%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP270-1 : 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 : 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 07:28:31 AM UTC 2026
% Result : Unsatisfiable 267.63s 35.40s
% Output : CNFRefutation 267.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 23
% Syntax : Number of formulae : 253 ( 46 unt; 0 def)
% Number of atoms : 611 ( 610 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 536 ( 178 ~; 358 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 6 ( 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 : 86 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_6,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_11,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_18,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = 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_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_22,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
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_c7
| multiply(VAR_1,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
cnf(c_30,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(A,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_35,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(A,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_9945,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_9946,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_9945]) ).
cnf(c_49,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_9946]) ).
cnf(c_59,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_60,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_63,plain,
( multiply(sk_c5,A) = multiply(sk_c6,multiply(sk_c7,A))
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_9947,plain,
( multiply(multiply(A,sk_c6),sk_c7) = multiply(A,sk_c5)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_64,plain,
( multiply(A,multiply(sk_c6,sk_c7)) = multiply(A,sk_c5)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_9947]) ).
cnf(c_65,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_9948,plain,
( multiply(multiply(A,sk_c3),sk_c6) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_67,plain,
( multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_9948]) ).
cnf(c_68,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_9949,plain,
( multiply(sk_c6,A) = multiply(sk_c4,multiply(sk_c5,A))
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_18,c_3]) ).
cnf(c_69,plain,
( multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9949]) ).
cnf(c_9950,plain,
( multiply(multiply(A,sk_c3),sk_c6) = multiply(A,sk_c7)
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_75,plain,
( multiply(A,multiply(sk_c3,sk_c6)) = multiply(A,sk_c7)
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3,c_9950]) ).
cnf(c_76,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_9951,plain,
( multiply(sk_c6,A) = multiply(sk_c4,multiply(sk_c5,A))
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_23,c_3]) ).
cnf(c_77,plain,
( multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c6,A)
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_9951]) ).
cnf(c_80,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_81,plain,
( multiply(sk_c7,sk_c2) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_26,c_2]) ).
cnf(c_82,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_565,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_49]) ).
cnf(c_566,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_49]) ).
cnf(c_567,plain,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_49]) ).
cnf(c_569,plain,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_49]) ).
cnf(c_592,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_49,c_49]) ).
cnf(c_593,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_592,c_565]) ).
cnf(c_594,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_593,c_2]) ).
cnf(c_9952,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(identity,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_594,c_35]) ).
cnf(c_9953,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(identity,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9952]) ).
cnf(c_9954,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9953]) ).
cnf(c_9955,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9954]) ).
cnf(c_9956,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_9955]) ).
cnf(c_9957,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_9956]) ).
cnf(c_613,plain,
( multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_9957]) ).
cnf(c_661,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_59,c_2]) ).
cnf(c_745,plain,
( multiply(sk_c7,sk_c2) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_80,c_2]) ).
cnf(c_9958,plain,
( multiply(identity,sk_c5) != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_594,c_613]) ).
cnf(c_813,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_9958]) ).
cnf(c_9959,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_68,c_49]) ).
cnf(c_877,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_593,c_9959]) ).
cnf(c_878,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_877,c_2]) ).
cnf(c_9960,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_661,c_49]) ).
cnf(c_982,plain,
( inverse(sk_c7) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_593,c_9960]) ).
cnf(c_9961,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| multiply(sk_c7,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_745,c_49]) ).
cnf(c_1167,plain,
( inverse(sk_c7) = sk_c3
| multiply(sk_c7,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_593,c_9961]) ).
cnf(c_9962,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9,c_567]) ).
cnf(c_1812,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_9962]) ).
cnf(c_9963,plain,
( multiply(sk_c5,sk_c3) = multiply(sk_c6,identity)
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_65,c_63]) ).
cnf(c_9964,plain,
( multiply(sk_c5,sk_c3) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_593,c_9963]) ).
cnf(c_1815,plain,
( multiply(sk_c5,sk_c3) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9964]) ).
cnf(c_9965,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_569]) ).
cnf(c_1899,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_9965]) ).
cnf(c_9966,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c3)
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_1815,c_69]) ).
cnf(c_2186,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,sk_c3)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9966]) ).
cnf(c_9967,plain,
( multiply(sk_c6,sk_c3) = identity
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2186,c_878]) ).
cnf(c_2245,plain,
( multiply(sk_c6,sk_c3) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9967]) ).
