%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP348-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 148.78s 25.17s
% Output : CNFRefutation 148.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 20
% Syntax : Number of formulae : 293 ( 36 unt; 0 def)
% Number of atoms : 676 ( 675 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 493 ( 110 ~; 383 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( inverse(sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c3,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c4) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c4) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_21,axiom,
! [VAR_0,VAR_1,VAR_2] :
( multiply(VAR_2,sk_c5) != sk_c6
| inverse(VAR_2) != sk_c6
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(VAR_1,sk_c4) != sk_c5
| inverse(VAR_1) != sk_c5
| multiply(VAR_0,sk_c5) != sk_c6
| inverse(VAR_0) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(B,sk_c4) != sk_c5
| inverse(B) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
cnf(c_25907,plain,
( multiply(A,sk_c5) != sk_c6
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(B,sk_c4) != sk_c5
| inverse(B) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(factor,[status(thm)],[c_24]) ).
cnf(c_25,plain,
( multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| multiply(B,sk_c4) != sk_c5
| inverse(B) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(copy,[status(thm)],[c_25907]) ).
cnf(c_26,plain,
( inverse(sk_c4) != sk_c5
| multiply(A,sk_c4) != sk_c5
| inverse(A) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_25908,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_25909,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_25908]) ).
cnf(c_29,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_25909]) ).
cnf(c_30,plain,
( multiply(sk_c5,sk_c4) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_25910,plain,
( multiply(sk_c6,A) = multiply(sk_c4,multiply(sk_c5,A))
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_31,plain,
( multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25910]) ).
cnf(c_25911,plain,
( multiply(multiply(A,sk_c4),sk_c5) = multiply(A,sk_c6)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_32,plain,
( multiply(A,multiply(sk_c4,sk_c5)) = multiply(A,sk_c6)
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_3,c_25911]) ).
cnf(c_36,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_37,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_38,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_39,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_25912,plain,
( multiply(sk_c6,A) = multiply(sk_c1,multiply(sk_c5,A))
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_44,plain,
( multiply(sk_c1,multiply(sk_c5,A)) = multiply(sk_c6,A)
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_25912]) ).
cnf(c_46,plain,
( multiply(sk_c5,sk_c2) = identity
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_47,plain,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_50,plain,
( multiply(sk_c5,sk_c4) = identity
| multiply(sk_c2,sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_93,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_29]) ).
cnf(c_97,plain,
( multiply(sk_c6,multiply(sk_c3,A)) = A
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_6,c_29]) ).
cnf(c_98,plain,
( multiply(inverse(sk_c3),sk_c6) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_7,c_29]) ).
cnf(c_99,plain,
( multiply(sk_c6,multiply(sk_c1,A)) = A
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_8,c_29]) ).
cnf(c_101,plain,
( multiply(sk_c6,multiply(sk_c1,A)) = A
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_29]) ).
cnf(c_105,plain,
( multiply(sk_c6,multiply(sk_c3,A)) = A
| multiply(sk_c1,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_29]) ).
cnf(c_106,plain,
( multiply(inverse(sk_c1),sk_c6) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_29]) ).
cnf(c_112,plain,
( multiply(inverse(sk_c2),sk_c5) = sk_c4
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_21,c_29]) ).
cnf(c_115,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_29,c_29]) ).
cnf(c_116,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_115,c_93]) ).
cnf(c_117,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_116,c_2]) ).
cnf(c_135,plain,
( multiply(sk_c6,multiply(sk_c3,A)) = A
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_38,c_29]) ).
cnf(c_177,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_115,c_2]) ).
cnf(c_25913,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_115,c_116]) ).
cnf(c_25914,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_116,c_25913]) ).
cnf(c_193,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_25914]) ).
cnf(c_195,plain,
( multiply(inverse(sk_c6),A) = multiply(sk_c3,A)
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_38,c_115]) ).
cnf(c_206,plain,
( inverse(sk_c6) = sk_c1
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_193]) ).
cnf(c_210,plain,
( inverse(sk_c5) = sk_c2
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_16,c_193]) ).
cnf(c_212,plain,
( inverse(sk_c5) = sk_c2
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_18,c_193]) ).
cnf(c_213,plain,
( inverse(sk_c5) = sk_c2
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_193]) ).
