%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP296-1 : 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 : n006.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 07:28:35 AM UTC 2026
% Result : Unsatisfiable 239.78s 32.79s
% Output : CNFRefutation 239.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 29
% Syntax : Number of formulae : 249 ( 28 unt; 0 def)
% Number of atoms : 662 ( 661 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 586 ( 173 ~; 413 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 77 ( 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_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_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_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_21,axiom,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_28,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_29,axiom,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_32,axiom,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_33,axiom,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_34,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_34) ).
cnf(c_37,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_34]) ).
fof(prove_this_37,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_c8
| multiply(VAR_1,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_37) ).
cnf(c_40,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_c8
| multiply(B,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_37]) ).
cnf(c_35598,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_35599,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_35598]) ).
cnf(c_47,plain,
( inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_35599]) ).
cnf(c_35600,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_35601,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_35600]) ).
cnf(c_54,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_35601]) ).
cnf(c_55,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_61,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_74,plain,
( multiply(sk_c6,sk_c5) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_77,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c8) = sk_c4 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_78,plain,
( multiply(sk_c8,sk_c3) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_80,plain,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_35602,plain,
( multiply(sk_c6,A) = multiply(sk_c2,multiply(sk_c8,A))
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_28,c_3]) ).
cnf(c_91,plain,
( multiply(sk_c2,multiply(sk_c8,A)) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_35602]) ).
cnf(c_97,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_104,plain,
( multiply(sk_c8,sk_c3) = identity
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_37,c_2]) ).
cnf(c_220,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_54]) ).
cnf(c_258,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_54,c_54]) ).
cnf(c_259,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_258,c_220]) ).
cnf(c_260,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_259,c_2]) ).
cnf(c_350,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_258,c_2]) ).
cnf(c_359,plain,
( multiply(inverse(sk_c8),A) = multiply(sk_c1,A)
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_258]) ).
cnf(c_365,plain,
( multiply(inverse(sk_c8),A) = multiply(sk_c2,A)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_34,c_258]) ).
cnf(c_35603,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_258,c_259]) ).
cnf(c_35604,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_259,c_35603]) ).
cnf(c_372,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_35604]) ).
cnf(c_35605,plain,
( multiply(inverse(sk_c6),sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_372,c_47]) ).
cnf(c_384,plain,
( identity != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_35605]) ).
cnf(c_392,plain,
( inverse(sk_c8) = sk_c1
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_372]) ).
cnf(c_393,plain,
( inverse(sk_c8) = sk_c1
| multiply(sk_c3,sk_c8) = sk_c4 ),
inference(paramod,[status(thm)],[c_18,c_372]) ).
cnf(c_402,plain,
( inverse(sk_c8) = sk_c2
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_35,c_372]) ).
cnf(c_403,plain,
( inverse(sk_c8) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c4 ),
inference(paramod,[status(thm)],[c_36,c_372]) ).
cnf(c_415,plain,
( inverse(sk_c8) = sk_c1
| multiply(sk_c8,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_78,c_372]) ).
cnf(c_417,plain,
( inverse(sk_c8) = sk_c2
| multiply(sk_c8,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_104,c_372]) ).
cnf(c_444,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_13,c_350]) ).
cnf(c_445,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_350]) ).
cnf(c_447,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_350]) ).
cnf(c_449,plain,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_350]) ).
cnf(c_452,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_25,c_350]) ).
cnf(c_453,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_27,c_350]) ).
cnf(c_455,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_33,c_350]) ).
cnf(c_457,plain,
( multiply(sk_c2,sk_c8) = identity
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_35,c_350]) ).
cnf(c_463,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c6,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_80,c_350]) ).
cnf(c_466,plain,
( multiply(sk_c2,sk_c8) = identity
| multiply(sk_c8,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_104,c_350]) ).
cnf(c_35606,plain,
( identity != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| identity != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_260,c_384]) ).
cnf(c_35607,plain,
( identity != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| identity != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_35606]) ).
cnf(c_35608,plain,
( identity != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_35607]) ).
cnf(c_958,plain,
( multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_35608]) ).
cnf(c_35609,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c6,identity)
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_61,c_55]) ).
cnf(c_35610,plain,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_259,c_35609]) ).
cnf(c_1039,plain,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_35610]) ).
cnf(c_35611,plain,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_402,c_392]) ).
cnf(c_1479,plain,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_35611]) ).
cnf(c_35612,plain,
( sk_c2 = sk_c1
| multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c3,sk_c8) = sk_c4 ),
inference(paramod,[status(thm)],[c_403,c_393]) ).