cnf(c_9968,plain,
( multiply(inverse(sk_c6),identity) = sk_c3
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2245,c_49]) ).
cnf(c_2249,plain,
( inverse(sk_c6) = sk_c3
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_593,c_9968]) ).
cnf(c_2255,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2249,c_2]) ).
cnf(c_9969,plain,
( multiply(A,identity) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2255,c_67]) ).
cnf(c_9970,plain,
( A = multiply(A,sk_c7)
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_593,c_9969]) ).
cnf(c_9971,plain,
( multiply(A,sk_c7) = A
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9970]) ).
cnf(c_2301,plain,
( multiply(A,sk_c7) = A
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9971]) ).
cnf(c_2372,plain,
( inverse(sk_c7) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2301,c_2]) ).
cnf(c_9972,plain,
( multiply(A,sk_c6) = multiply(A,sk_c5)
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2301,c_64]) ).
cnf(c_9973,plain,
( multiply(A,sk_c5) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9972]) ).
cnf(c_2387,plain,
( multiply(A,sk_c5) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9973]) ).
cnf(c_9974,plain,
( multiply(identity,multiply(sk_c7,A)) = A
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2372,c_49]) ).
cnf(c_2393,plain,
( multiply(sk_c7,A) = A
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9974]) ).
cnf(c_9975,plain,
( multiply(sk_c4,multiply(sk_c5,sk_c7)) = multiply(sk_c6,multiply(sk_c3,sk_c6))
| multiply(sk_c2,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_75,c_77]) ).
cnf(c_2581,plain,
( multiply(sk_c4,multiply(sk_c5,sk_c7)) = multiply(sk_c6,multiply(sk_c3,sk_c6))
| multiply(sk_c2,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_9975]) ).
cnf(c_9976,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_2393,c_2387]) ).
cnf(c_9977,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_9976]) ).
cnf(c_2757,plain,
multiply(sk_c7,sk_c5) = sk_c6,
inference(copy,[status(thm)],[c_9977]) ).
cnf(c_9978,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != sk_c7
| sk_c6 != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_2757,c_813]) ).
cnf(c_3917,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_9978]) ).
cnf(c_9979,plain,
multiply(sk_c6,A) = multiply(sk_c7,multiply(sk_c5,A)),
inference(paramod,[status(thm)],[c_2757,c_3]) ).
cnf(c_4610,plain,
multiply(sk_c7,multiply(sk_c5,A)) = multiply(sk_c6,A),
inference(copy,[status(thm)],[c_9979]) ).
cnf(c_4611,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c5,
inference(paramod,[status(thm)],[c_2757,c_49]) ).
cnf(c_4619,plain,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_982,c_4611]) ).
cnf(c_4620,plain,
( multiply(sk_c3,sk_c6) = sk_c5
| multiply(sk_c7,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_1167,c_4611]) ).
cnf(c_9980,plain,
( multiply(sk_c7,sk_c1) = identity
| sk_c5 = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_4619,c_60]) ).
cnf(c_4628,plain,
( sk_c5 = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_9980]) ).
cnf(c_9981,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4628,c_49]) ).
cnf(c_4635,plain,
( inverse(sk_c7) = sk_c1
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_593,c_9981]) ).
cnf(c_4640,plain,
( multiply(sk_c1,sk_c7) = identity
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4635,c_2]) ).
cnf(c_4643,plain,
( multiply(sk_c1,sk_c6) = sk_c5
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4635,c_4611]) ).
cnf(c_9982,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,identity)) = B,
inference(paramod,[status(thm)],[c_2,c_566]) ).
cnf(c_4644,plain,
multiply(inverse(multiply(A,inverse(B))),A) = B,
inference(paramod,[status(thm)],[c_593,c_9982]) ).
cnf(c_9983,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),A)),identity) = B,
inference(paramod,[status(thm)],[c_2,c_566]) ).
cnf(c_4645,plain,
inverse(multiply(inverse(multiply(A,B)),A)) = B,
inference(paramod,[status(thm)],[c_593,c_9983]) ).
cnf(c_4729,plain,
multiply(inverse(multiply(A,sk_c7)),multiply(A,sk_c6)) = sk_c5,
inference(paramod,[status(thm)],[c_2757,c_566]) ).
cnf(c_9984,plain,
( multiply(inverse(sk_c1),identity) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4640,c_49]) ).
