%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP266-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 07:28:30 AM UTC 2026
% Result : Unsatisfiable 14.17s 2.44s
% Output : CNFRefutation 14.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 21
% Syntax : Number of formulae : 263 ( 39 unt; 0 def)
% Number of atoms : 712 ( 711 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 749 ( 300 ~; 449 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 13 !; 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_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_8,axiom,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_32,axiom,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_33,axiom,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_34,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('theBenchmark.p',prove_this_34) ).
cnf(c_37,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_34]) ).
fof(prove_this_35,axiom,
( inverse(sk_c7) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('theBenchmark.p',prove_this_35) ).
cnf(c_38,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_35]) ).
fof(prove_this_38,axiom,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('theBenchmark.p',prove_this_38) ).
cnf(c_41,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_38]) ).
fof(prove_this_39,axiom,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('theBenchmark.p',prove_this_39) ).
cnf(c_42,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_39]) ).
fof(prove_this_40,axiom,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('theBenchmark.p',prove_this_40) ).
cnf(c_43,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_40]) ).
fof(prove_this_41,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('theBenchmark.p',prove_this_41) ).
cnf(c_44,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_41]) ).
fof(prove_this_42,axiom,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('theBenchmark.p',prove_this_42) ).
cnf(c_45,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_42]) ).
fof(prove_this_46,axiom,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('theBenchmark.p',prove_this_46) ).
cnf(c_49,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_46]) ).
fof(prove_this_47,axiom,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('theBenchmark.p',prove_this_47) ).
cnf(c_50,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_47]) ).
fof(prove_this_48,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c10 ),
file('theBenchmark.p',prove_this_48) ).
cnf(c_51,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_48]) ).
fof(prove_this_49,axiom,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('theBenchmark.p',prove_this_49) ).
cnf(c_52,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_49]) ).
fof(prove_this_50,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( inverse(VAR_7) != sk_c9
| multiply(VAR_7,sk_c9) != VAR_6
| multiply(sk_c9,VAR_6) != sk_c10
| inverse(VAR_5) != sk_c9
| multiply(VAR_5,sk_c9) != sk_c10
| inverse(VAR_4) != sk_c11
| multiply(VAR_4,sk_c11) != sk_c10
| inverse(VAR_3) != sk_c10
| multiply(VAR_3,sk_c10) != VAR_2
| multiply(sk_c10,VAR_2) != sk_c9
| inverse(VAR_1) != sk_c9
| multiply(VAR_1,sk_c9) != sk_c10
| inverse(VAR_0) != sk_c11
| multiply(VAR_0,sk_c11) != sk_c10 ),
file('theBenchmark.p',prove_this_50) ).
cnf(c_53,plain,
( inverse(V7) != sk_c9
| multiply(V7,sk_c9) != V6
| multiply(sk_c9,V6) != sk_c10
| inverse(F) != sk_c9
| multiply(F,sk_c9) != sk_c10
| inverse(E) != sk_c11
| multiply(E,sk_c11) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(clausify,[status(thm)],[prove_this_50]) ).
cnf(c_4751,plain,
( inverse(V6) != sk_c9
| multiply(V6,sk_c9) != F
| multiply(sk_c9,F) != sk_c10
| inverse(E) != sk_c9
| multiply(E,sk_c9) != sk_c10
| inverse(A) != sk_c11
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_54,plain,
( inverse(V6) != sk_c9
| multiply(V6,sk_c9) != F
| multiply(sk_c9,F) != sk_c10
| inverse(E) != sk_c9
| multiply(E,sk_c9) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4751]) ).
cnf(c_4752,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c10
| inverse(B) != sk_c9
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_54]) ).
cnf(c_57,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4752]) ).
cnf(c_4753,plain,
( inverse(B) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_62,plain,
( multiply(sk_c9,sk_c10) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4753]) ).
cnf(c_63,plain,
( multiply(B,sk_c9) != E
| multiply(sk_c9,E) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_68,plain,
( inverse(sk_c9) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_69,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c9
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_63]) ).
