%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP316-1 : 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 : n014.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 07:28:37 AM UTC 2026
% Result : Unsatisfiable 127.19s 17.62s
% Output : CNFRefutation 127.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 27
% Syntax : Number of formulae : 254 ( 25 unt; 0 def)
% Number of atoms : 782 ( 781 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 893 ( 365 ~; 528 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 10 !; 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_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_20,axiom,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_23,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_26,axiom,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_29,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c6
| multiply(VAR_4,sk_c6) != sk_c8
| inverse(VAR_3) != sk_c8
| multiply(VAR_3,sk_c8) != VAR_2
| multiply(sk_c8,VAR_2) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(VAR_1) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c6
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( inverse(E) != sk_c6
| multiply(E,sk_c6) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_31943,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_31944,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_31943]) ).
cnf(c_45,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_31944]) ).
cnf(c_31945,plain,
( multiply(sk_c7,A) = multiply(sk_c6,multiply(sk_c8,A))
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_46,plain,
( multiply(sk_c6,multiply(sk_c8,A)) = multiply(sk_c7,A)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_31945]) ).
cnf(c_68,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c8) = sk_c4 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_70,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_81,plain,
( multiply(sk_c6,sk_c5) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_87,plain,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_33,c_2]) ).
cnf(c_101,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(resolve,[status(thm)],[c_34,c_2]) ).
cnf(c_102,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(resolve,[status(thm)],[c_34,c_1]) ).
cnf(c_31946,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c8,identity) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(inverse(sk_c8)) != sk_c8
| multiply(inverse(sk_c8),sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_101]) ).
cnf(c_186,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c8,identity) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_31946]) ).
cnf(c_31947,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_102]) ).
cnf(c_31948,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(identity) != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_31947]) ).
cnf(c_189,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_31948]) ).
cnf(c_545,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_45]) ).
cnf(c_577,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_45,c_45]) ).
cnf(c_578,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_577,c_545]) ).
cnf(c_31949,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_578,c_186]) ).
cnf(c_579,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_31949]) ).
cnf(c_694,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_578,c_2]) ).
cnf(c_729,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_694,c_189]) ).
cnf(c_31950,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c6
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_694,c_579]) ).
cnf(c_31951,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c7
| sk_c7 != sk_c6
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_31950]) ).
cnf(c_31952,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_31951]) ).
cnf(c_761,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_31952]) ).
cnf(c_955,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_577,c_2]) ).
cnf(c_31953,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_577,c_578]) ).
cnf(c_31954,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_578,c_31953]) ).
cnf(c_978,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_31954]) ).
cnf(c_31955,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c7
| sk_c8 != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_978,c_761]) ).
cnf(c_1018,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_31955]) ).
cnf(c_31956,plain,
( A != sk_c6
| multiply(inverse(A),sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_978,c_1018]) ).
cnf(c_1163,plain,
( sk_c6 != A
| multiply(inverse(A),sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_31956]) ).
cnf(c_1164,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_1163]) ).
cnf(c_1166,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_955]) ).
cnf(c_1167,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_9,c_955]) ).
cnf(c_1168,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_13,c_955]) ).
cnf(c_1169,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_955]) ).
cnf(c_1170,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_955]) ).
cnf(c_1171,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_955]) ).
cnf(c_1173,plain,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_955]) ).
cnf(c_1175,plain,
( multiply(sk_c5,sk_c6) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_955]) ).
cnf(c_1177,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_27,c_955]) ).
cnf(c_1179,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_29,c_955]) ).
cnf(c_1182,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_32,c_955]) ).
cnf(c_1193,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c6,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_87,c_955]) ).
cnf(c_2620,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1173,c_2]) ).
cnf(c_2784,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_1175,c_2]) ).
cnf(c_31957,plain,
( identity = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1166,c_6]) ).
cnf(c_5645,plain,
( identity = sk_c4
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_31957]) ).
cnf(c_5653,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_5645,c_45]) ).