cnf(c_4735,plain,
( inverse(sk_c1) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_593,c_9984]) ).
cnf(c_4741,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c6
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4640,c_1899]) ).
cnf(c_9985,plain,
( multiply(sk_c7,sk_c2) = identity
| sk_c5 = sk_c7
| multiply(sk_c7,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_4620,c_81]) ).
cnf(c_4758,plain,
( sk_c5 = sk_c7
| multiply(sk_c7,sk_c2) = identity ),
inference(copy,[status(thm)],[c_9985]) ).
cnf(c_9986,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4758,c_49]) ).
cnf(c_4767,plain,
( inverse(sk_c7) = sk_c2
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_593,c_9986]) ).
cnf(c_4773,plain,
( multiply(sk_c2,sk_c7) = identity
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4767,c_2]) ).
cnf(c_4800,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c5
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4773,c_19]) ).
cnf(c_9987,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c6
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4741,c_49]) ).
cnf(c_9988,plain,
( sk_c5 = sk_c7
| identity = sk_c6
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4611,c_9987]) ).
cnf(c_4981,plain,
( identity = sk_c6
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9988]) ).
cnf(c_4982,plain,
( multiply(sk_c6,A) = A
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4981,c_1]) ).
cnf(c_4983,plain,
( multiply(A,sk_c6) = A
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4981,c_593]) ).
cnf(c_9989,plain,
( sk_c1 = sk_c5
| sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4983,c_4643]) ).
cnf(c_5079,plain,
( sk_c1 = sk_c5
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9989]) ).
cnf(c_9990,plain,
( inverse(sk_c5) = sk_c7
| sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_5079,c_4735]) ).
cnf(c_5095,plain,
( inverse(sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9990]) ).
cnf(c_9991,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7
| identity = sk_c5
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_4800,c_4982]) ).
cnf(c_9992,plain,
( sk_c5 = sk_c7
| identity = sk_c5
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9991]) ).
cnf(c_5330,plain,
( identity = sk_c5
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9992]) ).
cnf(c_5333,plain,
( inverse(sk_c5) = identity
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_5330,c_594]) ).
cnf(c_9993,plain,
( identity = sk_c7
| sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_5333,c_5095]) ).
cnf(c_5427,plain,
( identity = sk_c7
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9993]) ).
cnf(c_9994,plain,
( sk_c7 = sk_c5
| sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_5427,c_5330]) ).
cnf(c_9995,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9994]) ).
cnf(c_9996,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_9995]) ).
cnf(c_5441,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_9996]) ).
cnf(c_5560,plain,
multiply(inverse(multiply(A,sk_c7)),multiply(A,sk_c6)) = sk_c7,
inference(paramod,[status(thm)],[c_5441,c_4729]) ).
cnf(c_5620,plain,
multiply(inverse(sk_c7),sk_c6) = sk_c7,
inference(paramod,[status(thm)],[c_5441,c_4611]) ).
cnf(c_9997,plain,
multiply(sk_c7,multiply(sk_c7,A)) = multiply(sk_c6,A),
inference(paramod,[status(thm)],[c_5441,c_4610]) ).
cnf(c_5621,plain,
multiply(sk_c6,A) = multiply(sk_c7,multiply(sk_c7,A)),
inference(copy,[status(thm)],[c_9997]) ).
cnf(c_9998,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_3917]) ).
cnf(c_9999,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c7,multiply(sk_c7,sk_c7)) != sk_c5
| sk_c7 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_5621,c_9998]) ).
cnf(c_10000,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c7,multiply(sk_c7,sk_c7)) != sk_c7
| sk_c7 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_9999]) ).
cnf(c_10001,plain,
( sk_c7 != sk_c6
| identity != sk_c6
| multiply(sk_c7,multiply(sk_c7,sk_c7)) != sk_c7
| sk_c7 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_10000]) ).
cnf(c_10002,plain,
( sk_c6 != sk_c7
| identity != sk_c6
| multiply(sk_c7,multiply(sk_c7,sk_c7)) != sk_c7
| sk_c7 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_10001]) ).
cnf(c_10003,plain,
( sk_c6 != sk_c7
| identity != sk_c6
| multiply(sk_c7,multiply(sk_c7,sk_c7)) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_10002]) ).
cnf(c_6312,plain,
( identity != sk_c6
| multiply(sk_c7,multiply(sk_c7,sk_c7)) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_10003]) ).