cnf(c_25915,plain,
( multiply(sk_c4,identity) = multiply(sk_c6,sk_c4)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_30,c_31]) ).
cnf(c_25916,plain,
( sk_c4 = multiply(sk_c6,sk_c4)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_116,c_25915]) ).
cnf(c_25917,plain,
( multiply(sk_c6,sk_c4) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25916]) ).
cnf(c_227,plain,
( multiply(sk_c6,sk_c4) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25917]) ).
cnf(c_25918,plain,
identity = multiply(A,multiply(B,inverse(multiply(A,B)))),
inference(paramod,[status(thm)],[c_177,c_3]) ).
cnf(c_256,plain,
multiply(A,multiply(B,inverse(multiply(A,B)))) = identity,
inference(copy,[status(thm)],[c_25918]) ).
cnf(c_257,plain,
( multiply(sk_c4,sk_c5) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_4,c_177]) ).
cnf(c_271,plain,
( multiply(sk_c4,sk_c5) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_36,c_177]) ).
cnf(c_273,plain,
( multiply(sk_c4,sk_c5) = identity
| multiply(sk_c5,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_46,c_177]) ).
cnf(c_325,plain,
( inverse(sk_c6) = sk_c3
| inverse(sk_c6) = sk_c1 ),
inference(paramod,[status(thm)],[c_206,c_193]) ).
cnf(c_411,plain,
( multiply(sk_c5,sk_c4) = identity
| inverse(sk_c5) = sk_c2 ),
inference(paramod,[status(thm)],[c_210,c_2]) ).
cnf(c_434,plain,
( multiply(sk_c6,multiply(sk_c3,A)) = A
| inverse(sk_c5) = sk_c2 ),
inference(paramod,[status(thm)],[c_212,c_29]) ).
cnf(c_1002,plain,
( inverse(sk_c2) = sk_c5
| multiply(sk_c5,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_411,c_193]) ).
cnf(c_25919,plain,
( multiply(sk_c1,identity) = multiply(sk_c6,inverse(sk_c5))
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_177,c_44]) ).
cnf(c_25920,plain,
( sk_c1 = multiply(sk_c6,inverse(sk_c5))
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_116,c_25919]) ).
cnf(c_1098,plain,
( multiply(sk_c6,inverse(sk_c5)) = sk_c1
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_25920]) ).
cnf(c_1115,plain,
( multiply(inverse(sk_c2),sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_50,c_29]) ).
cnf(c_25921,plain,
multiply(inverse(A),identity) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_256,c_29]) ).
cnf(c_25922,plain,
inverse(A) = multiply(B,inverse(multiply(A,B))),
inference(paramod,[status(thm)],[c_116,c_25921]) ).
cnf(c_1144,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(copy,[status(thm)],[c_25922]) ).
cnf(c_25923,plain,
( multiply(sk_c6,multiply(sk_c4,inverse(sk_c4))) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_227,c_256]) ).
cnf(c_25924,plain,
( multiply(sk_c6,identity) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_177,c_25923]) ).
cnf(c_25925,plain,
( sk_c6 = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_116,c_25924]) ).
cnf(c_1162,plain,
( identity = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25925]) ).
cnf(c_1173,plain,
( multiply(inverse(sk_c5),sk_c4) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1162,c_29]) ).
cnf(c_25926,plain,
multiply(inverse(A),inverse(B)) = inverse(multiply(B,A)),
inference(paramod,[status(thm)],[c_1144,c_29]) ).
cnf(c_1188,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_25926]) ).
cnf(c_1198,plain,
( multiply(sk_c6,inverse(sk_c4)) = inverse(sk_c5)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1162,c_1144]) ).
cnf(c_25927,plain,
( multiply(A,identity) = multiply(A,sk_c6)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_257,c_32]) ).
cnf(c_25928,plain,
( A = multiply(A,sk_c6)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_116,c_25927]) ).
cnf(c_25929,plain,
( multiply(A,sk_c6) = A
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25928]) ).
cnf(c_1274,plain,
( multiply(A,sk_c6) = A
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25929]) ).
cnf(c_25930,plain,
( multiply(sk_c6,sk_c1) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_271,c_37]) ).
cnf(c_1332,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_25930]) ).
cnf(c_25931,plain,
( multiply(identity,A) = multiply(sk_c6,multiply(sk_c1,A))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1332,c_3]) ).
