_c1 != sk_c6
| multiply(sk_c3,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_19032,c_19029]) ).
cnf(c_19068,plain,
( multiply(sk_c3,sk_c6) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19032,c_14287]) ).
cnf(c_19272,plain,
( multiply(sk_c1,sk_c6) = sk_c6
| identity = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_18955,c_19068]) ).
cnf(c_19273,plain,
( identity = sk_c6
| identity = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_19032,c_19272]) ).
cnf(c_19088,plain,
( identity = sk_c6
| sk_c1 = sk_c6 ),
inference(copy,[status(thm)],[c_19273]) ).
cnf(c_19274,plain,
( inverse(sk_c6) = identity
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_19088,c_889]) ).
cnf(c_19275,plain,
( sk_c1 = identity
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_19047,c_19274]) ).
cnf(c_19103,plain,
( identity = sk_c1
| sk_c1 = sk_c6 ),
inference(copy,[status(thm)],[c_19275]) ).
cnf(c_19276,plain,
( sk_c1 = sk_c6
| sk_c1 = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_19103,c_19088]) ).
cnf(c_19277,plain,
( sk_c1 = sk_c6
| sk_c1 = sk_c6 ),
inference(copy,[status(thm)],[c_19276]) ).
cnf(c_19114,plain,
sk_c1 = sk_c6,
inference(copy,[status(thm)],[c_19277]) ).
cnf(c_19278,plain,
( identity = sk_c6
| sk_c6 != sk_c6
| multiply(sk_c3,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_19114,c_19053]) ).
cnf(c_19122,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c6) != sk_c6 ),
inference(copy,[status(thm)],[c_19278]) ).
cnf(c_19279,plain,
multiply(sk_c6,sk_c6) = identity,
inference(paramod,[status(thm)],[c_19114,c_19050]) ).
cnf(c_19280,plain,
sk_c5 = identity,
inference(paramod,[status(thm)],[c_14294,c_19279]) ).
cnf(c_19124,plain,
identity = sk_c5,
inference(copy,[status(thm)],[c_19280]) ).
cnf(c_19281,plain,
( sk_c1 != sk_c6
| sk_c5 != sk_c6 ),
inference(paramod,[status(thm)],[c_19124,c_19041]) ).
cnf(c_19282,plain,
( sk_c6 != sk_c6
| sk_c5 != sk_c6 ),
inference(paramod,[status(thm)],[c_19114,c_19281]) ).
cnf(c_19128,plain,
sk_c5 != sk_c6,
inference(copy,[status(thm)],[c_19282]) ).
cnf(c_19283,plain,
( sk_c5 = sk_c6
| multiply(sk_c3,sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_19124,c_19122]) ).
cnf(c_19144,plain,
multiply(sk_c3,sk_c6) != sk_c6,
inference(resolve,[status(thm)],[c_19128,c_19283]) ).
cnf(c_19284,plain,
( multiply(sk_c3,sk_c6) = sk_c6
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_19124,c_19068]) ).
cnf(c_19285,plain,
multiply(sk_c3,sk_c6) = sk_c6,
inference(resolve,[status(thm)],[c_19128,c_19284]) ).
cnf(c_19154,plain,
$false,
inference(resolve,[status(thm)],[c_19144,c_19285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP289-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n011.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 14:43:28 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 2251897 was started by sandbox on n011,
% 0.18/0.45 % Fri Sep 25 14:43:28 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 94.40/13.42
% 94.40/13.42 % given #500 (F,wt=38): 16586 identity != sk_c6 | sk_c5 != A | inverse(multiply(A,inverse(sk_c6))) != sk_c6 | multiply(A,sk_c6) != sk_c6. [back_rewrite(14919),rewrite([16454(15)])].
% 94.40/13.42
% 94.40/13.42 % SZS status Unsatisfiable for theBenchmark
% 94.40/13.42
% 94.40/13.42 % Proof 1 at 4.35 (+ 0.54) seconds.
% 94.40/13.42 % Length of proof is 172.
% 94.40/13.42 % Level of proof is 52.
% 94.40/13.42 % Maximum clause weight is 62.000.
% 94.40/13.42 % Given clauses 625.
% 94.40/13.42
% 94.40/13.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------