%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP239-1 : 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 07:28:27 AM UTC 2026
% Result : Unsatisfiable 40.08s 6.22s
% Output : CNFRefutation 40.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 19
% Syntax : Number of formulae : 235 ( 41 unt; 0 def)
% Number of atoms : 719 ( 718 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 877 ( 393 ~; 484 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 12 !; 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_3,axiom,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c6) = sk_c7
| inverse(sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_12,axiom,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_15,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_18,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_24,axiom,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_31,axiom,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_32,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_38,axiom,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_38) ).
cnf(c_41,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_38]) ).
fof(prove_this_39,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_39) ).
cnf(c_42,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_39]) ).
fof(prove_this_43,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( multiply(VAR_6,sk_c9) != sk_c8
| inverse(VAR_5) != VAR_6
| multiply(VAR_5,VAR_6) != sk_c8
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c9
| multiply(VAR_3,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c9
| inverse(VAR_2) != sk_c9
| multiply(VAR_2,sk_c9) != VAR_1
| multiply(sk_c9,VAR_1) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c9
| inverse(VAR_0) != sk_c9
| inverse(sk_c9) != sk_c8 ),
file('theBenchmark.p',prove_this_43) ).
cnf(c_46,plain,
( multiply(V6,sk_c9) != sk_c8
| inverse(F) != V6
| multiply(F,V6) != sk_c8
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c9
| multiply(D,sk_c8) != sk_c9
| inverse(D) != sk_c9
| inverse(C) != sk_c9
| multiply(C,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_43]) ).
cnf(c_47,plain,
( multiply(F,sk_c9) != sk_c8
| inverse(E) != F
| multiply(E,F) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(D,sk_c8) != sk_c9
| inverse(D) != sk_c9
| inverse(C) != sk_c9
| multiply(C,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_49,plain,
( multiply(F,sk_c9) != sk_c8
| inverse(E) != F
| multiply(E,F) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_6074,plain,
( multiply(F,sk_c9) != sk_c8
| inverse(E) != F
| multiply(E,F) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| multiply(A,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(C,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_50,plain,
( multiply(F,sk_c9) != sk_c8
| inverse(E) != F
| multiply(E,F) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(C,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6074]) ).
cnf(c_51,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(D,sk_c8) != sk_c9
| inverse(D) != sk_c9
| inverse(C) != sk_c9
| multiply(C,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_6075,plain,
( multiply(E,sk_c9) != sk_c8
| inverse(D) != E
| multiply(D,E) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_49]) ).
cnf(c_57,plain,
( multiply(E,sk_c9) != sk_c8
| inverse(D) != E
| multiply(D,E) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6075]) ).
cnf(c_59,plain,
( multiply(E,sk_c9) != sk_c8
| inverse(D) != E
| multiply(D,E) != sk_c8
| inverse(A) != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_50]) ).
cnf(c_67,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_51]) ).
cnf(c_84,plain,
( multiply(D,sk_c9) != sk_c8
| inverse(C) != D
| multiply(C,D) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_94,plain,
( multiply(B,sk_c9) != sk_c8
| inverse(sk_c9) != B
| inverse(A) != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_59]) ).
cnf(c_6076,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_67]) ).
cnf(c_107,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6076]) ).
cnf(c_135,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(A,sk_c8) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_84]) ).
cnf(c_6077,plain,
( multiply(sk_c9,sk_c9) != sk_c8
| inverse(A) != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_94]) ).
cnf(c_141,plain,
( inverse(A) != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6077]) ).
cnf(c_6078,plain,
( multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_107]) ).
cnf(c_147,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6078]) ).
cnf(c_6079,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_6080,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_6079]) ).
cnf(c_158,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_6080]) ).
cnf(c_168,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_173,plain,
( multiply(sk_c7,sk_c6) = identity
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_187,plain,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_190,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_195,plain,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_6081,plain,
( multiply(multiply(A,sk_c9),sk_c3) = multiply(A,sk_c8)
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_28,c_3]) ).