cnf(c_25932,plain,
( A = multiply(sk_c6,multiply(sk_c1,A))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_25931]) ).
cnf(c_1333,plain,
( multiply(sk_c6,multiply(sk_c1,A)) = A
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25932]) ).
cnf(c_25933,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1332,c_29]) ).
cnf(c_1335,plain,
( inverse(sk_c6) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_116,c_25933]) ).
cnf(c_1344,plain,
( inverse(sk_c1) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1335,c_193]) ).
cnf(c_25934,plain,
( multiply(sk_c5,sk_c2) = identity
| identity = sk_c6
| multiply(sk_c5,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_273,c_47]) ).
cnf(c_1376,plain,
( identity = sk_c6
| multiply(sk_c5,sk_c2) = identity ),
inference(copy,[status(thm)],[c_25934]) ).
cnf(c_25935,plain,
( multiply(inverse(sk_c5),identity) = sk_c2
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1376,c_29]) ).
cnf(c_1379,plain,
( inverse(sk_c5) = sk_c2
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_116,c_25935]) ).
cnf(c_1408,plain,
( multiply(sk_c2,multiply(sk_c5,A)) = A
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1379,c_29]) ).
cnf(c_25936,plain,
( multiply(sk_c2,sk_c4) = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1379,c_1173]) ).
cnf(c_1426,plain,
( multiply(sk_c2,sk_c4) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25936]) ).
cnf(c_25937,plain,
( inverse(inverse(sk_c5)) = multiply(inverse(inverse(sk_c4)),inverse(sk_c6))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1198,c_1188]) ).
cnf(c_25938,plain,
( sk_c5 = multiply(inverse(inverse(sk_c4)),inverse(sk_c6))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_193,c_25937]) ).
cnf(c_25939,plain,
( sk_c5 = multiply(sk_c4,inverse(sk_c6))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_193,c_25938]) ).
cnf(c_1941,plain,
( multiply(sk_c4,inverse(sk_c6)) = sk_c5
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25939]) ).
cnf(c_25940,plain,
( multiply(sk_c4,sk_c1) = sk_c5
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1335,c_1941]) ).
cnf(c_1963,plain,
( multiply(sk_c4,sk_c1) = sk_c5
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25940]) ).
cnf(c_1966,plain,
( multiply(inverse(sk_c4),sk_c5) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1963,c_29]) ).
cnf(c_25941,plain,
( inverse(sk_c1) = multiply(inverse(sk_c5),inverse(inverse(sk_c4)))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1966,c_1188]) ).
cnf(c_2262,plain,
( inverse(sk_c1) = multiply(inverse(sk_c5),sk_c4)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_193,c_25941]) ).
cnf(c_25942,plain,
( inverse(sk_c1) = multiply(sk_c2,sk_c4)
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1379,c_2262]) ).
cnf(c_4851,plain,
( inverse(sk_c1) = multiply(sk_c2,sk_c4)
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25942]) ).
cnf(c_25943,plain,
( sk_c5 = inverse(sk_c3)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_98,c_1274]) ).
cnf(c_25944,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25943]) ).
cnf(c_7179,plain,
( inverse(sk_c3) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25944]) ).
cnf(c_7180,plain,
( multiply(sk_c5,sk_c3) = identity
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_7179,c_2]) ).
cnf(c_25945,plain,
( sk_c5 = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_7179,c_6]) ).
cnf(c_25946,plain,
( sk_c6 = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25945]) ).
cnf(c_7181,plain,
( sk_c6 = sk_c5
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25946]) ).
cnf(c_7189,plain,
( multiply(inverse(sk_c5),sk_c4) = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_7181,c_29]) ).
cnf(c_25947,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),inverse(inverse(sk_c5)))
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_7189,c_1188]) ).
cnf(c_25948,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),sk_c5)
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_193,c_25947]) ).
cnf(c_7486,plain,
( multiply(inverse(sk_c4),sk_c5) = inverse(sk_c6)
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25948]) ).
cnf(c_25949,plain,
( multiply(sk_c4,identity) = multiply(sk_c6,sk_c3)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_7180,c_31]) ).
cnf(c_25950,plain,
( sk_c4 = multiply(sk_c6,sk_c3)
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_116,c_25949]) ).
cnf(c_25951,plain,
( multiply(sk_c6,sk_c3) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25950]) ).