cnf(c_1497,plain,
( sk_c2 = sk_c1
| multiply(sk_c3,sk_c8) = sk_c4 ),
inference(copy,[status(thm)],[c_35612]) ).
cnf(c_35613,plain,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c3) = identity
| multiply(sk_c8,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_417,c_415]) ).
cnf(c_1874,plain,
( sk_c2 = sk_c1
| multiply(sk_c8,sk_c3) = identity ),
inference(copy,[status(thm)],[c_35613]) ).
cnf(c_35614,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_1874,c_54]) ).
cnf(c_1879,plain,
( inverse(sk_c8) = sk_c3
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_259,c_35614]) ).
cnf(c_1880,plain,
( multiply(sk_c3,sk_c8) = identity
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_1879,c_2]) ).
cnf(c_35615,plain,
( sk_c2 = sk_c1
| identity = sk_c4
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_1880,c_1497]) ).
cnf(c_2106,plain,
( identity = sk_c4
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_35615]) ).
cnf(c_2108,plain,
( multiply(A,sk_c4) = A
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_2106,c_259]) ).
cnf(c_35616,plain,
( sk_c2 = sk_c1
| sk_c8 = sk_c7
| sk_c2 = sk_c1 ),
inference(paramod,[status(thm)],[c_2108,c_1479]) ).
cnf(c_35617,plain,
( sk_c2 = sk_c1
| sk_c7 = sk_c8
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_35616]) ).
cnf(c_2481,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c1 ),
inference(copy,[status(thm)],[c_35617]) ).
cnf(c_4316,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_449,c_2]) ).
cnf(c_35618,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_444,c_12]) ).
cnf(c_10455,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_35618]) ).
cnf(c_35619,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_445,c_14]) ).
cnf(c_10478,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_35619]) ).
cnf(c_35620,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| identity = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_447,c_11]) ).
cnf(c_10526,plain,
( identity = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_35620]) ).
cnf(c_10569,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10526,c_54]) ).
cnf(c_35621,plain,
( identity = sk_c4
| multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_452,c_24]) ).
cnf(c_10621,plain,
( identity = sk_c4
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_35621]) ).
cnf(c_10626,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10621,c_54]) ).
cnf(c_35622,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_453,c_26]) ).
cnf(c_10710,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_35622]) ).
cnf(c_10715,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10710,c_54]) ).
cnf(c_35623,plain,
( sk_c6 = sk_c4
| identity = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10715,c_10569]) ).
cnf(c_10751,plain,
( sk_c4 = sk_c6
| identity = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_35623]) ).
cnf(c_35624,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_455,c_32]) ).
cnf(c_10808,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_35624]) ).
cnf(c_10820,plain,
( multiply(inverse(sk_c2),sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10808,c_54]) ).
cnf(c_35625,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| identity = sk_c6
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_457,c_29]) ).
cnf(c_10889,plain,
( identity = sk_c6
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_35625]) ).
cnf(c_10894,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10889,c_54]) ).
cnf(c_10926,plain,
( sk_c4 = sk_c6
| identity = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10894,c_10715]) ).
cnf(c_35626,plain,
( sk_c4 = sk_c6
| sk_c6 = sk_c7
| identity = sk_c8
| sk_c4 = sk_c6
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10926,c_10751]) ).
cnf(c_35627,plain,
( sk_c4 = sk_c6
| sk_c7 = sk_c6
| identity = sk_c8
| sk_c4 = sk_c6
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_35626]) ).
cnf(c_35628,plain,
( sk_c4 = sk_c6
| sk_c7 = sk_c6
| sk_c4 = sk_c6
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_35627]) ).
cnf(c_11082,plain,
( sk_c7 = sk_c6
| sk_c4 = sk_c6
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_35628]) ).
cnf(c_35629,plain,
( multiply(sk_c6,sk_c5) = identity
| identity = sk_c7
| multiply(sk_c6,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_463,c_74]) ).
cnf(c_11493,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c5) = identity ),
inference(copy,[status(thm)],[c_35629]) ).
cnf(c_35630,plain,
( multiply(inverse(sk_c6),identity) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11493,c_54]) ).
cnf(c_11499,plain,
( inverse(sk_c6) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_259,c_35630]) ).
cnf(c_11504,plain,
( multiply(sk_c5,sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11499,c_2]) ).
cnf(c_35631,plain,
( multiply(sk_c8,sk_c3) = identity
| identity = sk_c6
| multiply(sk_c8,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_466,c_97]) ).
cnf(c_11707,plain,
( identity = sk_c6
| multiply(sk_c8,sk_c3) = identity ),
inference(copy,[status(thm)],[c_35631]) ).
