%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP211-1 : 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 07:28:22 AM UTC 2026
% Result : Unsatisfiable 14.89s 2.50s
% Output : CNFRefutation 14.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 21
% Syntax : Number of formulae : 236 ( 44 unt; 0 def)
% Number of atoms : 588 ( 587 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 595 ( 243 ~; 352 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 11 !; 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,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_13,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_16,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_26,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c8
| multiply(VAR_5,sk_c8) != VAR_4
| multiply(sk_c8,VAR_4) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_3) != sk_c8
| multiply(VAR_2,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c8
| multiply(VAR_1,sk_c7) != sk_c8
| inverse(VAR_0) != VAR_1
| multiply(VAR_0,VAR_1) != sk_c8 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(D) != sk_c8
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
cnf(c_35,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_10168,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| multiply(C,sk_c7) != sk_c8
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_36,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(copy,[status(thm)],[c_10168]) ).
cnf(c_10169,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| inverse(B) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(factor,[status(thm)],[c_35]) ).
cnf(c_45,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(copy,[status(thm)],[c_10169]) ).
cnf(c_46,plain,
( multiply(C,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_55,plain,
( multiply(B,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(factor,[status(thm)],[c_45]) ).
cnf(c_10170,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_10171,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_10170]) ).
cnf(c_59,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_10171]) ).
cnf(c_10172,plain,
( multiply(sk_c8,A) = multiply(sk_c1,multiply(sk_c2,A))
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_67,plain,
( multiply(sk_c1,multiply(sk_c2,A)) = multiply(sk_c8,A)
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_10172]) ).
cnf(c_78,plain,
( multiply(sk_c2,sk_c1) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_10173,plain,
( multiply(multiply(A,sk_c8),sk_c6) = multiply(A,sk_c7)
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_11,c_3]) ).
cnf(c_85,plain,
( multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7)
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_3,c_10173]) ).
cnf(c_89,plain,
( multiply(sk_c2,sk_c1) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_90,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_10174,plain,
( multiply(sk_c8,A) = multiply(sk_c2,multiply(sk_c7,A))
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_98,plain,
( multiply(sk_c2,multiply(sk_c7,A)) = multiply(sk_c8,A)
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_10174]) ).
cnf(c_109,plain,
( multiply(sk_c8,sk_c3) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_10175,plain,
( multiply(multiply(A,sk_c8),sk_c6) = multiply(A,sk_c7)
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_116,plain,
( multiply(A,multiply(sk_c8,sk_c6)) = multiply(A,sk_c7)
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_3,c_10175]) ).
cnf(c_121,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_232,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_59]) ).
cnf(c_284,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_59,c_59]) ).
cnf(c_285,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_284,c_232]) ).
cnf(c_356,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_285,c_2]) ).
cnf(c_10176,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| inverse(identity) != sk_c8
| multiply(identity,sk_c7) != sk_c8
| multiply(identity,identity) != sk_c8 ),
inference(resolve,[status(thm)],[c_356,c_55]) ).
cnf(c_10177,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| inverse(identity) != sk_c8
| multiply(identity,sk_c7) != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10176]) ).
cnf(c_10178,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_10177]) ).
cnf(c_10179,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_356,c_10178]) ).
cnf(c_10180,plain,
( sk_c8 != A
| multiply(sk_c8,A) != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_10179]) ).
cnf(c_443,plain,
( sk_c8 != A
| multiply(sk_c8,A) != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10180]) ).
cnf(c_10181,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_78,c_59]) ).
cnf(c_451,plain,
( inverse(sk_c2) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10181]) ).
cnf(c_455,plain,
( multiply(sk_c1,sk_c2) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_451,c_2]) ).
cnf(c_10182,plain,
( sk_c8 != identity
| sk_c8 != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_443]) ).
cnf(c_10183,plain,
( sk_c8 != identity
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10182]) ).
cnf(c_10184,plain,
( identity != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10183]) ).
cnf(c_10185,plain,
( identity != sk_c8
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10184]) ).
cnf(c_520,plain,
( sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10185]) ).
cnf(c_10186,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_89,c_59]) ).
cnf(c_560,plain,
( inverse(sk_c2) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10186]) ).
cnf(c_565,plain,
( multiply(sk_c1,sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_560,c_2]) ).
cnf(c_10187,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_90,c_59]) ).
cnf(c_573,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_285,c_10187]) ).
cnf(c_576,plain,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_573,c_2]) ).