cnf(c_7502,plain,
( multiply(sk_c6,sk_c3) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25951]) ).
cnf(c_25952,plain,
( multiply(inverse(inverse(sk_c4)),inverse(sk_c6)) = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_7486,c_29]) ).
cnf(c_7759,plain,
( multiply(sk_c4,inverse(sk_c6)) = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_193,c_25952]) ).
cnf(c_25953,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_11,c_106]) ).
cnf(c_8490,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_25953]) ).
cnf(c_25954,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_112]) ).
cnf(c_8984,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_25954]) ).
cnf(c_25955,plain,
( multiply(sk_c6,sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_1274,c_97]) ).
cnf(c_9257,plain,
( multiply(sk_c6,sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25955]) ).
cnf(c_25956,plain,
( sk_c6 = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_9257,c_7502]) ).
cnf(c_25957,plain,
( sk_c4 = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25956]) ).
cnf(c_9626,plain,
( sk_c4 = sk_c6
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(copy,[status(thm)],[c_25957]) ).
cnf(c_9629,plain,
( multiply(inverse(sk_c5),sk_c4) = sk_c6
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9626,c_29]) ).
cnf(c_25958,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),inverse(inverse(sk_c5)))
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9629,c_1188]) ).
cnf(c_25959,plain,
( inverse(sk_c6) = multiply(inverse(sk_c4),sk_c5)
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_193,c_25958]) ).
cnf(c_9824,plain,
( multiply(inverse(sk_c4),sk_c5) = inverse(sk_c6)
| sk_c4 = sk_c6 ),
inference(copy,[status(thm)],[c_25959]) ).
cnf(c_25960,plain,
( multiply(inverse(inverse(sk_c4)),inverse(sk_c6)) = sk_c5
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9824,c_29]) ).
cnf(c_10247,plain,
( multiply(sk_c4,inverse(sk_c6)) = sk_c5
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_193,c_25960]) ).
cnf(c_25961,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c1,sk_c5) = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_8490,c_105]) ).
cnf(c_10392,plain,
( multiply(sk_c1,sk_c5) = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_25961]) ).
cnf(c_25962,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| identity = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_10392,c_1333]) ).
cnf(c_10537,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_25962]) ).
cnf(c_25963,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_10392,c_99]) ).
cnf(c_10540,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_25963]) ).
cnf(c_25964,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_10392,c_101]) ).
cnf(c_10541,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_25964]) ).
cnf(c_10550,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10537,c_29]) ).
cnf(c_10771,plain,
( inverse(sk_c5) = sk_c4
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_10540,c_193]) ).
cnf(c_10834,plain,
( inverse(sk_c6) = sk_c3
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_10541,c_193]) ).
cnf(c_25965,plain,
( inverse(sk_c6) = multiply(inverse(sk_c5),inverse(inverse(sk_c6)))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10550,c_1188]) ).
cnf(c_10874,plain,
( inverse(sk_c6) = multiply(inverse(sk_c5),sk_c6)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_193,c_25965]) ).
cnf(c_25966,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c1
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10874,c_1335]) ).
cnf(c_11120,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c1
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25966]) ).
cnf(c_25967,plain,
( inverse(sk_c1) = multiply(inverse(sk_c6),inverse(inverse(sk_c5)))
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11120,c_1188]) ).
cnf(c_11210,plain,
( inverse(sk_c1) = multiply(inverse(sk_c6),sk_c5)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_193,c_25967]) ).
cnf(c_25968,plain,
( inverse(sk_c1) = multiply(sk_c1,sk_c5)
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1335,c_11210]) ).
cnf(c_11510,plain,
( inverse(sk_c1) = multiply(sk_c1,sk_c5)
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25968]) ).
cnf(c_25969,plain,
( inverse(multiply(sk_c1,sk_c5)) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11510,c_193]) ).
cnf(c_11530,plain,
( multiply(inverse(sk_c5),inverse(sk_c1)) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1188,c_25969]) ).
cnf(c_25970,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c6,sk_c1) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_39,c_135]) ).
cnf(c_11773,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_25970]) ).
cnf(c_25971,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_11773,c_29]) ).
cnf(c_12582,plain,
( inverse(sk_c6) = sk_c1
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_116,c_25971]) ).
cnf(c_25972,plain,
( sk_c1 = sk_c3
| multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_12582,c_10834]) ).