cnf(c_4754,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4755,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_4754]) ).
cnf(c_70,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_4755]) ).
cnf(c_99,plain,
( multiply(sk_c11,sk_c1) = identity
| inverse(sk_c5) = sk_c11 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_193,plain,
( multiply(sk_c9,sk_c6) = identity
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(paramod,[status(thm)],[c_42,c_2]) ).
cnf(c_215,plain,
( multiply(sk_c10,sk_c3) = identity
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_49,c_2]) ).
cnf(c_217,plain,
( multiply(sk_c10,sk_c3) = identity
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_50,c_2]) ).
cnf(c_220,plain,
( multiply(sk_c10,sk_c3) = identity
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_51,c_2]) ).
cnf(c_223,plain,
( multiply(sk_c10,sk_c3) = identity
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_52,c_2]) ).
cnf(c_226,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_70]) ).
cnf(c_290,plain,
( multiply(inverse(sk_c10),sk_c9) = sk_c4
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_35,c_70]) ).
cnf(c_293,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_36,c_70]) ).
cnf(c_294,plain,
( multiply(inverse(sk_c10),sk_c9) = sk_c4
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_37,c_70]) ).
cnf(c_296,plain,
( multiply(inverse(sk_c10),sk_c9) = sk_c4
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_38,c_70]) ).
cnf(c_303,plain,
( multiply(inverse(sk_c6),sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(paramod,[status(thm)],[c_41,c_70]) ).
cnf(c_307,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(paramod,[status(thm)],[c_43,c_70]) ).
cnf(c_321,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(paramod,[status(thm)],[c_50,c_70]) ).
cnf(c_326,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_70,c_70]) ).
cnf(c_327,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_326,c_226]) ).
cnf(c_333,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_327,c_2]) ).
cnf(c_4756,plain,
( multiply(inverse(sk_c11),identity) = sk_c1
| inverse(sk_c5) = sk_c11 ),
inference(paramod,[status(thm)],[c_99,c_70]) ).
cnf(c_337,plain,
( inverse(sk_c11) = sk_c1
| inverse(sk_c5) = sk_c11 ),
inference(paramod,[status(thm)],[c_327,c_4756]) ).
cnf(c_340,plain,
( multiply(sk_c1,sk_c11) = identity
| inverse(sk_c5) = sk_c11 ),
inference(paramod,[status(thm)],[c_337,c_2]) ).
cnf(c_4757,plain,
( multiply(inverse(sk_c10),identity) = sk_c3
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_215,c_70]) ).
cnf(c_610,plain,
( inverse(sk_c10) = sk_c3
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_327,c_4757]) ).
cnf(c_4758,plain,
( multiply(inverse(sk_c10),identity) = sk_c3
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_223,c_70]) ).
cnf(c_646,plain,
( inverse(sk_c10) = sk_c3
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_327,c_4758]) ).
cnf(c_4759,plain,
( inverse(sk_c5) = sk_c11
| identity = sk_c10
| inverse(sk_c5) = sk_c11 ),
inference(paramod,[status(thm)],[c_340,c_5]) ).
cnf(c_801,plain,
( identity = sk_c10
| inverse(sk_c5) = sk_c11 ),
inference(copy,[status(thm)],[c_4759]) ).
cnf(c_806,plain,
( multiply(sk_c11,sk_c5) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_801,c_2]) ).
cnf(c_4760,plain,
( multiply(inverse(sk_c11),identity) = sk_c5
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_806,c_70]) ).
cnf(c_815,plain,
( inverse(sk_c11) = sk_c5
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_327,c_4760]) ).
cnf(c_867,plain,
( multiply(sk_c5,sk_c11) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_815,c_2]) ).
cnf(c_4761,plain,
( identity = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_867,c_4]) ).
cnf(c_945,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_4761]) ).
cnf(c_4762,plain,
( identity = sk_c10
| inverse(sk_c1) = sk_c11
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_867,c_11]) ).
cnf(c_946,plain,
( inverse(sk_c1) = sk_c11
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_4762]) ).