cnf(c_35632,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11707,c_54]) ).
cnf(c_11714,plain,
( inverse(sk_c8) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_259,c_35632]) ).
cnf(c_12171,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c3
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1039,c_54]) ).
cnf(c_35633,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10478,c_359]) ).
cnf(c_16378,plain,
( identity = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_35633]) ).
cnf(c_35634,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c4
| multiply(sk_c8,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_4316,c_77]) ).
cnf(c_16747,plain,
( identity = sk_c4
| multiply(sk_c8,sk_c1) = identity ),
inference(copy,[status(thm)],[c_35634]) ).
cnf(c_35635,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_16747,c_54]) ).
cnf(c_16753,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_259,c_35635]) ).
cnf(c_16813,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_16753,c_2]) ).
cnf(c_35636,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c4
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_16753,c_10626]) ).
cnf(c_16888,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_35636]) ).
cnf(c_35637,plain,
( identity = sk_c4
| identity = sk_c7
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_16813,c_10455]) ).
cnf(c_16912,plain,
( identity = sk_c7
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_35637]) ).
cnf(c_16916,plain,
( multiply(A,sk_c4) = A
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16912,c_259]) ).
cnf(c_35638,plain,
( multiply(inverse(sk_c8),multiply(sk_c8,A)) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_91,c_365]) ).
cnf(c_35639,plain,
( A = multiply(sk_c6,A)
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_54,c_35638]) ).
cnf(c_35640,plain,
( multiply(sk_c6,A) = A
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_35639]) ).
cnf(c_16939,plain,
( multiply(sk_c6,A) = A
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_35640]) ).
cnf(c_35641,plain,
( identity = sk_c7
| sk_c8 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_16916,c_10526]) ).
cnf(c_35642,plain,
( identity = sk_c7
| sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_35641]) ).
cnf(c_17243,plain,
( sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_35642]) ).
cnf(c_17274,plain,
( multiply(A,sk_c7) = A
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_17243,c_259]) ).
cnf(c_35643,plain,
( sk_c7 = sk_c6
| sk_c4 = sk_c6
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_17243,c_11082]) ).
cnf(c_17295,plain,
( sk_c7 = sk_c6
| sk_c4 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35643]) ).
cnf(c_17990,plain,
( sk_c1 = sk_c6
| identity = sk_c4
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_17274,c_16888]) ).
cnf(c_35644,plain,
( sk_c7 = sk_c8
| sk_c4 = sk_c7
| sk_c1 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_17990,c_17243]) ).
cnf(c_18544,plain,
( sk_c4 = sk_c7
| sk_c1 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35644]) ).
cnf(c_35645,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c8
| sk_c1 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_18544,c_17295]) ).
cnf(c_35646,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c1 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35645]) ).
cnf(c_18752,plain,
( sk_c7 = sk_c6
| sk_c1 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35646]) ).
cnf(c_35647,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_18752,c_2481]) ).
cnf(c_18826,plain,
( sk_c2 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35647]) ).
cnf(c_35648,plain,
( multiply(inverse(sk_c6),sk_c6) = sk_c8
| identity = sk_c8
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_18826,c_10820]) ).
cnf(c_35649,plain,
( identity = sk_c8
| identity = sk_c8
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_35648]) ).
cnf(c_18865,plain,
( identity = sk_c8
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35649]) ).
cnf(c_35650,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_18865,c_17243]) ).
cnf(c_35651,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35650]) ).
cnf(c_35652,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35651]) ).
cnf(c_18899,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35652]) ).
cnf(c_35653,plain,
( multiply(A,sk_c6) = A
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_18899,c_17274]) ).
cnf(c_18947,plain,
( multiply(A,sk_c6) = A
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35653]) ).
cnf(c_35654,plain,
( identity = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_18947,c_10710]) ).
cnf(c_35655,plain,
( identity = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35654]) ).
cnf(c_19251,plain,
( identity = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35655]) ).
cnf(c_35656,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_19251,c_17243]) ).
cnf(c_35657,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35656]) ).
cnf(c_35658,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_35657]) ).
cnf(c_19351,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_35658]) ).
cnf(c_20036,plain,
( multiply(sk_c6,A) = A
| multiply(sk_c6,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_19351,c_16939]) ).
cnf(c_35659,plain,
( identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_19351,c_16378]) ).
cnf(c_20224,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_35659]) ).
cnf(c_35660,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c3
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_19351,c_12171]) ).
cnf(c_21253,plain,
( multiply(inverse(sk_c8),sk_c6) = sk_c3
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_19351,c_35660]) ).