cnf(c_12645,plain,
( sk_c1 = sk_c3
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_25972]) ).
cnf(c_12658,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| sk_c1 = sk_c3 ),
inference(paramod,[status(thm)],[c_12645,c_29]) ).
cnf(c_25973,plain,
( multiply(sk_c6,sk_c6) = sk_c5
| inverse(sk_c5) = sk_c2
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_8490,c_434]) ).
cnf(c_14377,plain,
( inverse(sk_c5) = sk_c2
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_25973]) ).
cnf(c_25974,plain,
( sk_c2 = sk_c4
| multiply(sk_c6,sk_c6) = sk_c5
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_14377,c_10771]) ).
cnf(c_14419,plain,
( sk_c2 = sk_c4
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(copy,[status(thm)],[c_25974]) ).
cnf(c_14430,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| sk_c2 = sk_c4 ),
inference(paramod,[status(thm)],[c_14419,c_29]) ).
cnf(c_25975,plain,
( multiply(sk_c6,sk_c2) = sk_c1
| multiply(sk_c3,sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_213,c_1098]) ).
cnf(c_14970,plain,
( multiply(sk_c6,sk_c2) = sk_c1
| multiply(sk_c3,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_25975]) ).
cnf(c_14981,plain,
( multiply(inverse(sk_c3),sk_c6) = sk_c5
| multiply(sk_c6,sk_c2) = sk_c1 ),
inference(paramod,[status(thm)],[c_14970,c_29]) ).
cnf(c_25976,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = identity
| multiply(sk_c5,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_1002,c_1115]) ).
cnf(c_15026,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| multiply(sk_c5,sk_c4) = identity ),
inference(copy,[status(thm)],[c_25976]) ).
cnf(c_25977,plain,
( multiply(inverse(sk_c5),identity) = sk_c4
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_15026,c_29]) ).
cnf(c_15038,plain,
( inverse(sk_c5) = sk_c4
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_116,c_25977]) ).
cnf(c_15044,plain,
( multiply(sk_c4,sk_c5) = identity
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_15038,c_2]) ).
cnf(c_25978,plain,
( multiply(sk_c5,sk_c5) = sk_c4
| identity = sk_c6
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(paramod,[status(thm)],[c_15044,c_8984]) ).
cnf(c_15197,plain,
( identity = sk_c6
| multiply(sk_c5,sk_c5) = sk_c4 ),
inference(copy,[status(thm)],[c_25978]) ).
cnf(c_25979,plain,
( multiply(sk_c2,sk_c4) = sk_c5
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15197,c_1408]) ).
cnf(c_15204,plain,
( multiply(sk_c2,sk_c4) = sk_c5
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25979]) ).
cnf(c_25980,plain,
( sk_c5 = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15204,c_1426]) ).
cnf(c_25981,plain,
( sk_c6 = sk_c5
| identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25980]) ).
cnf(c_15220,plain,
( sk_c6 = sk_c5
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25981]) ).
cnf(c_25982,plain,
( inverse(sk_c1) = sk_c5
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15204,c_4851]) ).
cnf(c_15222,plain,
( inverse(sk_c1) = sk_c5
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25982]) ).
cnf(c_25983,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| multiply(sk_c6,sk_c1) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_39,c_195]) ).
cnf(c_15231,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_25983]) ).
cnf(c_15243,plain,
( inverse(sk_c6) = identity
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_15220,c_117]) ).
cnf(c_25984,plain,
( multiply(inverse(sk_c5),sk_c5) = sk_c1
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15222,c_11530]) ).
cnf(c_25985,plain,
( identity = sk_c1
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_25984]) ).
cnf(c_15309,plain,
( identity = sk_c1
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25985]) ).
cnf(c_15318,plain,
( inverse(sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15309,c_117]) ).
cnf(c_25986,plain,
( multiply(sk_c4,identity) = sk_c5
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_15243,c_7759]) ).
cnf(c_25987,plain,
( sk_c4 = sk_c5
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_116,c_25986]) ).
cnf(c_15373,plain,
( sk_c4 = sk_c5
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25987]) ).
cnf(c_25988,plain,
( multiply(identity,sk_c5) = sk_c6
| sk_c1 = sk_c3
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_15243,c_12658]) ).
cnf(c_25989,plain,
( sk_c5 = sk_c6
| sk_c1 = sk_c3
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1,c_25988]) ).
