%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP290-1 : 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 : n005.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 07:28:34 AM UTC 2026
% Result : Unsatisfiable 249.88s 33.03s
% Output : CNFRefutation 249.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 27
% Syntax : Number of formulae : 242 ( 24 unt; 0 def)
% Number of atoms : 635 ( 634 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 558 ( 165 ~; 393 |; 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 : 66 ( 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_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c7) = 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_22,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
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_28,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
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_c8,sk_c7) != 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_c8,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_32230,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_32231,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_32230]) ).
cnf(c_50,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_32231]) ).
cnf(c_32232,plain,
( multiply(sk_c7,A) = multiply(sk_c6,multiply(sk_c8,A))
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_51,plain,
( multiply(sk_c6,multiply(sk_c8,A)) = multiply(sk_c7,A)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_32232]) ).
cnf(c_57,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_73,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c8) = sk_c4 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_75,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_83,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_86,plain,
( multiply(sk_c6,sk_c5) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_90,plain,
( multiply(sk_c8,sk_c3) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_92,plain,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_33,c_2]) ).
cnf(c_32233,plain,
A = multiply(identity,A),
inference(copy,[status(thm)],[c_1]) ).
cnf(c_32234,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c8
| inverse(C) != sk_c8
| multiply(sk_c8,multiply(identity,multiply(C,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_c8,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_34,c_32233]) ).
cnf(c_108,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c8
| inverse(C) != sk_c8
| multiply(sk_c8,multiply(C,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_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_32234]) ).
cnf(c_690,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_50]) ).
cnf(c_722,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_50,c_50]) ).
cnf(c_723,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_722,c_690]) ).
cnf(c_786,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_723,c_2]) ).
cnf(c_938,plain,
( multiply(inverse(sk_c6),multiply(sk_c7,A)) = multiply(sk_c8,A)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_51,c_50]) ).
cnf(c_1027,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_722,c_2]) ).
cnf(c_32235,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_722,c_723]) ).
cnf(c_32236,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_723,c_32235]) ).
cnf(c_1053,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_32236]) ).
cnf(c_1202,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_1027]) ).
cnf(c_1203,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_9,c_1027]) ).
cnf(c_1204,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_13,c_1027]) ).
cnf(c_1205,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_1027]) ).
cnf(c_1206,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_1027]) ).
cnf(c_1207,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_1027]) ).
cnf(c_1209,plain,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_1027]) ).
cnf(c_1211,plain,
( multiply(sk_c5,sk_c6) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_1027]) ).
cnf(c_1213,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_27,c_1027]) ).
cnf(c_1218,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_32,c_1027]) ).
cnf(c_1232,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c8,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_90,c_1027]) ).
cnf(c_1233,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c6,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_92,c_1027]) ).
cnf(c_32237,plain,
( multiply(sk_c6,identity) = multiply(sk_c7,sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_57,c_51]) ).
cnf(c_32238,plain,
( sk_c6 = multiply(sk_c7,sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_723,c_32237]) ).
cnf(c_32239,plain,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_32238]) ).
cnf(c_2112,plain,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_32239]) ).
cnf(c_2793,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1209,c_2]) ).
cnf(c_2959,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_1211,c_2]) ).
cnf(c_32240,plain,
( identity = sk_c4
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1202,c_6]) ).
cnf(c_5682,plain,
( identity = sk_c4
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_32240]) ).
cnf(c_32241,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1203,c_8]) ).
cnf(c_5836,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_32241]) ).
cnf(c_32242,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1204,c_12]) ).
cnf(c_5885,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_32242]) ).
cnf(c_6121,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_5885,c_50]) ).
cnf(c_32243,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1205,c_14]) ).
cnf(c_6140,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_32243]) ).
cnf(c_32244,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| identity = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1206,c_10]) ).
cnf(c_6426,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_32244]) ).
cnf(c_6434,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6426,c_50]) ).
cnf(c_32245,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| identity = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_1207,c_11]) ).
cnf(c_6766,plain,
( identity = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_32245]) ).
cnf(c_32246,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1213,c_26]) ).
cnf(c_7314,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_32246]) ).
cnf(c_32247,plain,
( multiply(sk_c8,sk_c3) = identity
| identity = sk_c6
| multiply(sk_c8,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_1232,c_83]) ).