cnf(c_10188,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_109,c_59]) ).
cnf(c_653,plain,
( inverse(sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10188]) ).
cnf(c_10189,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_67]) ).
cnf(c_792,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_10189]) ).
cnf(c_793,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| multiply(sk_c1,multiply(sk_c2,A)) = multiply(sk_c8,A) ),
inference(paramod,[status(thm)],[c_67,c_59]) ).
cnf(c_10190,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_121,c_59]) ).
cnf(c_905,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10190]) ).
cnf(c_917,plain,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_905,c_2]) ).
cnf(c_10191,plain,
( inverse(sk_c4) = sk_c8
| identity = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_455,c_4]) ).
cnf(c_1169,plain,
( identity = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(copy,[status(thm)],[c_10191]) ).
cnf(c_1394,plain,
( sk_c7 != sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(resolve,[status(thm)],[c_1169,c_520]) ).
cnf(c_1403,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1169,c_2]) ).
cnf(c_1405,plain,
( inverse(sk_c8) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_1169,c_356]) ).
cnf(c_10192,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1403,c_59]) ).
cnf(c_1424,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10192]) ).
cnf(c_10193,plain,
( identity = sk_c3
| inverse(sk_c4) = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_1405,c_653]) ).
cnf(c_1697,plain,
( identity = sk_c3
| inverse(sk_c4) = sk_c8 ),
inference(copy,[status(thm)],[c_10193]) ).
cnf(c_1719,plain,
( multiply(sk_c3,A) = A
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_1697,c_1]) ).
cnf(c_10194,plain,
( multiply(sk_c4,multiply(sk_c8,sk_c6)) = sk_c8
| inverse(sk_c1) = sk_c2
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_10,c_85]) ).
cnf(c_2307,plain,
( multiply(sk_c4,multiply(sk_c8,sk_c6)) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(copy,[status(thm)],[c_10194]) ).
cnf(c_10195,plain,
( inverse(sk_c5) = sk_c8
| identity = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_565,c_8]) ).
cnf(c_2390,plain,
( identity = sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_10195]) ).
cnf(c_2427,plain,
( multiply(sk_c8,sk_c5) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2390,c_2]) ).
cnf(c_10196,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2427,c_59]) ).
cnf(c_2477,plain,
( inverse(sk_c8) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10196]) ).
cnf(c_10197,plain,
( sk_c5 = sk_c4
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2477,c_1424]) ).
cnf(c_2529,plain,
( sk_c5 = sk_c4
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_10197]) ).
cnf(c_10198,plain,
( multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c8,multiply(sk_c7,A))
| multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_98,c_67]) ).
cnf(c_2994,plain,
( multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c8,multiply(sk_c7,A))
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_10198]) ).
cnf(c_10199,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c2
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_576,c_12]) ).
cnf(c_3844,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(copy,[status(thm)],[c_10199]) ).
cnf(c_3855,plain,
( multiply(sk_c2,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3844,c_2]) ).
cnf(c_10200,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3855,c_59]) ).
cnf(c_3878,plain,
( inverse(sk_c2) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_285,c_10200]) ).
cnf(c_3912,plain,
( multiply(sk_c1,sk_c2) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3878,c_2]) ).
cnf(c_3987,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| identity = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_3912,c_7]) ).
cnf(c_10201,plain,
( multiply(sk_c4,multiply(sk_c8,sk_c6)) = sk_c8
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_116]) ).
cnf(c_4211,plain,
( multiply(sk_c4,multiply(sk_c8,sk_c6)) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10201]) ).
cnf(c_10202,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_917,c_22]) ).
cnf(c_4274,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10202]) ).
cnf(c_4307,plain,
( inverse(sk_c6) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_4274,c_356]) ).
cnf(c_10203,plain,
( inverse(sk_c6) = sk_c6
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_4274,c_4307]) ).
cnf(c_4717,plain,
( inverse(sk_c6) = sk_c6
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10203]) ).
cnf(c_10204,plain,
( inverse(sk_c4) = sk_c8
| sk_c7 = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_1719,c_24]) ).
cnf(c_5243,plain,
( sk_c7 = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(copy,[status(thm)],[c_10204]) ).
cnf(c_10205,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c4) = sk_c8 ),
inference(resolve,[status(thm)],[c_5243,c_1394]) ).
cnf(c_5272,plain,
inverse(sk_c4) = sk_c8,
inference(copy,[status(thm)],[c_10205]) ).