cnf(c_972,plain,
( multiply(sk_c11,sk_c1) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_946,c_2]) ).
cnf(c_4763,plain,
( multiply(inverse(sk_c11),identity) = sk_c1
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_972,c_70]) ).
cnf(c_1322,plain,
( inverse(sk_c11) = sk_c1
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_327,c_4763]) ).
cnf(c_1351,plain,
( multiply(sk_c1,sk_c11) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1322,c_2]) ).
cnf(c_4764,plain,
( identity = sk_c10
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1351,c_945]) ).
cnf(c_4765,plain,
( identity = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_4764]) ).
cnf(c_1843,plain,
identity = sk_c10,
inference(copy,[status(thm)],[c_4765]) ).
cnf(c_4766,plain,
inverse(sk_c10) = identity,
inference(paramod,[status(thm)],[c_1843,c_333]) ).
cnf(c_2045,plain,
inverse(sk_c10) = sk_c10,
inference(paramod,[status(thm)],[c_1843,c_4766]) ).
cnf(c_2046,plain,
multiply(A,sk_c10) = A,
inference(paramod,[status(thm)],[c_1843,c_327]) ).
cnf(c_2048,plain,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_1843,c_220]) ).
cnf(c_2049,plain,
( multiply(sk_c10,sk_c3) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_1843,c_217]) ).
cnf(c_4767,plain,
( multiply(sk_c9,sk_c6) = identity
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_2046,c_193]) ).
cnf(c_4768,plain,
( multiply(sk_c9,sk_c6) = sk_c10
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_1843,c_4767]) ).
cnf(c_2053,plain,
( multiply(sk_c9,sk_c6) = sk_c10
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4768]) ).
cnf(c_2071,plain,
multiply(inverse(A),A) = sk_c10,
inference(paramod,[status(thm)],[c_1843,c_2]) ).
cnf(c_2072,plain,
multiply(sk_c10,A) = A,
inference(paramod,[status(thm)],[c_1843,c_1]) ).
cnf(c_4769,plain,
( sk_c10 = sk_c3
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_2045,c_646]) ).
cnf(c_2080,plain,
( sk_c3 = sk_c10
| inverse(sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_4769]) ).
cnf(c_4770,plain,
( sk_c10 = sk_c3
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_2045,c_610]) ).
cnf(c_2082,plain,
( sk_c3 = sk_c10
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_4770]) ).
cnf(c_4771,plain,
( multiply(sk_c10,sk_c9) = sk_c4
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_2045,c_296]) ).
cnf(c_4772,plain,
( sk_c9 = sk_c4
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_2072,c_4771]) ).
cnf(c_2083,plain,
( sk_c4 = sk_c9
| inverse(sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_4772]) ).
cnf(c_4773,plain,
( multiply(sk_c10,sk_c9) = sk_c4
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_2045,c_294]) ).
cnf(c_4774,plain,
( sk_c9 = sk_c4
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_2072,c_4773]) ).
cnf(c_2084,plain,
( sk_c4 = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_4774]) ).
cnf(c_4775,plain,
( multiply(sk_c10,sk_c9) = sk_c4
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_2045,c_290]) ).
cnf(c_4776,plain,
( sk_c9 = sk_c4
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_2072,c_4775]) ).
cnf(c_2086,plain,
( sk_c4 = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_4776]) ).
cnf(c_4777,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c9
| inverse(sk_c10) != sk_c9
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2072,c_69]) ).
cnf(c_4778,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c9
| sk_c10 != sk_c9
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2045,c_4777]) ).
cnf(c_4779,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| sk_c9 != sk_c9
| sk_c10 != sk_c9
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2072,c_4778]) ).
cnf(c_4780,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| B != sk_c9
| sk_c9 != sk_c9
| sk_c10 != sk_c9
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2046,c_4779]) ).
cnf(c_4781,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| B != sk_c9
| sk_c9 != sk_c9
| sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4780]) ).
cnf(c_4782,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| sk_c9 != B
| sk_c9 != sk_c9
| sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4781]) ).
cnf(c_4783,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| sk_c9 != B
| sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4782]) ).
