%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP333-1 : 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 : n001.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 07:28:39 AM UTC 2026
% Result : Unsatisfiable 32.13s 4.48s
% Output : CNFRefutation 32.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 19
% Syntax : Number of formulae : 268 ( 34 unt; 0 def)
% Number of atoms : 691 ( 690 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 675 ( 252 ~; 423 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 96 ( 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,
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(clausify,[status(thm)],[prove_this_1]) ).
cnf(c_5,plain,
sk_c5 = multiply(sk_c6,sk_c7),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_this_2,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_7,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
cnf(c_9,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_8]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_10,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
cnf(c_14,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7)
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_13]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_15,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_17,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
cnf(c_19,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7)
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_18]) ).
fof(prove_this_13,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_20,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_16,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_25,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
cnf(c_8704,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_26,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_8704]) ).
fof(prove_this_17,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_27,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
cnf(c_28,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_27]) ).
fof(prove_this_18,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c6
| multiply(VAR_3,sk_c6) != sk_c5
| inverse(VAR_2) != sk_c7
| multiply(VAR_2,sk_c7) != sk_c6
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_1) != sk_c6
| inverse(VAR_0) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_29,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c5
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
cnf(c_8705,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c5
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_8706,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c5
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_8705]) ).
cnf(c_8707,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != multiply(sk_c6,sk_c7)
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_8706]) ).
cnf(c_8708,plain,
( inverse(D) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(D,sk_c6)
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(copy,[status(thm)],[c_8707]) ).
cnf(c_30,plain,
( inverse(D) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(D,sk_c6)
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_8708]) ).
cnf(c_31,plain,
( inverse(C) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(C,sk_c6)
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(A,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_33,plain,
( multiply(sk_c6,sk_c7) != multiply(B,sk_c6)
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_34,plain,
( multiply(sk_c6,sk_c7) != multiply(A,sk_c6)
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(A,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(factor,[status(thm)],[c_31]) ).
cnf(c_8709,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_8710,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_8709]) ).
cnf(c_35,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_8710]) ).
cnf(c_8711,plain,
( multiply(multiply(A,sk_c1),sk_c6) = multiply(A,sk_c7)
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_37,plain,
( multiply(A,multiply(sk_c1,sk_c6)) = multiply(A,sk_c7)
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_8711]) ).
cnf(c_8712,plain,
( multiply(multiply(A,sk_c4),sk_c6) = multiply(A,multiply(sk_c6,sk_c7))
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_46,plain,
( multiply(A,multiply(sk_c4,sk_c6)) = multiply(A,multiply(sk_c6,sk_c7))
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_8712]) ).
cnf(c_53,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_54,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_58,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_59,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_64,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_69,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_8713,plain,
( multiply(multiply(A,sk_c2),multiply(sk_c6,sk_c7)) = multiply(A,sk_c6)
| multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_26,c_3]) ).
cnf(c_78,plain,
( multiply(A,multiply(sk_c2,multiply(sk_c6,sk_c7))) = multiply(A,sk_c6)
| multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_3,c_8713]) ).
cnf(c_81,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_8714,plain,
( multiply(sk_c6,sk_c7) != multiply(identity,sk_c6)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(identity,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(identity) != sk_c6
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_34]) ).
cnf(c_8715,plain,
( multiply(sk_c6,sk_c7) != multiply(identity,sk_c6)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_8714]) ).
cnf(c_8716,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_8715]) ).
cnf(c_8717,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_8716]) ).
cnf(c_84,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_8717]) ).
cnf(c_87,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_35]) ).
cnf(c_98,plain,
( multiply(inverse(sk_c3),sk_c6) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_11,c_35]) ).
cnf(c_102,plain,
( multiply(inverse(sk_c4),multiply(sk_c6,sk_c7)) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_35]) ).
cnf(c_110,plain,
( multiply(inverse(sk_c4),multiply(sk_c6,sk_c7)) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_35]) ).
cnf(c_121,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_35,c_35]) ).