cnf(c_31958,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1167,c_8]) ).
cnf(c_5765,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_31958]) ).
cnf(c_5772,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_5765,c_45]) ).
cnf(c_31959,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1168,c_12]) ).
cnf(c_5803,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_31959]) ).
cnf(c_31960,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1169,c_14]) ).
cnf(c_6013,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_31960]) ).
cnf(c_31961,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| identity = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1170,c_10]) ).
cnf(c_6231,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_31961]) ).
cnf(c_6237,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6231,c_45]) ).
cnf(c_31962,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| identity = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_1171,c_11]) ).
cnf(c_6473,plain,
( identity = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_31962]) ).
cnf(c_31963,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1177,c_26]) ).
cnf(c_6838,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_31963]) ).
cnf(c_31964,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| identity = sk_c6
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_1179,c_23]) ).
cnf(c_7222,plain,
( identity = sk_c6
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_31964]) ).
cnf(c_7234,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_7222,c_45]) ).
cnf(c_31965,plain,
( multiply(sk_c6,sk_c5) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_1193,c_81]) ).
cnf(c_9173,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c5) = identity ),
inference(copy,[status(thm)],[c_31965]) ).
cnf(c_31966,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9173,c_45]) ).
cnf(c_9176,plain,
( inverse(sk_c6) = sk_c5
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_578,c_31966]) ).
cnf(c_9179,plain,
( multiply(sk_c5,sk_c6) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9176,c_2]) ).
cnf(c_9603,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9179,c_1182]) ).
cnf(c_31967,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c4
| multiply(sk_c8,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2620,c_68]) ).
cnf(c_9613,plain,
( identity = sk_c4
| multiply(sk_c8,sk_c1) = identity ),
inference(copy,[status(thm)],[c_31967]) ).
cnf(c_31968,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_9613,c_45]) ).
cnf(c_9729,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_578,c_31968]) ).
cnf(c_9740,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_9729,c_2]) ).
cnf(c_31969,plain,
( identity = sk_c4
| identity = sk_c7
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_9740,c_5803]) ).
cnf(c_9862,plain,
( identity = sk_c7
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_31969]) ).
cnf(c_9927,plain,
( multiply(A,sk_c4) = A
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9862,c_578]) ).
cnf(c_31970,plain,
( multiply(inverse(sk_c6),sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(resolve,[status(thm)],[c_729,c_978]) ).
cnf(c_31971,plain,
( identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_31970]) ).
cnf(c_10031,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_31971]) ).
cnf(c_31972,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(inverse(sk_c7),sk_c7) != sk_c6
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(resolve,[status(thm)],[c_10031,c_978]) ).
cnf(c_10044,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_31972]) ).
cnf(c_31973,plain,
( identity = sk_c7
| sk_c8 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9927,c_6473]) ).
cnf(c_31974,plain,
( identity = sk_c7
| sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31973]) ).
cnf(c_10163,plain,
( sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_31974]) ).
cnf(c_10173,plain,
( multiply(A,sk_c7) = A
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10163,c_578]) ).
cnf(c_10174,plain,
( inverse(sk_c7) = identity
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10163,c_694]) ).
cnf(c_31975,plain,
( multiply(identity,sk_c6) = sk_c8
| identity = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10174,c_5772]) ).
cnf(c_10459,plain,
( sk_c6 = sk_c8
| identity = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_31975]) ).
cnf(c_10993,plain,
( identity = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10173,c_6838]) ).
cnf(c_31976,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10459,c_10163]) ).
cnf(c_31977,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_31976]) ).
cnf(c_31978,plain,
( sk_c7 = sk_c8
| sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_31977]) ).
cnf(c_11232,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_31978]) ).
cnf(c_31979,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10993,c_10163]) ).
cnf(c_31980,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_31979]) ).
cnf(c_31981,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_31980]) ).
cnf(c_11832,plain,
( sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_31981]) ).
cnf(c_31982,plain,
( sk_c2 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_11232,c_11832]) ).