cnf(c_7080,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(paramod,[status(thm)],[c_5441,c_2757]) ).
cnf(c_10004,plain,
( multiply(sk_c4,multiply(sk_c5,sk_c7)) = multiply(sk_c6,multiply(sk_c3,sk_c6))
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_2581]) ).
cnf(c_10005,plain,
( multiply(sk_c4,multiply(sk_c7,sk_c7)) = multiply(sk_c6,multiply(sk_c3,sk_c6))
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_10004]) ).
cnf(c_10006,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c6,multiply(sk_c3,sk_c6))
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_7080,c_10005]) ).
cnf(c_7092,plain,
( multiply(sk_c4,sk_c6) = multiply(sk_c7,multiply(sk_c7,multiply(sk_c3,sk_c6)))
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_5621,c_10006]) ).
cnf(c_10007,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,multiply(sk_c7,sk_c7)) = sk_c5 ),
inference(paramod,[status(thm)],[c_5621,c_1812]) ).
cnf(c_10008,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_7080,c_10007]) ).
cnf(c_10009,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_10008]) ).
cnf(c_7139,plain,
multiply(sk_c7,sk_c6) = sk_c7,
inference(copy,[status(thm)],[c_10009]) ).
cnf(c_10010,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_76]) ).
cnf(c_7186,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c4)) = identity
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_5621,c_10010]) ).
cnf(c_7193,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_28]) ).
cnf(c_7196,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_5441,c_21]) ).
cnf(c_7329,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c4)) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_5621,c_82]) ).
cnf(c_10011,plain,
( identity != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_7080,c_6312]) ).
cnf(c_10012,plain,
( identity != sk_c6
| sk_c7 != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_7139,c_10011]) ).
cnf(c_8584,plain,
( identity != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_10012]) ).
cnf(c_10013,plain,
multiply(inverse(sk_c7),sk_c7) = sk_c6,
inference(paramod,[status(thm)],[c_7139,c_49]) ).
cnf(c_8942,plain,
identity = sk_c6,
inference(paramod,[status(thm)],[c_2,c_10013]) ).
cnf(c_10014,plain,
( identity != sk_c6
| sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_8942,c_8584]) ).
cnf(c_10015,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_8942,c_10014]) ).
cnf(c_10016,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_10015]) ).
cnf(c_9042,plain,
sk_c6 != sk_c7,
inference(copy,[status(thm)],[c_10016]) ).
cnf(c_9261,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c4)) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_8942,c_7329]) ).
cnf(c_9290,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c4)) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_8942,c_7186]) ).
cnf(c_10017,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_8942,c_594]) ).
cnf(c_9402,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_8942,c_10017]) ).
cnf(c_9403,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_8942,c_593]) ).
cnf(c_10018,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_8942,c_1]) ).
cnf(c_9410,plain,
multiply(sk_c7,multiply(sk_c7,A)) = A,
inference(paramod,[status(thm)],[c_5621,c_10018]) ).
cnf(c_9801,plain,
( sk_c3 = sk_c7
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_9403,c_7196]) ).
cnf(c_10019,plain,
( sk_c4 = multiply(sk_c7,multiply(sk_c7,multiply(sk_c3,sk_c6)))
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_9403,c_7092]) ).
cnf(c_10020,plain,
( sk_c4 = multiply(sk_c7,multiply(sk_c7,sk_c3))
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_9403,c_10019]) ).
cnf(c_9807,plain,
( sk_c4 = sk_c3
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_9410,c_10020]) ).
cnf(c_9809,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_9403,c_5620]) ).
cnf(c_9812,plain,
multiply(inverse(multiply(A,sk_c7)),A) = sk_c7,
inference(paramod,[status(thm)],[c_9403,c_5560]) ).
cnf(c_9828,plain,
( sk_c4 = sk_c6
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_9410,c_9290]) ).
cnf(c_9835,plain,
( sk_c4 = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_9410,c_9261]) ).
cnf(c_9850,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_9410,c_5621]) ).
cnf(c_10021,plain,
( multiply(inverse(multiply(A,sk_c7)),A) = sk_c2
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9835,c_4644]) ).
cnf(c_10022,plain,
( sk_c7 = sk_c2
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9812,c_10021]) ).
cnf(c_9873,plain,
( sk_c2 = sk_c7
| sk_c4 = sk_c6 ),
inference(copy,[status(thm)],[c_10022]) ).