cnf(c_8763,plain,
( identity = sk_c6
| multiply(sk_c8,sk_c3) = identity ),
inference(copy,[status(thm)],[c_32247]) ).
cnf(c_32248,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_8763,c_50]) ).
cnf(c_8770,plain,
( inverse(sk_c8) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_723,c_32248]) ).
cnf(c_32249,plain,
( multiply(sk_c6,sk_c5) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_1233,c_86]) ).
cnf(c_9504,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c5) = identity ),
inference(copy,[status(thm)],[c_32249]) ).
cnf(c_32250,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9504,c_50]) ).
cnf(c_9507,plain,
( inverse(sk_c6) = sk_c5
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_723,c_32250]) ).
cnf(c_9510,plain,
( multiply(sk_c5,sk_c6) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9507,c_2]) ).
cnf(c_9878,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9510,c_1218]) ).
cnf(c_32251,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c4
| multiply(sk_c8,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2793,c_73]) ).
cnf(c_10012,plain,
( identity = sk_c4
| multiply(sk_c8,sk_c1) = identity ),
inference(copy,[status(thm)],[c_32251]) ).
cnf(c_32252,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10012,c_50]) ).
cnf(c_10016,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_723,c_32252]) ).
cnf(c_10028,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10016,c_2]) ).
cnf(c_10033,plain,
( inverse(sk_c1) = sk_c8
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10016,c_1053]) ).
cnf(c_32253,plain,
( multiply(sk_c8,sk_c7) = sk_c8
| identity = sk_c4
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10033,c_6121]) ).
cnf(c_10262,plain,
( multiply(sk_c8,sk_c7) = sk_c8
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_32253]) ).
cnf(c_32254,plain,
( identity = sk_c4
| identity = sk_c7
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10028,c_5885]) ).
cnf(c_10267,plain,
( identity = sk_c7
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_32254]) ).
cnf(c_10269,plain,
( multiply(A,sk_c4) = A
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10267,c_723]) ).
cnf(c_32255,plain,
( identity = sk_c4
| sk_c8 = sk_c6
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10262,c_5682]) ).
cnf(c_32256,plain,
( identity = sk_c4
| sk_c6 = sk_c8
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_32255]) ).
cnf(c_10437,plain,
( sk_c6 = sk_c8
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_32256]) ).
cnf(c_10440,plain,
( inverse(sk_c4) = identity
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_10437,c_786]) ).
cnf(c_32257,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,multiply(B,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(inverse(sk_c7),sk_c7) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_108,c_1053]) ).
cnf(c_10478,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,multiply(B,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_32257]) ).
cnf(c_10489,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c8,multiply(A,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_10478]) ).
cnf(c_32258,plain,
( inverse(sk_c4) = sk_c4
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_10437,c_10440]) ).
cnf(c_10654,plain,
( inverse(sk_c4) = sk_c4
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32258]) ).
cnf(c_10659,plain,
( multiply(sk_c4,sk_c4) = identity
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_10654,c_2]) ).
cnf(c_32259,plain,
( identity = sk_c7
| sk_c8 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10269,c_6766]) ).
cnf(c_32260,plain,
( identity = sk_c7
| sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_32259]) ).
cnf(c_10728,plain,
( sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_32260]) ).
cnf(c_10904,plain,
( multiply(A,sk_c7) = A
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10728,c_723]) ).
cnf(c_32261,plain,
( identity = sk_c8
| sk_c8 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10904,c_5836]) ).
cnf(c_11508,plain,
( identity = sk_c8
| sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32261]) ).
cnf(c_11516,plain,
( identity = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10904,c_7314]) ).
cnf(c_32262,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_11508,c_10728]) ).
cnf(c_32263,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32262]) ).
cnf(c_32264,plain,
( sk_c7 = sk_c8
| sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32263]) ).
cnf(c_12007,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32264]) ).
cnf(c_32265,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_11516,c_10728]) ).
cnf(c_32266,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32265]) ).
cnf(c_32267,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32266]) ).
cnf(c_12231,plain,
( sk_c2 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32267]) ).
cnf(c_32268,plain,
( sk_c2 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_12007,c_12231]) ).
cnf(c_12257,plain,
( sk_c2 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32268]) ).