cnf(c_233,plain,
( multiply(A,multiply(sk_c9,sk_c3)) = multiply(A,sk_c8)
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_3,c_6081]) ).
cnf(c_278,plain,
( multiply(sk_c9,sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_42,c_2]) ).
cnf(c_279,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_42,c_2]) ).
cnf(c_315,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_158]) ).
cnf(c_364,plain,
( multiply(inverse(sk_c5),sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_27,c_158]) ).
cnf(c_378,plain,
( multiply(inverse(sk_c5),sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(paramod,[status(thm)],[c_34,c_158]) ).
cnf(c_401,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_158,c_158]) ).
cnf(c_402,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_401,c_315]) ).
cnf(c_479,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_402,c_2]) ).
cnf(c_6082,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(identity,sk_c8) != sk_c8
| inverse(identity) != sk_c8
| multiply(identity,sk_c9) != A
| multiply(sk_c9,A) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_479,c_135]) ).
cnf(c_6083,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(identity,sk_c8) != sk_c8
| inverse(identity) != sk_c8
| multiply(identity,sk_c9) != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_6082]) ).
cnf(c_6084,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(identity,sk_c8) != sk_c8
| inverse(identity) != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_6083]) ).
cnf(c_6085,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| multiply(identity,sk_c8) != sk_c8
| identity != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_479,c_6084]) ).
cnf(c_6086,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| sk_c8 != sk_c8
| identity != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_6085]) ).
cnf(c_563,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6086]) ).
cnf(c_6087,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_168,c_158]) ).
cnf(c_626,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_402,c_6087]) ).
cnf(c_635,plain,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_626,c_2]) ).
cnf(c_6088,plain,
( multiply(inverse(sk_c7),identity) = sk_c6
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_173,c_158]) ).
cnf(c_734,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_402,c_6088]) ).
cnf(c_747,plain,
( multiply(sk_c6,sk_c7) = identity
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_734,c_2]) ).
cnf(c_6089,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| sk_c9 != identity
| sk_c9 != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_402,c_563]) ).
cnf(c_6090,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| sk_c9 != identity
| sk_c8 != sk_c9
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6089]) ).
cnf(c_6091,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6090]) ).
cnf(c_6092,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6091]) ).
cnf(c_820,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6092]) ).
cnf(c_6093,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_190,c_158]) ).
cnf(c_1092,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_402,c_6093]) ).
cnf(c_6094,plain,
( inverse(sk_c6) = sk_c7
| sk_c1 = sk_c8
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1092,c_9]) ).
cnf(c_1098,plain,
( sk_c1 = sk_c8
| inverse(sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_6094]) ).
cnf(c_1104,plain,
( multiply(sk_c7,sk_c6) = identity
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_1098,c_2]) ).
cnf(c_6095,plain,
( multiply(inverse(sk_c7),identity) = sk_c6
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_1104,c_158]) ).
cnf(c_1116,plain,
( inverse(sk_c7) = sk_c6
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_402,c_6095]) ).
cnf(c_1134,plain,
( multiply(sk_c6,sk_c7) = identity
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_1116,c_2]) ).
cnf(c_6096,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_187,c_158]) ).
cnf(c_1362,plain,
( inverse(sk_c9) = sk_c1
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_402,c_6096]) ).
cnf(c_6097,plain,
( multiply(inverse(sk_c9),identity) = sk_c2
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_278,c_158]) ).
cnf(c_1405,plain,
( inverse(sk_c9) = sk_c2
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_402,c_6097]) ).
cnf(c_6098,plain,
( inverse(sk_c5) = sk_c8
| sk_c2 = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_1405,c_7]) ).
cnf(c_1411,plain,
( sk_c2 = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_6098]) ).
cnf(c_6099,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_1411,c_35]) ).
cnf(c_1422,plain,
( multiply(sk_c8,sk_c9) = sk_c3
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_6099]) ).