cnf(c_122,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_121,c_87]) ).
cnf(c_134,plain,
( inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_84]) ).
cnf(c_146,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_122,c_2]) ).
cnf(c_8718,plain,
( inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_146,c_134]) ).
cnf(c_158,plain,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_8718]) ).
cnf(c_8719,plain,
( multiply(sk_c6,sk_c7) != multiply(identity,sk_c6)
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(identity,multiply(sk_c6,sk_c7)) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_146,c_33]) ).
cnf(c_8720,plain,
( multiply(sk_c6,sk_c7) != multiply(identity,sk_c6)
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_8719]) ).
cnf(c_8721,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_8720]) ).
cnf(c_168,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_8721]) ).
cnf(c_8722,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_53,c_35]) ).
cnf(c_173,plain,
( inverse(sk_c6) = sk_c1
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_122,c_8722]) ).
cnf(c_176,plain,
( multiply(sk_c1,sk_c6) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_173,c_2]) ).
cnf(c_8723,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_54,c_35]) ).
cnf(c_181,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8723]) ).
cnf(c_182,plain,
( multiply(inverse(multiply(sk_c1,sk_c6)),sk_c7) = identity
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_37,c_2]) ).
cnf(c_198,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_181,c_2]) ).
cnf(c_203,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_58,c_2]) ).
cnf(c_8724,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_58,c_35]) ).
cnf(c_206,plain,
( inverse(sk_c6) = sk_c1
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8724]) ).
cnf(c_210,plain,
( multiply(sk_c1,sk_c6) = identity
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_206,c_2]) ).
cnf(c_8725,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_59,c_35]) ).
cnf(c_217,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8725]) ).
cnf(c_8726,plain,
( inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_168]) ).
cnf(c_291,plain,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_8726]) ).
cnf(c_8727,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_64,c_35]) ).
cnf(c_367,plain,
( inverse(sk_c7) = sk_c3
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8727]) ).
cnf(c_373,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_367,c_2]) ).
cnf(c_8728,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_69,c_35]) ).
cnf(c_448,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8728]) ).
cnf(c_461,plain,
( multiply(inverse(sk_c6),multiply(sk_c4,sk_c6)) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_35,c_46]) ).
cnf(c_8729,plain,
( inverse(sk_c3) = sk_c7
| identity = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_176,c_7]) ).
cnf(c_500,plain,
( identity = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_8729]) ).
cnf(c_509,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_500,c_2]) ).
cnf(c_8730,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_509,c_35]) ).
cnf(c_536,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_122,c_8730]) ).
cnf(c_551,plain,
( multiply(sk_c3,sk_c7) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_536,c_2]) ).
cnf(c_8731,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_198,c_11]) ).
cnf(c_654,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8731]) ).
cnf(c_664,plain,
( multiply(sk_c6,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_654,c_2]) ).
cnf(c_667,plain,
( inverse(sk_c6) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_654,c_146]) ).
cnf(c_8732,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_664,c_35]) ).
cnf(c_690,plain,
( inverse(sk_c6) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8732]) ).
cnf(c_718,plain,
( inverse(sk_c6) = identity
| inverse(sk_c6) = sk_c1 ),
inference(paramod,[status(thm)],[c_690,c_146]) ).
cnf(c_8733,plain,
( identity = sk_c4
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_667,c_217]) ).
cnf(c_751,plain,
( identity = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8733]) ).
cnf(c_8734,plain,
( inverse(sk_c6) = sk_c6
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_654,c_667]) ).
cnf(c_758,plain,
( inverse(sk_c6) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8734]) ).
cnf(c_763,plain,
( multiply(sk_c6,sk_c1) = identity
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_751,c_2]) ).
cnf(c_8735,plain,
( sk_c4 = sk_c6
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_751,c_654]) ).
cnf(c_772,plain,
( sk_c4 = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8735]) ).
cnf(c_8736,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_763,c_35]) ).
cnf(c_862,plain,
( inverse(sk_c6) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_122,c_8736]) ).