cnf(c_2090,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(B) != sk_c10
| sk_c9 != B
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4783]) ).
cnf(c_2248,plain,
( inverse(sk_c9) = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(paramod,[status(thm)],[c_2046,c_321]) ).
cnf(c_4784,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c8
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_2046,c_307]) ).
cnf(c_4785,plain,
( inverse(sk_c9) = sk_c8
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_2046,c_4784]) ).
cnf(c_2251,plain,
( inverse(sk_c9) = sk_c8
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4785]) ).
cnf(c_4786,plain,
( multiply(inverse(sk_c6),sk_c10) = sk_c9
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_2046,c_303]) ).
cnf(c_4787,plain,
( inverse(sk_c6) = sk_c9
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_2046,c_4786]) ).
cnf(c_2253,plain,
( inverse(sk_c6) = sk_c9
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4787]) ).
cnf(c_4788,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c8
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_2072,c_293]) ).
cnf(c_2256,plain,
( inverse(sk_c9) = sk_c8
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_2046,c_4788]) ).
cnf(c_4789,plain,
( inverse(sk_c9) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c10
| sk_c10 != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2046,c_68]) ).
cnf(c_4790,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c10 != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2046,c_4789]) ).
cnf(c_4791,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4790]) ).
cnf(c_2300,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4791]) ).
cnf(c_4792,plain,
( inverse(sk_c7) = sk_c9
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_2046,c_45]) ).
cnf(c_2301,plain,
( inverse(sk_c7) = sk_c9
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4792]) ).
cnf(c_4793,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c3 = sk_c4 ),
inference(paramod,[status(thm)],[c_2046,c_44]) ).
cnf(c_2302,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4793]) ).
cnf(c_2310,plain,
( sk_c3 = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_2072,c_2049]) ).
cnf(c_2311,plain,
( sk_c3 = sk_c10
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_2072,c_2048]) ).
cnf(c_4794,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_2090]) ).
cnf(c_4795,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| sk_c10 != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2045,c_4794]) ).
cnf(c_2450,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4795]) ).
cnf(c_4796,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c10 != sk_c9
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2045,c_2300]) ).
cnf(c_4797,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c10 != sk_c9
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_2072,c_4796]) ).
cnf(c_4798,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4797]) ).
cnf(c_4799,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4798]) ).
cnf(c_2661,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_4799]) ).
cnf(c_4800,plain,
( inverse(sk_c6) = sk_c9
| sk_c4 = sk_c10
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_2082,c_2253]) ).
cnf(c_2886,plain,
( sk_c4 = sk_c10
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_4800]) ).
cnf(c_4801,plain,
( inverse(sk_c9) = sk_c8
| sk_c9 = sk_c3
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_2256,c_2251]) ).
cnf(c_4802,plain,
( inverse(sk_c9) = sk_c8
| sk_c3 = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_4801]) ).
cnf(c_2918,plain,
( sk_c3 = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_4802]) ).
cnf(c_4803,plain,
( inverse(sk_c7) = sk_c9
| sk_c4 = sk_c10
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_2080,c_2301]) ).
cnf(c_2921,plain,
( sk_c4 = sk_c10
| inverse(sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_4803]) ).
cnf(c_4804,plain,
( sk_c10 = sk_c9
| inverse(sk_c6) = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_2886,c_2086]) ).
cnf(c_4805,plain,
( sk_c9 = sk_c10
| inverse(sk_c6) = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_4804]) ).
cnf(c_3025,plain,
( sk_c9 = sk_c10
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_4805]) ).
cnf(c_4806,plain,
( sk_c10 = sk_c9
| inverse(sk_c7) = sk_c9
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_2921,c_2083]) ).
cnf(c_4807,plain,
( sk_c9 = sk_c10
| inverse(sk_c7) = sk_c9
| inverse(sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_4806]) ).
cnf(c_3126,plain,
( sk_c9 = sk_c10
| inverse(sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_4807]) ).
cnf(c_4808,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_2053,c_70]) ).