cnf(c_6100,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_279,c_158]) ).
cnf(c_1561,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_402,c_6100]) ).
cnf(c_6101,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_195,c_158]) ).
cnf(c_1577,plain,
( inverse(sk_c9) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_402,c_6101]) ).
cnf(c_6102,plain,
( identity = sk_c9
| inverse(sk_c9) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_635,c_6]) ).
cnf(c_1972,plain,
( identity = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_6102]) ).
cnf(c_1990,plain,
( inverse(sk_c9) = identity
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_1972,c_479]) ).
cnf(c_6103,plain,
( identity = sk_c8
| inverse(sk_c9) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_747,c_8]) ).
cnf(c_3693,plain,
( identity = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_6103]) ).
cnf(c_6104,plain,
( inverse(sk_c9) = sk_c8
| inverse(sk_c9) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_3693,c_1990]) ).
cnf(c_6105,plain,
( inverse(sk_c9) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_6104]) ).
cnf(c_3738,plain,
inverse(sk_c9) = sk_c8,
inference(copy,[status(thm)],[c_6105]) ).
cnf(c_6106,plain,
( sk_c8 = sk_c4
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_3738,c_1577]) ).
cnf(c_3969,plain,
( sk_c4 = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_6106]) ).
cnf(c_6107,plain,
( sk_c8 = sk_c1
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_3738,c_1362]) ).
cnf(c_3991,plain,
( sk_c1 = sk_c8
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_6107]) ).
cnf(c_6108,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3738,c_820]) ).
cnf(c_4075,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_6108]) ).
cnf(c_6109,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3738,c_147]) ).
cnf(c_4179,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c9 ),
inference(copy,[status(thm)],[c_6109]) ).
cnf(c_6110,plain,
( inverse(A) != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3738,c_141]) ).
cnf(c_6111,plain,
( inverse(A) != sk_c8
| sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3738,c_6110]) ).
cnf(c_4181,plain,
( inverse(A) != sk_c8
| sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(copy,[status(thm)],[c_6111]) ).
cnf(c_4198,plain,
multiply(sk_c8,sk_c9) = identity,
inference(paramod,[status(thm)],[c_3738,c_2]) ).
cnf(c_4199,plain,
multiply(sk_c8,multiply(sk_c9,A)) = A,
inference(paramod,[status(thm)],[c_3738,c_158]) ).
cnf(c_4201,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| identity != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c9 ),
inference(paramod,[status(thm)],[c_4198,c_4179]) ).
cnf(c_6112,plain,
( identity != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(paramod,[status(thm)],[c_4198,c_4075]) ).
cnf(c_4204,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_6112]) ).
cnf(c_4275,plain,
( identity = sk_c3
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_4198,c_1422]) ).
cnf(c_6113,plain,
multiply(inverse(sk_c8),identity) = sk_c9,
inference(paramod,[status(thm)],[c_4198,c_158]) ).
cnf(c_4358,plain,
inverse(sk_c8) = sk_c9,
inference(paramod,[status(thm)],[c_402,c_6113]) ).
cnf(c_6114,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| identity != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_4358,c_4201]) ).
cnf(c_4376,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| identity != sk_c8
| multiply(sk_c9,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(copy,[status(thm)],[c_6114]) ).
cnf(c_6115,plain,
( sk_c9 = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_4358,c_1561]) ).
cnf(c_4406,plain,
( sk_c5 = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(copy,[status(thm)],[c_6115]) ).
cnf(c_4463,plain,
multiply(sk_c9,sk_c8) = identity,
inference(paramod,[status(thm)],[c_4358,c_2]) ).
cnf(c_6116,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| identity != sk_c8
| identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(paramod,[status(thm)],[c_4463,c_4376]) ).
cnf(c_6117,plain,
( identity != sk_c9
| identity != sk_c8
| identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(paramod,[status(thm)],[c_4463,c_6116]) ).