cnf(c_11858,plain,
( sk_c2 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_31982]) ).
cnf(c_31983,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c8
| multiply(sk_c8,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2784,c_70]) ).
cnf(c_12354,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c1) = identity ),
inference(copy,[status(thm)],[c_31983]) ).
cnf(c_31984,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12354,c_45]) ).
cnf(c_12360,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_578,c_31984]) ).
cnf(c_12373,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12360,c_2]) ).
cnf(c_31985,plain,
( identity = sk_c8
| identity = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12373,c_6013]) ).
cnf(c_12492,plain,
( identity = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_31985]) ).
cnf(c_12494,plain,
( multiply(A,sk_c7) = A
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12492,c_578]) ).
cnf(c_12495,plain,
( inverse(sk_c7) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12492,c_694]) ).
cnf(c_31986,plain,
( multiply(identity,sk_c6) = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12495,c_5772]) ).
cnf(c_31987,plain,
( sk_c6 = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_31986]) ).
cnf(c_12533,plain,
( sk_c6 = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_31987]) ).
cnf(c_12653,plain,
( inverse(sk_c8) = identity
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_12533,c_694]) ).
cnf(c_31988,plain,
( multiply(identity,sk_c7) = sk_c4
| identity = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_12653,c_7234]) ).
cnf(c_31989,plain,
( sk_c7 = sk_c4
| identity = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_31988]) ).
cnf(c_12764,plain,
( sk_c4 = sk_c7
| identity = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31989]) ).
cnf(c_31990,plain,
( inverse(sk_c8) = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_12533,c_12653]) ).
cnf(c_12809,plain,
( inverse(sk_c8) = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31990]) ).
cnf(c_12824,plain,
( multiply(sk_c8,sk_c8) = identity
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_12809,c_2]) ).
cnf(c_31991,plain,
( multiply(sk_c6,identity) = multiply(sk_c7,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_12824,c_46]) ).
cnf(c_31992,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_578,c_31991]) ).
cnf(c_31993,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31992]) ).
cnf(c_13587,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31993]) ).
cnf(c_31994,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c4 = sk_c7
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_12764,c_12533]) ).
cnf(c_31995,plain,
( sk_c6 = sk_c8
| sk_c4 = sk_c7
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31994]) ).
cnf(c_14424,plain,
( sk_c4 = sk_c7
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31995]) ).
cnf(c_31996,plain,
( identity = sk_c7
| identity = sk_c7
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_14424,c_9862]) ).
cnf(c_14439,plain,
( identity = sk_c7
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31996]) ).
cnf(c_14440,plain,
( multiply(sk_c7,A) = A
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_14439,c_1]) ).
cnf(c_31997,plain,
( sk_c8 = sk_c6
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_14440,c_13587]) ).
cnf(c_31998,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31997]) ).
cnf(c_31999,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_31998]) ).
cnf(c_15233,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_31999]) ).
cnf(c_32000,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_10044]) ).
cnf(c_32001,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c8
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_32000]) ).
cnf(c_32002,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_32001]) ).
cnf(c_32003,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_32002]) ).
cnf(c_17476,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_32003]) ).
cnf(c_32004,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_9603]) ).
cnf(c_17606,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_32004]) ).
cnf(c_18933,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_15233,c_6237]) ).
cnf(c_19022,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c8
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_15233,c_5653]) ).
cnf(c_32005,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_1164]) ).
cnf(c_32006,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c8 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_32005]) ).
cnf(c_32007,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_32006]) ).
cnf(c_32008,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c7
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_32007]) ).
cnf(c_32009,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_32008]) ).
cnf(c_21548,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c8
| identity != sk_c7
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_32009]) ).
cnf(c_32010,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_4]) ).
cnf(c_22202,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_15233,c_32010]) ).
cnf(c_32011,plain,
( identity = sk_c2
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_17606,c_12494]) ).
cnf(c_30636,plain,
( identity = sk_c2
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_32011]) ).