cnf(c_10023,plain,
( inverse(multiply(inverse(sk_c7),sk_c2)) = sk_c7
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9801,c_4645]) ).
cnf(c_9908,plain,
( inverse(multiply(sk_c7,sk_c2)) = sk_c7
| sk_c3 = sk_c7 ),
inference(paramod,[status(thm)],[c_9809,c_10023]) ).
cnf(c_10024,plain,
( inverse(multiply(inverse(sk_c7),sk_c2)) = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_9807,c_4645]) ).
cnf(c_9909,plain,
( inverse(multiply(sk_c7,sk_c2)) = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_9809,c_10024]) ).
cnf(c_10025,plain,
( inverse(multiply(inverse(sk_c7),sk_c2)) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9828,c_4645]) ).
cnf(c_9934,plain,
( inverse(multiply(sk_c7,sk_c2)) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9809,c_10025]) ).
cnf(c_10026,plain,
( multiply(inverse(multiply(A,sk_c7)),A) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7193,c_4644]) ).
cnf(c_10027,plain,
( sk_c7 = sk_c2
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_9812,c_10026]) ).
cnf(c_9936,plain,
( sk_c2 = sk_c7
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_10027]) ).
cnf(c_10028,plain,
( sk_c2 = sk_c7
| multiply(sk_c6,sk_c7) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_9873,c_9936]) ).
cnf(c_10029,plain,
( sk_c2 = sk_c7
| sk_c7 = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_9850,c_10028]) ).
cnf(c_10030,plain,
( sk_c2 = sk_c7
| sk_c6 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_10029]) ).
cnf(c_10031,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_10030]) ).
cnf(c_9941,plain,
sk_c2 = sk_c7,
inference(resolve,[status(thm)],[c_9042,c_10031]) ).
cnf(c_10032,plain,
( inverse(multiply(sk_c7,sk_c7)) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9941,c_9934]) ).
cnf(c_10033,plain,
( inverse(sk_c6) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_7080,c_10032]) ).
cnf(c_10034,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_9402,c_10033]) ).
cnf(c_9942,plain,
sk_c4 = sk_c6,
inference(resolve,[status(thm)],[c_9042,c_10034]) ).
cnf(c_10035,plain,
( inverse(multiply(sk_c7,sk_c2)) = sk_c7
| sk_c6 = sk_c3 ),
inference(paramod,[status(thm)],[c_9942,c_9909]) ).
cnf(c_10036,plain,
( inverse(multiply(sk_c7,sk_c7)) = sk_c7
| sk_c6 = sk_c3 ),
inference(paramod,[status(thm)],[c_9941,c_10035]) ).
cnf(c_10037,plain,
( inverse(sk_c6) = sk_c7
| sk_c6 = sk_c3 ),
inference(paramod,[status(thm)],[c_7080,c_10036]) ).
cnf(c_10038,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c3 ),
inference(paramod,[status(thm)],[c_9402,c_10037]) ).
cnf(c_10039,plain,
( sk_c6 = sk_c7
| sk_c3 = sk_c6 ),
inference(copy,[status(thm)],[c_10038]) ).
cnf(c_9943,plain,
sk_c3 = sk_c6,
inference(resolve,[status(thm)],[c_9042,c_10039]) ).
cnf(c_10040,plain,
( inverse(multiply(sk_c7,sk_c2)) = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_9943,c_9908]) ).
cnf(c_10041,plain,
( inverse(multiply(sk_c7,sk_c7)) = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_9941,c_10040]) ).
cnf(c_10042,plain,
( inverse(sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_7080,c_10041]) ).
cnf(c_10043,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_9402,c_10042]) ).
cnf(c_10044,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_10043]) ).
cnf(c_9944,plain,
$false,
inference(resolve,[status(thm)],[c_9042,c_10044]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP270-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:41:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2248023 was started by sandbox2 on n011,
% 0.09/0.36 % Fri Sep 25 14:41:58 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 267.63/35.40
% 267.63/35.40 % SZS status Unsatisfiable for theBenchmark
% 267.63/35.40
% 267.63/35.40 % Proof 1 at 2.04 (+ 0.36) seconds.
% 267.63/35.40 % Length of proof is 130.
% 267.63/35.40 % Level of proof is 34.
% 267.63/35.40 % Maximum clause weight is 56.000.
% 267.63/35.40 % Given clauses 342.
% 267.63/35.40
% 267.63/35.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------