cnf(c_5594,plain,
multiply(sk_c8,sk_c4) = identity,
inference(paramod,[status(thm)],[c_5272,c_2]) ).
cnf(c_10206,plain,
( multiply(sk_c4,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| inverse(sk_c4) != sk_c8
| multiply(sk_c4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c4
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_5594,c_55]) ).
cnf(c_10207,plain,
( multiply(sk_c4,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| sk_c8 != sk_c8
| multiply(sk_c4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c4
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_5272,c_10206]) ).
cnf(c_5627,plain,
( multiply(sk_c4,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c4
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10207]) ).
cnf(c_10208,plain,
multiply(inverse(sk_c8),identity) = sk_c4,
inference(paramod,[status(thm)],[c_5594,c_59]) ).
cnf(c_5631,plain,
inverse(sk_c8) = sk_c4,
inference(paramod,[status(thm)],[c_285,c_10208]) ).
cnf(c_10209,plain,
( multiply(sk_c4,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| sk_c4 != sk_c4
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_5631,c_5627]) ).
cnf(c_5649,plain,
( multiply(sk_c4,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10209]) ).
cnf(c_6204,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,multiply(sk_c2,A)) = multiply(sk_c8,A) ),
inference(paramod,[status(thm)],[c_5631,c_793]) ).
cnf(c_6273,plain,
multiply(sk_c4,sk_c8) = identity,
inference(paramod,[status(thm)],[c_5631,c_2]) ).
cnf(c_6276,plain,
multiply(sk_c4,multiply(sk_c8,A)) = A,
inference(paramod,[status(thm)],[c_5631,c_59]) ).
cnf(c_6306,plain,
( identity != A
| multiply(sk_c8,A) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_6273,c_5649]) ).
cnf(c_6430,plain,
( sk_c6 = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_6276,c_4211]) ).
cnf(c_6449,plain,
( sk_c6 = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_6276,c_2307]) ).
cnf(c_6451,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| identity != sk_c8 ),
inference(factor,[status(thm)],[c_6306]) ).
cnf(c_6536,plain,
( sk_c5 = sk_c4
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8 ),
inference(resolve,[status(thm)],[c_6451,c_2529]) ).
cnf(c_10210,plain,
( multiply(sk_c8,identity) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| inverse(sk_c4) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(resolve,[status(thm)],[c_6273,c_46]) ).
cnf(c_10211,plain,
( multiply(sk_c8,identity) != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| sk_c8 != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(paramod,[status(thm)],[c_5272,c_10210]) ).
cnf(c_10212,plain,
( sk_c8 != sk_c7
| multiply(sk_c4,sk_c7) != sk_c8
| sk_c8 != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(paramod,[status(thm)],[c_285,c_10211]) ).
cnf(c_10213,plain,
( sk_c7 != sk_c8
| multiply(sk_c4,sk_c7) != sk_c8
| sk_c8 != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(copy,[status(thm)],[c_10212]) ).
cnf(c_6609,plain,
( sk_c7 != sk_c8
| multiply(sk_c4,sk_c7) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(copy,[status(thm)],[c_10213]) ).
cnf(c_10214,plain,
( identity = sk_c8
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_6430,c_4274]) ).
cnf(c_7309,plain,
( identity = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10214]) ).
cnf(c_10215,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_6430,c_4717]) ).
cnf(c_10216,plain,
( sk_c4 = sk_c6
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_5631,c_10215]) ).
cnf(c_10217,plain,
( sk_c6 = sk_c4
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10216]) ).
cnf(c_7313,plain,
( sk_c6 = sk_c4
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10217]) ).
cnf(c_7322,plain,
( multiply(sk_c2,sk_c1) = identity
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_6449,c_2]) ).
cnf(c_7372,plain,
( sk_c7 != sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(resolve,[status(thm)],[c_7309,c_520]) ).
cnf(c_10218,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_7313,c_21]) ).
cnf(c_10219,plain,
( identity = sk_c7
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_5594,c_10218]) ).
cnf(c_7676,plain,
( identity = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10219]) ).
cnf(c_10220,plain,
( sk_c7 = sk_c8
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_7676,c_7309]) ).
cnf(c_7973,plain,
( sk_c7 = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_10220]) ).
cnf(c_10221,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(resolve,[status(thm)],[c_7973,c_7372]) ).
cnf(c_8223,plain,
inverse(sk_c3) = sk_c8,
inference(copy,[status(thm)],[c_10221]) ).