cnf(c_4466,plain,
( identity != sk_c9
| identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(copy,[status(thm)],[c_6117]) ).
cnf(c_6118,plain,
( inverse(sk_c8) != sk_c8
| sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(resolve,[status(thm)],[c_4181,c_4358]) ).
cnf(c_6119,plain,
( sk_c9 != sk_c8
| sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(paramod,[status(thm)],[c_4358,c_6118]) ).
cnf(c_6120,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(copy,[status(thm)],[c_6119]) ).
cnf(c_4917,plain,
( sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(copy,[status(thm)],[c_6120]) ).
cnf(c_6121,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_4406,c_41]) ).
cnf(c_6122,plain,
( identity = sk_c9
| inverse(sk_c2) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_4463,c_6121]) ).
cnf(c_4991,plain,
( identity = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(copy,[status(thm)],[c_6122]) ).
cnf(c_6123,plain,
( inverse(sk_c9) = identity
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_4991,c_479]) ).
cnf(c_6124,plain,
( sk_c8 = identity
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_3738,c_6123]) ).
cnf(c_5019,plain,
( identity = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(copy,[status(thm)],[c_6124]) ).
cnf(c_6125,plain,
( sk_c8 = sk_c9
| inverse(sk_c2) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_5019,c_4991]) ).
cnf(c_5103,plain,
( sk_c8 = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(copy,[status(thm)],[c_6125]) ).
cnf(c_5163,plain,
( multiply(sk_c9,sk_c2) = identity
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_5103,c_2]) ).
cnf(c_6126,plain,
( multiply(sk_c8,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_3969,c_19]) ).
cnf(c_5302,plain,
( multiply(sk_c8,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_6126]) ).
cnf(c_6127,plain,
( sk_c8 = identity
| sk_c1 = sk_c8
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_3991,c_1134]) ).
cnf(c_6128,plain,
( identity = sk_c8
| sk_c1 = sk_c8
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_6127]) ).
cnf(c_5348,plain,
( identity = sk_c8
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_6128]) ).
cnf(c_6129,plain,
( multiply(sk_c1,multiply(sk_c9,sk_c3)) = sk_c9
| inverse(sk_c5) = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_233]) ).
cnf(c_5357,plain,
( multiply(sk_c1,multiply(sk_c9,sk_c3)) = sk_c9
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_6129]) ).
cnf(c_5379,plain,
( sk_c8 != sk_c9
| identity != sk_c9
| sk_c1 = sk_c8 ),
inference(resolve,[status(thm)],[c_5348,c_4204]) ).
cnf(c_6130,plain,
( inverse(sk_c8) = identity
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_5348,c_479]) ).
cnf(c_6131,plain,
( sk_c9 = identity
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_4358,c_6130]) ).
cnf(c_5384,plain,
( identity = sk_c9
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_6131]) ).
cnf(c_6132,plain,
( sk_c9 = sk_c8
| sk_c1 = sk_c8
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_5384,c_5348]) ).
cnf(c_6133,plain,
( sk_c8 = sk_c9
| sk_c1 = sk_c8
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_6132]) ).
cnf(c_5427,plain,
( sk_c8 = sk_c9
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_6133]) ).
cnf(c_6134,plain,
( sk_c1 = sk_c8
| sk_c8 != sk_c9
| sk_c1 = sk_c8 ),
inference(resolve,[status(thm)],[c_5379,c_5384]) ).
cnf(c_5511,plain,
( sk_c8 != sk_c9
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_6134]) ).
cnf(c_6135,plain,
( sk_c1 = sk_c8
| sk_c1 = sk_c8 ),
inference(resolve,[status(thm)],[c_5511,c_5427]) ).
cnf(c_5544,plain,
sk_c1 = sk_c8,
inference(copy,[status(thm)],[c_6135]) ).
cnf(c_6136,plain,
( multiply(sk_c8,multiply(sk_c9,sk_c3)) = sk_c9
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_5544,c_5357]) ).