cnf(c_3728,plain,
( inverse(sk_c9) = sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_2046,c_4808]) ).
cnf(c_4809,plain,
( sk_c6 = sk_c8
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_3728,c_2251]) ).
cnf(c_4810,plain,
( sk_c8 = sk_c6
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4809]) ).
cnf(c_3746,plain,
( sk_c8 = sk_c6
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4810]) ).
cnf(c_4811,plain,
multiply(inverse(inverse(A)),sk_c10) = A,
inference(paramod,[status(thm)],[c_2071,c_70]) ).
cnf(c_3887,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_2046,c_4811]) ).
cnf(c_4812,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2071,c_2450]) ).
cnf(c_4813,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c11 != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_3887,c_4812]) ).
cnf(c_4814,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c11 != sk_c11 ),
inference(copy,[status(thm)],[c_4813]) ).
cnf(c_3890,plain,
( multiply(sk_c9,sk_c9) != sk_c10
| sk_c9 != sk_c10 ),
inference(copy,[status(thm)],[c_4814]) ).
cnf(c_4815,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2071,c_2661]) ).
cnf(c_4816,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c11 != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_3887,c_4815]) ).
cnf(c_4817,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c11 != sk_c11 ),
inference(copy,[status(thm)],[c_4816]) ).
cnf(c_3891,plain,
( inverse(sk_c9) != sk_c10
| sk_c9 != sk_c10 ),
inference(copy,[status(thm)],[c_4817]) ).
cnf(c_3937,plain,
( sk_c8 != sk_c10
| sk_c9 != sk_c10
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_2251,c_3891]) ).
cnf(c_3942,plain,
( sk_c8 != sk_c10
| sk_c9 != sk_c10
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_2918,c_3891]) ).
cnf(c_4818,plain,
( inverse(sk_c10) != sk_c10
| sk_c9 != sk_c10
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_3025,c_3891]) ).
cnf(c_4819,plain,
( sk_c10 != sk_c10
| sk_c9 != sk_c10
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_2045,c_4818]) ).
cnf(c_3943,plain,
( sk_c9 != sk_c10
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_4819]) ).
cnf(c_4820,plain,
( inverse(sk_c10) != sk_c10
| sk_c9 != sk_c10
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_3126,c_3891]) ).
cnf(c_4821,plain,
( sk_c10 != sk_c10
| sk_c9 != sk_c10
| inverse(sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_2045,c_4820]) ).
cnf(c_3944,plain,
( sk_c9 != sk_c10
| inverse(sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_4821]) ).
cnf(c_4822,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(resolve,[status(thm)],[c_3943,c_3025]) ).
cnf(c_4077,plain,
inverse(sk_c6) = sk_c9,
inference(copy,[status(thm)],[c_4822]) ).
cnf(c_4079,plain,
multiply(sk_c9,sk_c6) = sk_c10,
inference(paramod,[status(thm)],[c_4077,c_2071]) ).
cnf(c_4823,plain,
multiply(inverse(sk_c9),sk_c10) = sk_c6,
inference(paramod,[status(thm)],[c_4079,c_70]) ).
cnf(c_4080,plain,
inverse(sk_c9) = sk_c6,
inference(paramod,[status(thm)],[c_2046,c_4823]) ).
cnf(c_4094,plain,
( sk_c6 != sk_c10
| sk_c9 != sk_c10 ),
inference(paramod,[status(thm)],[c_4080,c_3891]) ).
cnf(c_4824,plain,
( sk_c6 = sk_c8
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4080,c_2256]) ).
cnf(c_4134,plain,
( sk_c8 = sk_c6
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_4824]) ).
cnf(c_4825,plain,
( sk_c6 = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(paramod,[status(thm)],[c_4080,c_2248]) ).
cnf(c_4135,plain,
( sk_c8 = sk_c6
| inverse(sk_c3) = sk_c10 ),
inference(copy,[status(thm)],[c_4825]) ).
cnf(c_4165,plain,
multiply(sk_c6,sk_c9) = sk_c10,
inference(paramod,[status(thm)],[c_4080,c_2071]) ).