cnf(c_8737,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c6) = sk_c1
| inverse(sk_c6) = sk_c1 ),
inference(paramod,[status(thm)],[c_862,c_718]) ).
cnf(c_918,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c6) = sk_c1 ),
inference(copy,[status(thm)],[c_8737]) ).
cnf(c_8738,plain,
( inverse(sk_c4) = sk_c6
| identity = sk_c7
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_210,c_10]) ).
cnf(c_1149,plain,
( identity = sk_c7
| inverse(sk_c4) = sk_c6 ),
inference(copy,[status(thm)],[c_8738]) ).
cnf(c_1182,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1149,c_2]) ).
cnf(c_8739,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1182,c_35]) ).
cnf(c_1196,plain,
( inverse(sk_c6) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_122,c_8739]) ).
cnf(c_8740,plain,
( identity = sk_c6
| inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_373,c_16]) ).
cnf(c_1578,plain,
( identity = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(copy,[status(thm)],[c_8740]) ).
cnf(c_1590,plain,
( multiply(inverse(multiply(sk_c2,multiply(sk_c6,sk_c7))),sk_c6) = identity
| multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_78,c_2]) ).
cnf(c_1600,plain,
( multiply(sk_c6,sk_c2) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1578,c_2]) ).
cnf(c_1602,plain,
( inverse(sk_c6) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1578,c_146]) ).
cnf(c_8741,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1600,c_35]) ).
cnf(c_1623,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8741]) ).
cnf(c_8742,plain,
( sk_c2 = sk_c1
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1623,c_690]) ).
cnf(c_1672,plain,
( sk_c2 = sk_c1
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_8742]) ).
cnf(c_1698,plain,
( multiply(sk_c6,A) = A
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_1672,c_1]) ).
cnf(c_8743,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_81,c_35]) ).
cnf(c_1839,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8743]) ).
cnf(c_8744,plain,
( identity = sk_c4
| inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1602,c_448]) ).
cnf(c_1876,plain,
( identity = sk_c4
| inverse(sk_c2) = sk_c6 ),
inference(copy,[status(thm)],[c_8744]) ).
cnf(c_8745,plain,
( sk_c4 = sk_c6
| inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1876,c_1578]) ).
cnf(c_1897,plain,
( sk_c4 = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(copy,[status(thm)],[c_8745]) ).
cnf(c_8746,plain,
( inverse(inverse(sk_c7)) != sk_c7
| sk_c7 != sk_c6
| identity != sk_c6
| sk_c7 != sk_c6
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_1698,c_158]) ).
cnf(c_2123,plain,
( inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6
| sk_c7 != sk_c6
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_8746]) ).
cnf(c_8747,plain,
( multiply(inverse(sk_c6),multiply(sk_c6,sk_c7)) = sk_c6
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_772,c_102]) ).
cnf(c_8748,plain,
( sk_c7 = sk_c6
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_35,c_8747]) ).
cnf(c_2878,plain,
( sk_c7 = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8748]) ).
cnf(c_2890,plain,
( multiply(sk_c6,sk_c1) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2878,c_2]) ).
cnf(c_8749,plain,
( inverse(sk_c6) = sk_c3
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_2878,c_181]) ).
cnf(c_2904,plain,
( inverse(sk_c6) = sk_c3
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8749]) ).
cnf(c_8750,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2890,c_35]) ).
cnf(c_2941,plain,
( inverse(sk_c6) = sk_c1
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8750]) ).
cnf(c_8751,plain,
( sk_c3 = sk_c6
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_2904,c_758]) ).
cnf(c_3378,plain,
( sk_c3 = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8751]) ).
cnf(c_8752,plain,
( multiply(inverse(sk_c6),sk_c6) = sk_c7
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_3378,c_98]) ).
cnf(c_8753,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_8752]) ).
cnf(c_3464,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_8753]) ).
cnf(c_3470,plain,
( multiply(sk_c6,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3464,c_2]) ).