cnf(c_25990,plain,
( sk_c6 = sk_c5
| sk_c1 = sk_c3
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25989]) ).
cnf(c_15384,plain,
( sk_c1 = sk_c3
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25990]) ).
cnf(c_25991,plain,
( multiply(identity,sk_c5) = sk_c6
| sk_c2 = sk_c4
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_15243,c_14430]) ).
cnf(c_25992,plain,
( sk_c5 = sk_c6
| sk_c2 = sk_c4
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1,c_25991]) ).
cnf(c_25993,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c4
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25992]) ).
cnf(c_15396,plain,
( sk_c2 = sk_c4
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25993]) ).
cnf(c_25994,plain,
( inverse(sk_c6) = sk_c3
| inverse(sk_c6) = sk_c3
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_15384,c_325]) ).
cnf(c_15519,plain,
( inverse(sk_c6) = sk_c3
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25994]) ).
cnf(c_25995,plain,
( sk_c2 = sk_c5
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_15373,c_15396]) ).
cnf(c_15554,plain,
( sk_c2 = sk_c5
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_25995]) ).
cnf(c_25996,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15318,c_1344]) ).
cnf(c_25997,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25996]) ).
cnf(c_15653,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_25997]) ).
cnf(c_15744,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| multiply(sk_c6,sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_15653,c_15231]) ).
cnf(c_25998,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_15653,c_117]) ).
cnf(c_19105,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_15653,c_25998]) ).
cnf(c_19106,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_15653,c_116]) ).
cnf(c_19120,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_15653,c_1]) ).
cnf(c_25999,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_19120,c_15744]) ).
cnf(c_26000,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_19105,c_25999]) ).
cnf(c_26001,plain,
( sk_c5 = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_19120,c_26000]) ).
cnf(c_19335,plain,
( sk_c6 = sk_c5
| sk_c1 = sk_c6 ),
inference(copy,[status(thm)],[c_26001]) ).
cnf(c_26002,plain,
( sk_c6 = sk_c3
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_19105,c_15519]) ).
cnf(c_19340,plain,
( sk_c3 = sk_c6
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_26002]) ).
cnf(c_26003,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_19105,c_10247]) ).
cnf(c_19622,plain,
( sk_c4 = sk_c5
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_19106,c_26003]) ).
cnf(c_26004,plain,
( multiply(inverse(sk_c3),sk_c6) = sk_c5
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_19120,c_14981]) ).
cnf(c_20626,plain,
( inverse(sk_c3) = sk_c5
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_19106,c_26004]) ).
cnf(c_26005,plain,
( inverse(sk_c4) != sk_c5
| multiply(A,sk_c4) != sk_c5
| inverse(A) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c6
| sk_c5 != sk_c4 ),
inference(paramod,[status(thm)],[c_19106,c_26]) ).
cnf(c_22757,plain,
( inverse(sk_c4) != sk_c5
| multiply(A,sk_c4) != sk_c5
| inverse(A) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c6
| sk_c4 != sk_c5 ),
inference(copy,[status(thm)],[c_26005]) ).
cnf(c_26006,plain,
( inverse(sk_c6) = sk_c5
| sk_c2 = sk_c1
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_19340,c_20626]) ).
cnf(c_26007,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c1
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_19105,c_26006]) ).
cnf(c_23943,plain,
( sk_c2 = sk_c1
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_26007]) ).
cnf(c_26008,plain,
( sk_c1 = sk_c5
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_23943,c_15554]) ).
cnf(c_23973,plain,
( sk_c1 = sk_c5
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_26008]) ).
cnf(c_26009,plain,
( sk_c6 = sk_c5
| sk_c5 = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_23973,c_19335]) ).
cnf(c_26010,plain,
( sk_c6 = sk_c5
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_26009]) ).
cnf(c_26011,plain,
( sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_26010]) ).
cnf(c_24090,plain,
sk_c6 = sk_c5,
inference(copy,[status(thm)],[c_26011]) ).
cnf(c_26012,plain,
( inverse(sk_c4) != sk_c5
| multiply(A,sk_c4) != sk_c5
| inverse(A) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c6
| inverse(sk_c4) != sk_c5
| sk_c4 != sk_c5 ),
inference(paramod,[status(thm)],[c_24090,c_22757]) ).