cnf(c_32012,plain,
( identity = sk_c8
| identity = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_11858,c_30636]) ).
cnf(c_30645,plain,
( identity = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32012]) ).
cnf(c_32013,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_30645,c_10163]) ).
cnf(c_32014,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32013]) ).
cnf(c_32015,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32014]) ).
cnf(c_30830,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_32015]) ).
cnf(c_32016,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_22202]) ).
cnf(c_32017,plain,
( multiply(sk_c8,sk_c8) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32016]) ).
cnf(c_31539,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(copy,[status(thm)],[c_32017]) ).
cnf(c_32018,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c8
| identity != sk_c7
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_21548]) ).
cnf(c_32019,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c8
| identity != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_31539,c_32018]) ).
cnf(c_32020,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32019]) ).
cnf(c_32021,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32020]) ).
cnf(c_32022,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_31539,c_32021]) ).
cnf(c_32023,plain,
( multiply(inverse(sk_c7),sk_c8) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32022]) ).
cnf(c_32024,plain,
( multiply(inverse(sk_c8),sk_c8) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32023]) ).
cnf(c_32025,plain,
( identity != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_32024]) ).
cnf(c_32026,plain,
( identity != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_32025]) ).
cnf(c_32027,plain,
( identity != sk_c8
| sk_c8 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_32026]) ).
cnf(c_32028,plain,
( identity != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_32027]) ).
cnf(c_31645,plain,
identity != sk_c8,
inference(copy,[status(thm)],[c_32028]) ).
cnf(c_32029,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c8
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_30830,c_19022]) ).
cnf(c_32030,plain,
( identity = sk_c8
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_2,c_32029]) ).
cnf(c_31868,plain,
identity = sk_c4,
inference(resolve,[status(thm)],[c_31645,c_32030]) ).
cnf(c_32031,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_31868,c_18933]) ).
cnf(c_32032,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| sk_c4 = sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32031]) ).
cnf(c_32033,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c8
| sk_c4 = sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32032]) ).
cnf(c_32034,plain,
( identity = sk_c8
| sk_c4 = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_32033]) ).
cnf(c_32035,plain,
( sk_c4 = sk_c8
| sk_c4 = sk_c8 ),
inference(paramod,[status(thm)],[c_31868,c_32034]) ).
cnf(c_31890,plain,
sk_c4 = sk_c8,
inference(copy,[status(thm)],[c_32035]) ).
cnf(c_32036,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_17476]) ).
cnf(c_32037,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_31539,c_32036]) ).
cnf(c_32038,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32037]) ).
cnf(c_32039,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| sk_c4 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_31868,c_32038]) ).
cnf(c_32040,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_31890,c_32039]) ).
cnf(c_32041,plain,
( sk_c8 != sk_c7
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_31539,c_32040]) ).
cnf(c_32042,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_30830,c_32041]) ).
cnf(c_32043,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_32042]) ).
cnf(c_32044,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_32043]) ).
cnf(c_32045,plain,
sk_c8 != sk_c8,
inference(copy,[status(thm)],[c_32044]) ).
cnf(c_31942,plain,
$false,
inference(copy,[status(thm)],[c_32045]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP316-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:45:17 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 472939 was started by sandbox2 on n014,
% 0.17/0.44 % Fri Sep 25 14:45:17 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 127.19/17.62
% 127.19/17.62 % given #500 (T,wt=7): 12375 identity = sk_c8 | inverse(sk_c1) = sk_c8. [para(12360(b,1),978(a,1,1))].
% 127.19/17.62
% 127.19/17.62 % SZS status Unsatisfiable for theBenchmark
% 127.19/17.62
% 127.19/17.62 % Proof 1 at 15.16 (+ 1.82) seconds.
% 127.19/17.62 % Length of proof is 124.
% 127.19/17.62 % Level of proof is 26.
% 127.19/17.62 % Maximum clause weight is 51.000.
% 127.19/17.62 % Given clauses 842.
% 127.19/17.62
% 127.19/17.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------