cnf(c_4826,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c7) = sk_c9 ),
inference(resolve,[status(thm)],[c_3944,c_3126]) ).
cnf(c_4329,plain,
inverse(sk_c7) = sk_c9,
inference(copy,[status(thm)],[c_4826]) ).
cnf(c_4358,plain,
multiply(sk_c9,sk_c7) = sk_c10,
inference(paramod,[status(thm)],[c_4329,c_2071]) ).
cnf(c_4827,plain,
multiply(inverse(sk_c9),sk_c10) = sk_c7,
inference(paramod,[status(thm)],[c_4358,c_70]) ).
cnf(c_4828,plain,
multiply(sk_c6,sk_c10) = sk_c7,
inference(paramod,[status(thm)],[c_4080,c_4827]) ).
cnf(c_4829,plain,
sk_c6 = sk_c7,
inference(paramod,[status(thm)],[c_2046,c_4828]) ).
cnf(c_4370,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_4829]) ).
cnf(c_4830,plain,
( sk_c3 = sk_c10
| multiply(sk_c6,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_4370,c_2311]) ).
cnf(c_4831,plain,
( sk_c3 = sk_c10
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_4165,c_4830]) ).
cnf(c_4497,plain,
( sk_c3 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4831]) ).
cnf(c_4832,plain,
( multiply(sk_c6,sk_c9) = sk_c8
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_4370,c_2302]) ).
cnf(c_4833,plain,
( sk_c10 = sk_c8
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_4165,c_4832]) ).
cnf(c_4498,plain,
( sk_c8 = sk_c10
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4833]) ).
cnf(c_4834,plain,
( sk_c4 = sk_c9
| multiply(sk_c6,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_4370,c_2084]) ).
cnf(c_4835,plain,
( sk_c4 = sk_c9
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_4165,c_4834]) ).
cnf(c_4512,plain,
( sk_c4 = sk_c9
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4835]) ).
cnf(c_4836,plain,
( sk_c9 != sk_c10
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(resolve,[status(thm)],[c_4498,c_3937]) ).
cnf(c_4574,plain,
( sk_c9 != sk_c10
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4836]) ).
cnf(c_4837,plain,
( sk_c10 = sk_c6
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_4498,c_3746]) ).
cnf(c_4838,plain,
( sk_c6 = sk_c10
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4837]) ).
cnf(c_4576,plain,
( sk_c6 = sk_c10
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4838]) ).
cnf(c_4839,plain,
( sk_c8 = sk_c10
| sk_c4 = sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_4497,c_4498]) ).
cnf(c_4582,plain,
( sk_c4 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4839]) ).
cnf(c_4840,plain,
( sk_c10 = sk_c6
| sk_c4 = sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4512,c_4134]) ).
cnf(c_4841,plain,
( sk_c6 = sk_c10
| sk_c4 = sk_c9
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_4840]) ).
cnf(c_4588,plain,
( sk_c6 = sk_c10
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_4841]) ).
cnf(c_4842,plain,
( sk_c8 = sk_c10
| sk_c9 = sk_c3
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_4512,c_4498]) ).
cnf(c_4843,plain,
( sk_c8 = sk_c10
| sk_c3 = sk_c9
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4842]) ).
cnf(c_4594,plain,
( sk_c3 = sk_c9
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4843]) ).
cnf(c_4844,plain,
( inverse(sk_c10) = sk_c9
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_4576,c_4077]) ).
cnf(c_4845,plain,
( sk_c10 = sk_c9
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_2045,c_4844]) ).
cnf(c_4595,plain,
( sk_c9 = sk_c10
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_4845]) ).
cnf(c_4846,plain,
( sk_c10 = sk_c9
| sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_4582,c_4512]) ).
cnf(c_4847,plain,
( sk_c9 = sk_c10
| sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4846]) ).
cnf(c_4623,plain,
( sk_c9 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4847]) ).
cnf(c_4848,plain,
( inverse(sk_c10) = sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4588,c_4077]) ).