cnf(c_8754,plain,
( multiply(inverse(sk_c6),multiply(sk_c6,sk_c7)) = sk_c6
| inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1897,c_110]) ).
cnf(c_8755,plain,
( sk_c7 = sk_c6
| inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_35,c_8754]) ).
cnf(c_3828,plain,
( sk_c7 = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(copy,[status(thm)],[c_8755]) ).
cnf(c_4188,plain,
( multiply(sk_c6,sk_c2) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3828,c_2]) ).
cnf(c_8756,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3470,c_35]) ).
cnf(c_4797,plain,
( inverse(sk_c6) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_122,c_8756]) ).
cnf(c_8757,plain,
( sk_c1 = sk_c4
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_4797,c_1196]) ).
cnf(c_8758,plain,
( sk_c4 = sk_c1
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_8757]) ).
cnf(c_4856,plain,
( sk_c4 = sk_c1
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_8758]) ).
cnf(c_4872,plain,
( multiply(A,sk_c7) = A
| sk_c4 = sk_c1 ),
inference(paramod,[status(thm)],[c_4856,c_122]) ).
cnf(c_8759,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_121,c_122]) ).
cnf(c_8760,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_122,c_8759]) ).
cnf(c_5193,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_8760]) ).
cnf(c_8761,plain,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(inverse(inverse(A))) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_121,c_291]) ).
cnf(c_8762,plain,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_5193,c_8761]) ).
cnf(c_8763,plain,
( sk_c7 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_5193,c_8762]) ).
cnf(c_5206,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_8763]) ).
cnf(c_8764,plain,
( sk_c7 != sk_c7
| identity != sk_c6
| sk_c7 != sk_c6
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_5193,c_2123]) ).
cnf(c_5416,plain,
( identity != sk_c6
| sk_c7 != sk_c6
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_8764]) ).
cnf(c_8765,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(inverse(sk_c6)) != sk_c6
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_5206]) ).
cnf(c_8766,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c6 != sk_c6
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_5193,c_8765]) ).
cnf(c_5638,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_8766]) ).
cnf(c_5639,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(multiply(A,B)) != sk_c6
| multiply(A,multiply(B,sk_c6)) != sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_5206]) ).
cnf(c_8767,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| multiply(A,identity) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_5639]) ).
cnf(c_8768,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| A != sk_c7 ),
inference(paramod,[status(thm)],[c_122,c_8767]) ).
cnf(c_6058,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(multiply(A,inverse(sk_c6))) != sk_c6
| sk_c7 != A ),
inference(copy,[status(thm)],[c_8768]) ).
cnf(c_8769,plain,
( sk_c2 = sk_c1
| sk_c7 != sk_c6
| sk_c2 = sk_c1 ),
inference(resolve,[status(thm)],[c_5416,c_1672]) ).
cnf(c_6390,plain,
( sk_c7 != sk_c6
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_8769]) ).
cnf(c_8770,plain,
( sk_c6 = identity
| identity = sk_c7
| multiply(inverse(multiply(sk_c1,sk_c6)),sk_c7) = identity ),
inference(paramod,[status(thm)],[c_182,c_551]) ).
cnf(c_6822,plain,
( identity = sk_c6
| identity = sk_c7
| multiply(inverse(multiply(sk_c1,sk_c6)),sk_c7) = identity ),
inference(copy,[status(thm)],[c_8770]) ).
cnf(c_8771,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_4188,c_35]) ).
cnf(c_7119,plain,
( inverse(sk_c6) = sk_c2
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_122,c_8771]) ).
cnf(c_8772,plain,
( sk_c2 = sk_c1
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_7119,c_2941]) ).
cnf(c_7231,plain,
( sk_c2 = sk_c1
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_8772]) ).
cnf(c_8773,plain,
( sk_c2 = sk_c1
| sk_c2 = sk_c1 ),
inference(resolve,[status(thm)],[c_7231,c_6390]) ).
cnf(c_7254,plain,
sk_c2 = sk_c1,
inference(copy,[status(thm)],[c_8773]) ).