cnf(c_5553,plain,
( sk_c3 = sk_c9
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_4199,c_6136]) ).
cnf(c_6137,plain,
( multiply(sk_c8,sk_c8) = sk_c9
| multiply(sk_c8,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_5544,c_5302]) ).
cnf(c_5563,plain,
multiply(sk_c8,sk_c8) = sk_c9,
inference(copy,[status(thm)],[c_6137]) ).
cnf(c_6138,plain,
( sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_5563,c_4917]) ).
cnf(c_5683,plain,
( sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_6138]) ).
cnf(c_6139,plain,
( identity != sk_c9
| identity != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_5563,c_4466]) ).
cnf(c_5698,plain,
( identity != sk_c9
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_6139]) ).
cnf(c_6140,plain,
multiply(inverse(sk_c8),sk_c9) = sk_c8,
inference(paramod,[status(thm)],[c_5563,c_158]) ).
cnf(c_5721,plain,
multiply(sk_c9,sk_c9) = sk_c8,
inference(paramod,[status(thm)],[c_4358,c_6140]) ).
cnf(c_6141,plain,
( sk_c8 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_5721,c_5683]) ).
cnf(c_6142,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_5721,c_6141]) ).
cnf(c_6143,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9 ),
inference(copy,[status(thm)],[c_6142]) ).
cnf(c_5734,plain,
sk_c8 != sk_c9,
inference(copy,[status(thm)],[c_6143]) ).
cnf(c_5745,plain,
multiply(sk_c9,sk_c2) = identity,
inference(resolve,[status(thm)],[c_5734,c_5163]) ).
cnf(c_5771,plain,
multiply(sk_c8,A) = multiply(sk_c9,multiply(sk_c9,A)),
inference(paramod,[status(thm)],[c_5721,c_3]) ).
cnf(c_6144,plain,
multiply(inverse(sk_c9),identity) = sk_c2,
inference(paramod,[status(thm)],[c_5745,c_158]) ).
cnf(c_6145,plain,
multiply(sk_c8,identity) = sk_c2,
inference(paramod,[status(thm)],[c_3738,c_6144]) ).
cnf(c_6146,plain,
sk_c8 = sk_c2,
inference(paramod,[status(thm)],[c_402,c_6145]) ).
cnf(c_5825,plain,
sk_c2 = sk_c8,
inference(copy,[status(thm)],[c_6146]) ).
cnf(c_6147,plain,
( multiply(inverse(sk_c5),sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c3 ),
inference(paramod,[status(thm)],[c_5825,c_378]) ).
cnf(c_6148,plain,
( multiply(inverse(sk_c5),sk_c9) = sk_c8
| multiply(sk_c9,multiply(sk_c9,sk_c9)) = sk_c3 ),
inference(paramod,[status(thm)],[c_5771,c_6147]) ).
cnf(c_6149,plain,
( multiply(inverse(sk_c5),sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c3 ),
inference(paramod,[status(thm)],[c_5721,c_6148]) ).
cnf(c_5836,plain,
( multiply(inverse(sk_c5),sk_c9) = sk_c8
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_4463,c_6149]) ).
cnf(c_6150,plain,
( identity = sk_c9
| inverse(sk_c5) = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_5553,c_4275]) ).
cnf(c_5856,plain,
( identity = sk_c9
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_6150]) ).
cnf(c_5869,plain,
( identity != sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(resolve,[status(thm)],[c_5856,c_5698]) ).
cnf(c_6151,plain,
( inverse(sk_c9) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_5856,c_479]) ).
cnf(c_6152,plain,
( sk_c8 = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_3738,c_6151]) ).
cnf(c_5874,plain,
( identity = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_6152]) ).
cnf(c_6153,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(resolve,[status(thm)],[c_5874,c_5869]) ).
cnf(c_5927,plain,
inverse(sk_c5) = sk_c8,
inference(copy,[status(thm)],[c_6153]) ).