cnf(c_8317,plain,
multiply(sk_c8,sk_c3) = identity,
inference(paramod,[status(thm)],[c_8223,c_2]) ).
cnf(c_10222,plain,
multiply(inverse(sk_c8),identity) = sk_c3,
inference(paramod,[status(thm)],[c_8317,c_59]) ).
cnf(c_10223,plain,
multiply(sk_c4,identity) = sk_c3,
inference(paramod,[status(thm)],[c_5631,c_10222]) ).
cnf(c_8453,plain,
sk_c4 = sk_c3,
inference(paramod,[status(thm)],[c_285,c_10223]) ).
cnf(c_9010,plain,
( sk_c7 != sk_c8
| multiply(sk_c3,sk_c7) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(paramod,[status(thm)],[c_8453,c_6609]) ).
cnf(c_10224,plain,
( sk_c5 = sk_c4
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c3,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_8453,c_6536]) ).
cnf(c_9041,plain,
( sk_c5 = sk_c3
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c3,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_8453,c_10224]) ).
cnf(c_9087,plain,
( identity != A
| multiply(sk_c8,A) != sk_c7
| multiply(sk_c3,sk_c7) != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_8453,c_6306]) ).
cnf(c_9101,plain,
multiply(sk_c3,sk_c8) = identity,
inference(paramod,[status(thm)],[c_8453,c_6273]) ).
cnf(c_9132,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,multiply(sk_c2,A)) = multiply(sk_c8,A) ),
inference(paramod,[status(thm)],[c_8453,c_6204]) ).
cnf(c_10225,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_8453,c_25]) ).
cnf(c_9563,plain,
multiply(sk_c3,sk_c7) = sk_c8,
inference(copy,[status(thm)],[c_10225]) ).
cnf(c_10226,plain,
( sk_c7 != sk_c8
| multiply(sk_c7,sk_c7) != sk_c8
| inverse(sk_c3) != sk_c7
| multiply(sk_c3,sk_c7) != sk_c8 ),
inference(factor,[status(thm)],[c_9010]) ).
cnf(c_10227,plain,
( sk_c7 != sk_c8
| multiply(sk_c7,sk_c7) != sk_c8
| inverse(sk_c3) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_9563,c_10226]) ).
cnf(c_10228,plain,
( sk_c7 != sk_c8
| multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8223,c_10227]) ).
cnf(c_10229,plain,
( sk_c7 != sk_c8
| multiply(sk_c7,sk_c7) != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_10228]) ).
cnf(c_10230,plain,
( sk_c7 != sk_c8
| multiply(sk_c7,sk_c7) != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_10229]) ).
cnf(c_9576,plain,
( multiply(sk_c7,sk_c7) != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_10230]) ).
cnf(c_10231,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c3,sk_c7) != sk_c8
| identity != sk_c8 ),
inference(factor,[status(thm)],[c_9087]) ).
cnf(c_10232,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_9563,c_10231]) ).
cnf(c_9579,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_10232]) ).
cnf(c_10233,plain,
( sk_c8 = sk_c6
| multiply(sk_c1,multiply(sk_c2,A)) = multiply(sk_c8,A) ),
inference(paramod,[status(thm)],[c_9563,c_9132]) ).
cnf(c_9602,plain,
( sk_c6 = sk_c8
| multiply(sk_c1,multiply(sk_c2,A)) = multiply(sk_c8,A) ),
inference(copy,[status(thm)],[c_10233]) ).
cnf(c_10234,plain,
( sk_c5 = sk_c3
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_9563,c_9041]) ).
cnf(c_9605,plain,
( sk_c5 = sk_c3
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_10234]) ).
cnf(c_10235,plain,
multiply(inverse(sk_c3),sk_c8) = sk_c7,
inference(paramod,[status(thm)],[c_9563,c_59]) ).
cnf(c_9831,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(paramod,[status(thm)],[c_8223,c_10235]) ).
cnf(c_10236,plain,
( sk_c5 = sk_c3
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_9831,c_9605]) ).
cnf(c_9856,plain,
sk_c5 = sk_c3,
inference(copy,[status(thm)],[c_10236]) ).
cnf(c_10237,plain,
( sk_c7 != sk_c7
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_9831,c_9579]) ).
cnf(c_9857,plain,
identity != sk_c8,
inference(copy,[status(thm)],[c_10237]) ).
cnf(c_10238,plain,
( multiply(sk_c3,sk_c8) = sk_c6
| identity = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9856,c_3987]) ).