cnf(c_7465,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c1,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_7254,c_1839]) ).
cnf(c_7482,plain,
( multiply(inverse(multiply(sk_c1,multiply(sk_c6,sk_c7))),sk_c6) = identity
| multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_7254,c_1590]) ).
cnf(c_7661,plain,
( identity != sk_c6
| identity != sk_c7
| sk_c4 = sk_c1 ),
inference(resolve,[status(thm)],[c_4872,c_5638]) ).
cnf(c_8774,plain,
( sk_c4 = sk_c1
| identity != sk_c6
| sk_c4 = sk_c1 ),
inference(resolve,[status(thm)],[c_7661,c_4856]) ).
cnf(c_7763,plain,
( identity != sk_c6
| sk_c4 = sk_c1 ),
inference(copy,[status(thm)],[c_8774]) ).
cnf(c_7778,plain,
( inverse(sk_c6) = sk_c1
| sk_c4 = sk_c1 ),
inference(resolve,[status(thm)],[c_7763,c_690]) ).
cnf(c_8775,plain,
( sk_c7 != sk_c6
| sk_c4 = sk_c1
| sk_c4 = sk_c1 ),
inference(paramod,[status(thm)],[c_4856,c_7763]) ).
cnf(c_7789,plain,
( sk_c7 != sk_c6
| sk_c4 = sk_c1 ),
inference(copy,[status(thm)],[c_8775]) ).
cnf(c_8776,plain,
( inverse(sk_c6) = sk_c1
| inverse(sk_c6) = sk_c1
| inverse(sk_c6) = sk_c1 ),
inference(paramod,[status(thm)],[c_7778,c_918]) ).
cnf(c_8777,plain,
( inverse(sk_c6) = sk_c1
| inverse(sk_c6) = sk_c1 ),
inference(copy,[status(thm)],[c_8776]) ).
cnf(c_7805,plain,
inverse(sk_c6) = sk_c1,
inference(copy,[status(thm)],[c_8777]) ).
cnf(c_8778,plain,
( sk_c1 = sk_c4
| multiply(sk_c1,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_7805,c_7465]) ).
cnf(c_7815,plain,
( sk_c4 = sk_c1
| multiply(sk_c1,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(copy,[status(thm)],[c_8778]) ).
cnf(c_7854,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| inverse(multiply(A,sk_c1)) != sk_c6
| sk_c7 != A ),
inference(paramod,[status(thm)],[c_7805,c_6058]) ).
cnf(c_7912,plain,
( multiply(sk_c1,multiply(sk_c4,sk_c6)) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_7805,c_461]) ).
cnf(c_7915,plain,
multiply(sk_c1,sk_c6) = identity,
inference(paramod,[status(thm)],[c_7805,c_2]) ).
cnf(c_7916,plain,
multiply(sk_c1,multiply(sk_c6,A)) = A,
inference(paramod,[status(thm)],[c_7805,c_35]) ).
cnf(c_7919,plain,
( multiply(sk_c1,multiply(sk_c4,sk_c6)) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_7915,c_7912]) ).
cnf(c_8779,plain,
( identity = sk_c6
| identity = sk_c7
| multiply(inverse(identity),sk_c7) = identity ),
inference(paramod,[status(thm)],[c_7915,c_6822]) ).
cnf(c_8780,plain,
( identity = sk_c6
| identity = sk_c7
| multiply(identity,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_146,c_8779]) ).
cnf(c_8781,plain,
( identity = sk_c6
| identity = sk_c7
| sk_c7 = identity ),
inference(paramod,[status(thm)],[c_1,c_8780]) ).
cnf(c_8782,plain,
( identity = sk_c6
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_8781]) ).
cnf(c_7989,plain,
( identity = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_8782]) ).
cnf(c_8078,plain,
( sk_c4 = sk_c1
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_7916,c_7815]) ).
cnf(c_8108,plain,
( multiply(inverse(sk_c7),sk_c6) = identity
| multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_7916,c_7482]) ).