cnf(c_21726,plain,
( multiply(sk_c5,sk_c6) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_19351,c_11504]) ).
cnf(c_35661,plain,
( multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_19351,c_958]) ).
cnf(c_35662,plain,
( multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| identity != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_19351,c_35661]) ).
cnf(c_35663,plain,
( multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_19351,c_35662]) ).
cnf(c_35664,plain,
( multiply(sk_c6,sk_c8) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_19351,c_35663]) ).
cnf(c_25755,plain,
( multiply(sk_c6,sk_c8) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_35664]) ).
cnf(c_26267,plain,
multiply(sk_c6,sk_c8) = sk_c8,
inference(factor,[status(thm)],[c_20036]) ).
cnf(c_35665,plain,
( sk_c8 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_26267,c_25755]) ).
cnf(c_29632,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_35665]) ).
cnf(c_35666,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_21726,c_20224]) ).
cnf(c_35667,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_35666]) ).
cnf(c_34267,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_35667]) ).
cnf(c_35668,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_34267,c_29632]) ).
cnf(c_34950,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_35668]) ).
cnf(c_35669,plain,
( inverse(sk_c8) = sk_c3
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_34267,c_11714]) ).
cnf(c_35202,plain,
( inverse(sk_c8) = sk_c3
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_35669]) ).
cnf(c_35670,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_34267,c_260]) ).
cnf(c_35492,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_34267,c_35670]) ).
cnf(c_35493,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_34267,c_259]) ).
cnf(c_35501,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_34267,c_1]) ).
cnf(c_35671,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_34950]) ).
cnf(c_35672,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_35493,c_35671]) ).
cnf(c_35673,plain,
( inverse(sk_c8) != sk_c8
| sk_c6 != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_35501,c_35672]) ).
cnf(c_35674,plain,
( sk_c8 != sk_c8
| sk_c6 != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_35492,c_35673]) ).
cnf(c_35675,plain,
( sk_c8 != sk_c8
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_35674]) ).
cnf(c_35676,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_35675]) ).
cnf(c_35570,plain,
sk_c6 != sk_c8,
inference(copy,[status(thm)],[c_35676]) ).
cnf(c_35677,plain,
( sk_c8 = sk_c3
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_35492,c_35202]) ).
cnf(c_35678,plain,
( sk_c3 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_35677]) ).
cnf(c_35586,plain,
sk_c3 = sk_c8,
inference(resolve,[status(thm)],[c_35570,c_35678]) ).
cnf(c_35679,plain,
( multiply(inverse(sk_c8),sk_c6) = sk_c3
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_35493,c_21253]) ).
cnf(c_35680,plain,
( multiply(sk_c8,sk_c6) = sk_c3
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_35492,c_35679]) ).
cnf(c_35681,plain,
( sk_c6 = sk_c3
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_35501,c_35680]) ).
cnf(c_35682,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_35586,c_35681]) ).
cnf(c_35683,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_35682]) ).
cnf(c_35684,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_35683]) ).
cnf(c_35597,plain,
$false,
inference(resolve,[status(thm)],[c_35570,c_35684]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP296-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.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 14:43:42 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 3140117 was started by sandbox2 on n006,
% 0.09/0.37 % Fri Sep 25 14:43:42 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 239.78/32.79
% 239.78/32.79 % given #500 (T,wt=8): 6866 sk_c2 = sk_c1 | multiply(sk_c5,sk_c5) = sk_c7. [para(3363(b,1),5803(b,2)),merge(b)].
% 239.78/32.79
% 239.78/32.79 % given #1000 (T,wt=7): 11499 identity = sk_c7 | inverse(sk_c6) = sk_c5. [para(11493(a,1),54(a,1,2)),rewrite([259(7)])].
% 239.78/32.79
% 239.78/32.79 % given #1500 (F,wt=28): 29276 multiply(sk_c8,sk_c8) != sk_c6 | multiply(sk_c8,sk_c8) != sk_c8 | inverse(sk_c8) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c8 | multiply(inverse(A),sk_c6) != sk_c8 | sk_c6 != A. [factor(25976,a,e),rewrite([26267(22)]),xx(e)].
% 239.78/32.79
% 239.78/32.79 % SZS status Unsatisfiable for theBenchmark
% 239.78/32.79
% 239.78/32.79 % Proof 1 at 27.77 (+ 4.41) seconds.
% 239.78/32.79 % Length of proof is 133.
% 239.78/32.79 % Level of proof is 28.
% 239.78/32.79 % Maximum clause weight is 56.000.
% 239.78/32.79 % Given clauses 1601.
% 239.78/32.79
% 239.78/32.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------