cnf(c_32269,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c8
| multiply(sk_c8,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2959,c_75]) ).
cnf(c_12930,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c1) = identity ),
inference(copy,[status(thm)],[c_32269]) ).
cnf(c_32270,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12930,c_50]) ).
cnf(c_12937,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_723,c_32270]) ).
cnf(c_12948,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12937,c_2]) ).
cnf(c_32271,plain,
( identity = sk_c8
| identity = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12948,c_6140]) ).
cnf(c_13079,plain,
( identity = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_32271]) ).
cnf(c_13082,plain,
( multiply(A,sk_c7) = A
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_13079,c_723]) ).
cnf(c_32272,plain,
( identity = sk_c8
| sk_c8 = sk_c6
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_13082,c_5836]) ).
cnf(c_32273,plain,
( identity = sk_c8
| sk_c6 = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_32272]) ).
cnf(c_13227,plain,
( sk_c6 = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_32273]) ).
cnf(c_32274,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c4
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_13227,c_10437]) ).
cnf(c_32275,plain,
( sk_c6 = sk_c8
| sk_c4 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32274]) ).
cnf(c_13298,plain,
( sk_c4 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32275]) ).
cnf(c_32276,plain,
( multiply(sk_c4,sk_c4) = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_13227,c_10659]) ).
cnf(c_13301,plain,
( multiply(sk_c4,sk_c4) = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32276]) ).
cnf(c_32277,plain,
( inverse(sk_c8) = sk_c4
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_13298,c_10654]) ).
cnf(c_13377,plain,
( inverse(sk_c8) = sk_c4
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32277]) ).
cnf(c_32278,plain,
( multiply(sk_c8,sk_c4) = identity
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_13298,c_10659]) ).
cnf(c_13380,plain,
( multiply(sk_c8,sk_c4) = identity
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32278]) ).
cnf(c_13690,plain,
( sk_c4 = sk_c3
| identity = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_13377,c_8770]) ).
cnf(c_32279,plain,
( identity = sk_c7
| identity = sk_c7
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_13380,c_6766]) ).
cnf(c_14219,plain,
( identity = sk_c7
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32279]) ).
cnf(c_14222,plain,
( multiply(A,sk_c7) = A
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_14219,c_723]) ).
cnf(c_32280,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c4
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_14219,c_10437]) ).
cnf(c_32281,plain,
( sk_c6 = sk_c8
| sk_c4 = sk_c7
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32280]) ).
cnf(c_14246,plain,
( sk_c4 = sk_c7
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32281]) ).
cnf(c_32282,plain,
( multiply(sk_c7,sk_c4) = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_14246,c_13301]) ).
cnf(c_14268,plain,
( multiply(sk_c7,sk_c4) = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32282]) ).
cnf(c_32283,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c4 = sk_c3
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_13690,c_13227]) ).
cnf(c_32284,plain,
( sk_c6 = sk_c8
| sk_c4 = sk_c3
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32283]) ).
cnf(c_15515,plain,
( sk_c4 = sk_c3
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32284]) ).
cnf(c_32285,plain,
( multiply(sk_c7,sk_c3) = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_15515,c_14268]) ).
cnf(c_15590,plain,
( multiply(sk_c7,sk_c3) = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32285]) ).
cnf(c_32286,plain,
( sk_c8 = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_15590,c_2112]) ).
cnf(c_32287,plain,
( sk_c6 = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32286]) ).
cnf(c_15837,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32287]) ).
cnf(c_32288,plain,
( multiply(inverse(sk_c6),sk_c6) != sk_c8
| multiply(sk_c8,multiply(A,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_10489,c_1053]) ).
cnf(c_15942,plain,
( identity != sk_c8
| multiply(sk_c8,multiply(A,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_32288]) ).
cnf(c_32289,plain,
( identity != sk_c8
| multiply(sk_c8,multiply(identity,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| identity != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_786,c_15942]) ).
cnf(c_32290,plain,
( identity != sk_c8
| multiply(sk_c8,multiply(identity,sk_c8)) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_32289]) ).
cnf(c_32291,plain,
( identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| identity != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_32290]) ).
cnf(c_32292,plain,
( identity != sk_c8
| 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_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_32291]) ).
cnf(c_15972,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_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_32292]) ).