cnf(c_8783,plain,
( inverse(sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_7989,c_146]) ).
cnf(c_8784,plain,
( sk_c1 = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_7805,c_8783]) ).
cnf(c_8237,plain,
( identity = sk_c1
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_8784]) ).
cnf(c_8785,plain,
( sk_c4 = sk_c1
| sk_c4 = sk_c1 ),
inference(resolve,[status(thm)],[c_8078,c_7789]) ).
cnf(c_8251,plain,
sk_c4 = sk_c1,
inference(copy,[status(thm)],[c_8785]) ).
cnf(c_8786,plain,
( multiply(inverse(sk_c7),sk_c6) = identity
| multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_8251,c_8108]) ).
cnf(c_8787,plain,
( multiply(inverse(sk_c7),sk_c6) = identity
| identity = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_7915,c_8786]) ).
cnf(c_8279,plain,
( multiply(inverse(sk_c7),sk_c6) = identity
| multiply(sk_c6,sk_c7) = identity ),
inference(copy,[status(thm)],[c_8787]) ).
cnf(c_8788,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_8251,c_7919]) ).
cnf(c_8789,plain,
( multiply(sk_c1,identity) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_7915,c_8788]) ).
cnf(c_8316,plain,
( sk_c1 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_122,c_8789]) ).
cnf(c_8790,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_8251,c_203]) ).
cnf(c_8459,plain,
multiply(sk_c6,sk_c1) = identity,
inference(copy,[status(thm)],[c_8790]) ).
cnf(c_8791,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_8316,c_8237]) ).
cnf(c_8792,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_8791]) ).
cnf(c_8596,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_8792]) ).
cnf(c_8616,plain,
multiply(sk_c6,sk_c1) = sk_c7,
inference(paramod,[status(thm)],[c_8596,c_8459]) ).
cnf(c_8793,plain,
( multiply(inverse(sk_c7),sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8596,c_8279]) ).
cnf(c_8632,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8596,c_8793]) ).
cnf(c_8671,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| inverse(multiply(A,sk_c1)) != sk_c6
| sk_c7 != A ),
inference(paramod,[status(thm)],[c_8596,c_7854]) ).
cnf(c_8794,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_8596,c_146]) ).
cnf(c_8696,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_8596,c_8794]) ).
cnf(c_8697,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_8596,c_122]) ).
cnf(c_8699,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_8596,c_1]) ).
cnf(c_8795,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| inverse(multiply(sk_c6,sk_c1)) != sk_c6
| sk_c7 != sk_c6 ),
inference(factor,[status(thm)],[c_8671]) ).
cnf(c_8796,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_8616,c_8795]) ).
cnf(c_8797,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_8696,c_8796]) ).
cnf(c_8798,plain,
( sk_c6 != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_8697,c_8797]) ).
cnf(c_8799,plain,
( sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_8798]) ).
cnf(c_8700,plain,
sk_c7 != sk_c6,
inference(copy,[status(thm)],[c_8799]) ).
cnf(c_8800,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_8697,c_8632]) ).
cnf(c_8801,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_8696,c_8800]) ).
cnf(c_8802,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_8699,c_8801]) ).
cnf(c_8803,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_8802]) ).
cnf(c_8804,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_8803]) ).
cnf(c_8805,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_8804]) ).
cnf(c_8703,plain,
$false,
inference(resolve,[status(thm)],[c_8700,c_8805]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP333-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:52:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3587652 was started by sandbox2 on n001,
% 0.08/0.35 % Fri Sep 25 14:52:12 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 32.13/4.48
% 32.13/4.48 % SZS status Unsatisfiable for theBenchmark
% 32.13/4.48
% 32.13/4.48 % Proof 1 at 3.21 (+ 0.87) seconds.
% 32.13/4.48 % Length of proof is 147.
% 32.13/4.48 % Level of proof is 29.
% 32.13/4.48 % Maximum clause weight is 48.000.
% 32.13/4.48 % Given clauses 389.
% 32.13/4.48
% 32.13/4.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------