cnf(c_10239,plain,
( identity = sk_c6
| identity = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_9101,c_10238]) ).
cnf(c_10240,plain,
( identity = sk_c8
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_10239]) ).
cnf(c_9932,plain,
identity = sk_c6,
inference(resolve,[status(thm)],[c_9857,c_10240]) ).
cnf(c_10012,plain,
sk_c6 != sk_c8,
inference(paramod,[status(thm)],[c_9932,c_9857]) ).
cnf(c_10241,plain,
( multiply(sk_c2,sk_c1) = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_9932,c_7322]) ).
cnf(c_10057,plain,
multiply(sk_c2,sk_c1) = sk_c6,
inference(resolve,[status(thm)],[c_10012,c_10241]) ).
cnf(c_10083,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_9932,c_285]) ).
cnf(c_10091,plain,
multiply(sk_c1,multiply(sk_c2,A)) = multiply(sk_c8,A),
inference(resolve,[status(thm)],[c_10012,c_9602]) ).
cnf(c_10242,plain,
( multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c8,multiply(sk_c7,A))
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_10083,c_2994]) ).
cnf(c_10105,plain,
( multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c8,multiply(sk_c7,A))
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_10242]) ).
cnf(c_10243,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c7)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_10083,c_792]) ).
cnf(c_10109,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c8,sk_c7)
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_10243]) ).
cnf(c_10127,plain,
multiply(sk_c7,A) = multiply(sk_c8,multiply(sk_c8,A)),
inference(paramod,[status(thm)],[c_9831,c_3]) ).
cnf(c_10133,plain,
( multiply(sk_c1,multiply(sk_c8,A)) = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,A)))
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10127,c_10105]) ).
cnf(c_10136,plain,
( multiply(sk_c8,multiply(sk_c8,sk_c7)) != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_10127,c_9576]) ).
cnf(c_10244,plain,
multiply(inverse(sk_c2),sk_c6) = sk_c1,
inference(paramod,[status(thm)],[c_10057,c_59]) ).
cnf(c_10145,plain,
inverse(sk_c2) = sk_c1,
inference(paramod,[status(thm)],[c_10083,c_10244]) ).
cnf(c_10245,plain,
multiply(sk_c1,multiply(sk_c2,A)) = A,
inference(paramod,[status(thm)],[c_10145,c_59]) ).
cnf(c_10150,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_10091,c_10245]) ).
cnf(c_10246,plain,
( multiply(sk_c8,sk_c7) != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_10150,c_10136]) ).
cnf(c_10247,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_10150,c_10246]) ).
cnf(c_10160,plain,
sk_c7 != sk_c8,
inference(copy,[status(thm)],[c_10247]) ).
cnf(c_10248,plain,
( multiply(sk_c1,A) = multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,A)))
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10150,c_10133]) ).
cnf(c_10249,plain,
( multiply(sk_c1,A) = multiply(sk_c8,multiply(sk_c8,A))
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10150,c_10248]) ).
cnf(c_10250,plain,
( multiply(sk_c1,A) = multiply(sk_c8,A)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10150,c_10249]) ).
cnf(c_10251,plain,
( multiply(sk_c1,A) = A
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10150,c_10250]) ).
cnf(c_10162,plain,
multiply(sk_c1,A) = A,
inference(resolve,[status(thm)],[c_10160,c_10251]) ).
cnf(c_10252,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10162,c_10109]) ).
cnf(c_10253,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10150,c_10252]) ).
cnf(c_10254,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_10253]) ).
cnf(c_10255,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_10254]) ).
cnf(c_10167,plain,
$false,
inference(resolve,[status(thm)],[c_10160,c_10255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP211-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n005.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Fri Sep 25 14:38:16 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.33 % Process 3712252 was started by sandbox2 on n005,
% 0.06/0.33 % Fri Sep 25 14:38:16 2026
% 0.06/0.33 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/0.34
% 0.06/0.34 % From the command line: assign(max_seconds, 300).
% 14.89/2.50
% 14.89/2.50 % SZS status Unsatisfiable for theBenchmark
% 14.89/2.50
% 14.89/2.50 % Proof 1 at 1.69 (+ 0.43) seconds.
% 14.89/2.50 % Length of proof is 127.
% 14.89/2.50 % Level of proof is 32.
% 14.89/2.50 % Maximum clause weight is 50.000.
% 14.89/2.50 % Given clauses 414.
% 14.89/2.50
% 14.89/2.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------