cnf(c_32293,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_15837,c_14222]) ).
cnf(c_32294,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_32293]) ).
cnf(c_16169,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_32294]) ).
cnf(c_32295,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_c8,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_16169,c_15972]) ).
cnf(c_32296,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_c8,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_16169,c_32295]) ).
cnf(c_32297,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_c8,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_16169,c_32296]) ).
cnf(c_32298,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_32297]) ).
cnf(c_16279,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_32298]) ).
cnf(c_32299,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_16169,c_9878]) ).
cnf(c_18017,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_32299]) ).
cnf(c_19837,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16169,c_6434]) ).
cnf(c_32300,plain,
( multiply(inverse(sk_c6),multiply(sk_c7,A)) = multiply(sk_c8,A)
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_16169,c_938]) ).
cnf(c_22871,plain,
( multiply(inverse(sk_c8),multiply(sk_c7,A)) = multiply(sk_c8,A)
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_16169,c_32300]) ).
cnf(c_32301,plain,
( identity = sk_c2
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_18017,c_13082]) ).
cnf(c_30867,plain,
( identity = sk_c2
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_32301]) ).
cnf(c_32302,plain,
( identity = sk_c8
| identity = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_12257,c_30867]) ).
cnf(c_30876,plain,
( identity = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32302]) ).
cnf(c_32303,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_30876,c_10728]) ).
cnf(c_32304,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32303]) ).
cnf(c_32305,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_32304]) ).
cnf(c_30988,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_32305]) ).
cnf(c_32306,plain,
( multiply(inverse(sk_c8),multiply(sk_c7,A)) = multiply(sk_c8,A)
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_30988,c_22871]) ).
cnf(c_32307,plain,
( multiply(inverse(sk_c8),multiply(sk_c8,A)) = multiply(sk_c8,A)
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_30988,c_32306]) ).
cnf(c_32308,plain,
( A = multiply(sk_c8,A)
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_50,c_32307]) ).
cnf(c_31840,plain,
( multiply(sk_c8,A) = A
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(copy,[status(thm)],[c_32308]) ).
cnf(c_32309,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_30988,c_19837]) ).
cnf(c_32310,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_30988,c_32309]) ).
cnf(c_32311,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_32310]) ).
cnf(c_31984,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_32311]) ).
cnf(c_32312,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_30988,c_16279]) ).
cnf(c_32313,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_30988,c_32312]) ).
cnf(c_32314,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_31984,c_32313]) ).
cnf(c_32315,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_30988,c_32314]) ).
cnf(c_32316,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_32315]) ).
cnf(c_32317,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_32316]) ).
cnf(c_32111,plain,
multiply(sk_c8,sk_c8) != sk_c8,
inference(copy,[status(thm)],[c_32317]) ).
cnf(c_32318,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(factor,[status(thm)],[c_31840]) ).
cnf(c_32229,plain,
$false,
inference(resolve,[status(thm)],[c_32111,c_32318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP290-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 14:43:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3727524 was started by sandbox2 on n005,
% 0.09/0.37 % Fri Sep 25 14:43:48 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 249.88/33.03
% 249.88/33.03 % given #500 (A,wt=52): 119 multiply(sk_c8,sk_c7) != sk_c6 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c7) != sk_c6 | inverse(B) != sk_c7 | multiply(sk_c6,sk_c8) != sk_c7 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8 | multiply(sk_c5,sk_c6) != sk_c8 | multiply(sk_c1,sk_c8) = sk_c7. [resolve(34,k,15,b)].
% 249.88/33.03
% 249.88/33.03 % given #1000 (T,wt=7): 30123 sk_c3 = sk_c8 | inverse(sk_c1) = sk_c8. [para(29041(b,1),1053(a,1,1))].
% 249.88/33.03
% 249.88/33.03 % SZS status Unsatisfiable for theBenchmark
% 249.88/33.03
% 249.88/33.03 % Proof 1 at 28.52 (+ 3.94) seconds.
% 249.88/33.03 % Length of proof is 126.
% 249.88/33.03 % Level of proof is 27.
% 249.88/33.03 % Maximum clause weight is 51.000.
% 249.88/33.03 % Given clauses 1045.
% 249.88/33.03
% 249.88/33.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------