cnf(c_4849,plain,
( sk_c10 = sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_2045,c_4848]) ).
cnf(c_4626,plain,
( sk_c9 = sk_c10
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_4849]) ).
cnf(c_4850,plain,
( sk_c9 != sk_c10
| sk_c3 = sk_c9
| sk_c3 = sk_c9 ),
inference(resolve,[status(thm)],[c_4594,c_3942]) ).
cnf(c_4630,plain,
( sk_c9 != sk_c10
| sk_c3 = sk_c9 ),
inference(copy,[status(thm)],[c_4850]) ).
cnf(c_4851,plain,
( sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(resolve,[status(thm)],[c_4595,c_4574]) ).
cnf(c_4642,plain,
sk_c4 = sk_c3,
inference(copy,[status(thm)],[c_4851]) ).
cnf(c_4648,plain,
( sk_c9 = sk_c10
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_4642,c_4626]) ).
cnf(c_4852,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| sk_c9 != sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_4623,c_3890]) ).
cnf(c_4853,plain,
( sk_c9 != sk_c10
| sk_c9 != sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2072,c_4852]) ).
cnf(c_4689,plain,
( sk_c9 != sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4853]) ).
cnf(c_4854,plain,
( sk_c3 = sk_c9
| sk_c3 = sk_c9 ),
inference(resolve,[status(thm)],[c_4648,c_4630]) ).
cnf(c_4698,plain,
sk_c3 = sk_c9,
inference(copy,[status(thm)],[c_4854]) ).
cnf(c_4855,plain,
( sk_c8 = sk_c6
| inverse(sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_4698,c_4135]) ).
cnf(c_4723,plain,
( sk_c8 = sk_c6
| sk_c6 = sk_c10 ),
inference(paramod,[status(thm)],[c_4080,c_4855]) ).
cnf(c_4726,plain,
( sk_c9 = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_4698,c_2310]) ).
cnf(c_4856,plain,
( sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(resolve,[status(thm)],[c_4689,c_4623]) ).
cnf(c_4737,plain,
sk_c8 = sk_c10,
inference(copy,[status(thm)],[c_4856]) ).
cnf(c_4857,plain,
( sk_c9 = sk_c10
| multiply(sk_c9,sk_c10) = sk_c10 ),
inference(paramod,[status(thm)],[c_4737,c_4726]) ).
cnf(c_4858,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(paramod,[status(thm)],[c_2046,c_4857]) ).
cnf(c_4746,plain,
sk_c9 = sk_c10,
inference(copy,[status(thm)],[c_4858]) ).
cnf(c_4859,plain,
( sk_c10 = sk_c6
| sk_c6 = sk_c10 ),
inference(paramod,[status(thm)],[c_4737,c_4723]) ).
cnf(c_4860,plain,
( sk_c6 = sk_c10
| sk_c6 = sk_c10 ),
inference(copy,[status(thm)],[c_4859]) ).
cnf(c_4747,plain,
sk_c6 = sk_c10,
inference(copy,[status(thm)],[c_4860]) ).
cnf(c_4861,plain,
( sk_c6 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_4746,c_4094]) ).
cnf(c_4862,plain,
( sk_c10 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_4747,c_4861]) ).
cnf(c_4863,plain,
sk_c10 != sk_c10,
inference(copy,[status(thm)],[c_4862]) ).
cnf(c_4750,plain,
$false,
inference(copy,[status(thm)],[c_4863]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP266-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 14:43:52 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.35 % Process 425091 was started by sandbox on n003,
% 0.12/0.35 % Fri Sep 25 14:43:52 2026
% 0.12/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 14.17/2.44
% 14.17/2.44 % SZS status Unsatisfiable for theBenchmark
% 14.17/2.44
% 14.17/2.44 % Proof 1 at 1.53 (+ 0.49) seconds.
% 14.17/2.44 % Length of proof is 129.
% 14.17/2.44 % Level of proof is 32.
% 14.17/2.44 % Maximum clause weight is 68.000.
% 14.17/2.44 % Given clauses 400.
% 14.17/2.44
% 14.17/2.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------