cnf(c_26013,plain,
( inverse(sk_c4) != sk_c5
| multiply(A,sk_c4) != sk_c5
| inverse(A) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c5
| inverse(sk_c4) != sk_c5
| sk_c4 != sk_c5 ),
inference(paramod,[status(thm)],[c_24090,c_26012]) ).
cnf(c_24970,plain,
( multiply(A,sk_c4) != sk_c5
| inverse(A) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c5
| inverse(sk_c4) != sk_c5
| sk_c4 != sk_c5 ),
inference(copy,[status(thm)],[c_26013]) ).
cnf(c_26014,plain,
( sk_c4 = sk_c5
| sk_c4 = sk_c5 ),
inference(paramod,[status(thm)],[c_24090,c_19622]) ).
cnf(c_25764,plain,
sk_c4 = sk_c5,
inference(copy,[status(thm)],[c_26014]) ).
cnf(c_25870,plain,
multiply(A,sk_c5) = A,
inference(paramod,[status(thm)],[c_24090,c_19106]) ).
cnf(c_26015,plain,
inverse(sk_c5) = sk_c6,
inference(paramod,[status(thm)],[c_24090,c_19105]) ).
cnf(c_25871,plain,
inverse(sk_c5) = sk_c5,
inference(paramod,[status(thm)],[c_24090,c_26015]) ).
cnf(c_26016,plain,
( multiply(sk_c4,sk_c4) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c5
| inverse(sk_c4) != sk_c5
| sk_c4 != sk_c5 ),
inference(factor,[status(thm)],[c_24970]) ).
cnf(c_26017,plain,
( multiply(sk_c4,sk_c4) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c5
| inverse(sk_c4) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25764,c_26016]) ).
cnf(c_26018,plain,
( multiply(sk_c4,sk_c4) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c5
| inverse(sk_c5) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25764,c_26017]) ).
cnf(c_26019,plain,
( multiply(sk_c4,sk_c4) != sk_c5
| multiply(sk_c4,sk_c5) != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25871,c_26018]) ).
cnf(c_26020,plain,
( multiply(sk_c4,sk_c4) != sk_c5
| multiply(sk_c5,sk_c5) != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25764,c_26019]) ).
cnf(c_26021,plain,
( multiply(sk_c4,sk_c4) != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25870,c_26020]) ).
cnf(c_26022,plain,
( multiply(sk_c5,sk_c4) != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25764,c_26021]) ).
cnf(c_26023,plain,
( multiply(sk_c5,sk_c5) != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25764,c_26022]) ).
cnf(c_26024,plain,
( sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_25870,c_26023]) ).
cnf(c_26025,plain,
( sk_c5 != sk_c5
| sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(copy,[status(thm)],[c_26024]) ).
cnf(c_26026,plain,
( sk_c5 != sk_c5
| sk_c5 != sk_c5 ),
inference(copy,[status(thm)],[c_26025]) ).
cnf(c_26027,plain,
sk_c5 != sk_c5,
inference(copy,[status(thm)],[c_26026]) ).
cnf(c_25906,plain,
$false,
inference(copy,[status(thm)],[c_26027]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP348-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 14:50:47 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 1639779 was started by sandbox2 on n015,
% 0.09/5.38 % Fri Sep 25 14:50:47 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 148.78/25.17
% 148.78/25.17 % given #500 (F,wt=37): 9066 multiply(sk_c5,sk_c6) != sk_c4 | multiply(sk_c5,inverse(A)) != sk_c6 | sk_c6 != A | multiply(B,C) != sk_c5 | multiply(inverse(C),multiply(inverse(B),sk_c4)) != sk_c5 | inverse(sk_c4) != sk_c5 | multiply(sk_c4,sk_c5) != sk_c6. [para(1188(a,1),8554(e,1,1)),rewrite([3(20)]),flip(d)].
% 148.78/25.17
% 148.78/25.17 % SZS status Unsatisfiable for theBenchmark
% 148.78/25.17
% 148.78/25.17 % Proof 1 at 15.82 (+ 3.68) seconds.
% 148.78/25.17 % Length of proof is 152.
% 148.78/25.17 % Level of proof is 23.
% 148.78/25.17 % Maximum clause weight is 41.000.
% 148.78/25.17 % Given clauses 956.
% 148.78/25.17
% 148.78/25.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------