cnf(c_6154,plain,
( multiply(sk_c8,sk_c9) = sk_c8
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_5927,c_5836]) ).
cnf(c_6155,plain,
( multiply(sk_c9,multiply(sk_c9,sk_c9)) = sk_c8
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_5771,c_6154]) ).
cnf(c_6156,plain,
( multiply(sk_c9,sk_c8) = sk_c8
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_5721,c_6155]) ).
cnf(c_5930,plain,
( identity = sk_c8
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_4463,c_6156]) ).
cnf(c_6157,plain,
( multiply(sk_c8,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_5927,c_364]) ).
cnf(c_6158,plain,
( multiply(sk_c9,multiply(sk_c9,sk_c9)) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_5771,c_6157]) ).
cnf(c_6159,plain,
( multiply(sk_c9,sk_c8) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_5721,c_6158]) ).
cnf(c_5934,plain,
( identity = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_4463,c_6159]) ).
cnf(c_5937,plain,
( identity != sk_c9
| identity = sk_c3 ),
inference(resolve,[status(thm)],[c_5930,c_5698]) ).
cnf(c_6160,plain,
( inverse(sk_c8) = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_5930,c_479]) ).
cnf(c_6161,plain,
( sk_c9 = identity
| identity = sk_c3 ),
inference(paramod,[status(thm)],[c_4358,c_6160]) ).
cnf(c_5943,plain,
( identity = sk_c9
| identity = sk_c3 ),
inference(copy,[status(thm)],[c_6161]) ).
cnf(c_6162,plain,
( identity = sk_c3
| identity = sk_c3 ),
inference(resolve,[status(thm)],[c_5943,c_5937]) ).
cnf(c_5962,plain,
identity = sk_c3,
inference(copy,[status(thm)],[c_6162]) ).
cnf(c_5972,plain,
( sk_c3 = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_5962,c_5934]) ).
cnf(c_6163,plain,
inverse(sk_c3) = identity,
inference(paramod,[status(thm)],[c_5962,c_479]) ).
cnf(c_6023,plain,
inverse(sk_c3) = sk_c3,
inference(paramod,[status(thm)],[c_5962,c_6163]) ).
cnf(c_6024,plain,
multiply(A,sk_c3) = A,
inference(paramod,[status(thm)],[c_5962,c_402]) ).
cnf(c_6164,plain,
( sk_c3 = sk_c8
| sk_c9 = sk_c8 ),
inference(paramod,[status(thm)],[c_6024,c_5972]) ).
cnf(c_6165,plain,
( sk_c3 = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_6164]) ).
cnf(c_6048,plain,
sk_c3 = sk_c8,
inference(resolve,[status(thm)],[c_5734,c_6165]) ).
cnf(c_6166,plain,
inverse(sk_c8) = sk_c3,
inference(paramod,[status(thm)],[c_6048,c_6023]) ).
cnf(c_6167,plain,
sk_c9 = sk_c3,
inference(paramod,[status(thm)],[c_4358,c_6166]) ).
cnf(c_6168,plain,
sk_c9 = sk_c8,
inference(paramod,[status(thm)],[c_6048,c_6167]) ).
cnf(c_6169,plain,
sk_c8 = sk_c9,
inference(copy,[status(thm)],[c_6168]) ).
cnf(c_6073,plain,
$false,
inference(resolve,[status(thm)],[c_5734,c_6169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP239-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 14:40:01 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3714993 was started by sandbox2 on n005,
% 0.07/0.35 % Fri Sep 25 14:40:01 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 40.08/6.22
% 40.08/6.22 % SZS status Unsatisfiable for theBenchmark
% 40.08/6.22
% 40.08/6.22 % Proof 1 at 4.32 (+ 1.41) seconds.
% 40.08/6.22 % Length of proof is 120.
% 40.08/6.22 % Level of proof is 25.
% 40.08/6.22 % Maximum clause weight is 63.000.
% 40.08/6.22 % Given clauses 437.
% 40.08/6.22
% 40.08/6.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------