%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP364-1 : 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 : n012.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 07:28:43 AM UTC 2026
% Result : Unsatisfiable 144.87s 18.96s
% Output : CNFRefutation 144.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 87
% Number of leaves : 35
% Syntax : Number of formulae : 267 ( 27 unt; 0 def)
% Number of atoms : 750 ( 749 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 651 ( 168 ~; 483 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 3 ( 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 : 61 ( 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,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_14,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( multiply(sk_c9,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_29,axiom,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( inverse(sk_c5) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_32,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_33,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_37,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c9
| multiply(VAR_5,sk_c9) != VAR_4
| multiply(sk_c9,VAR_4) != sk_c8
| inverse(VAR_3) != sk_c9
| multiply(VAR_3,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(VAR_2) != sk_c7
| multiply(VAR_2,sk_c7) != sk_c9
| inverse(VAR_1) != sk_c9
| multiply(VAR_1,sk_c9) != VAR_0
| multiply(sk_c9,VAR_0) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
file('theBenchmark.p',prove_this_37) ).
cnf(c_40,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c8
| inverse(D) != sk_c9
| multiply(D,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_37]) ).
cnf(c_12601,plain,
( inverse(B) != sk_c9
| multiply(sk_c9,A) != sk_c8
| inverse(D) != sk_c9
| multiply(D,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_12602,plain,
( inverse(B) != sk_c9
| inverse(D) != sk_c9
| multiply(D,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_12601]) ).
cnf(c_46,plain,
( inverse(D) != sk_c9
| multiply(D,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_12602]) ).
cnf(c_57,plain,
multiply(multiply(A,identity),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_12603,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_59,plain,
multiply(inverse(A),multiply(A,B)) = multiply(identity,B),
inference(copy,[status(thm)],[c_12603]) ).
cnf(c_105,plain,
( multiply(sk_c9,sk_c4) = identity
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_162,plain,
( inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_46]) ).
cnf(c_264,plain,
( multiply(identity,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_162]) ).
cnf(c_12604,plain,
multiply(A,B) = multiply(A,multiply(identity,B)),
inference(paramod,[status(thm)],[c_57,c_3]) ).
cnf(c_480,plain,
multiply(A,multiply(identity,B)) = multiply(A,B),
inference(copy,[status(thm)],[c_12604]) ).
cnf(c_854,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(paramod,[status(thm)],[c_1,c_59]) ).
cnf(c_934,plain,
( multiply(inverse(sk_c1),sk_c2) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_18,c_854]) ).
cnf(c_937,plain,
( multiply(inverse(sk_c1),sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9 ),
inference(paramod,[status(thm)],[c_21,c_854]) ).
cnf(c_939,plain,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_23,c_854]) ).
cnf(c_942,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_26,c_854]) ).
cnf(c_946,plain,
( multiply(inverse(sk_c3),sk_c9) = sk_c7
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_30,c_854]) ).
cnf(c_949,plain,
( multiply(inverse(sk_c3),sk_c9) = sk_c7
| inverse(sk_c5) = sk_c9 ),
inference(paramod,[status(thm)],[c_33,c_854]) ).
cnf(c_951,plain,
( multiply(inverse(sk_c4),sk_c8) = sk_c9
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_35,c_854]) ).
cnf(c_12605,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_24,c_939]) ).
cnf(c_1114,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(copy,[status(thm)],[c_12605]) ).
cnf(c_12606,plain,
( sk_c9 = sk_c7
| inverse(sk_c1) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_1114,c_22]) ).
cnf(c_12607,plain,
( sk_c7 = sk_c9
| inverse(sk_c1) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(copy,[status(thm)],[c_12606]) ).
cnf(c_1122,plain,
( sk_c7 = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(copy,[status(thm)],[c_12607]) ).
cnf(c_1133,plain,
( multiply(sk_c9,sk_c1) = identity
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_1122,c_2]) ).
cnf(c_1147,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_1133,c_854]) ).
cnf(c_12608,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_27,c_942]) ).
cnf(c_1326,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(copy,[status(thm)],[c_12608]) ).
cnf(c_12609,plain,
( sk_c9 = sk_c8
| inverse(sk_c1) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_1326,c_25]) ).
cnf(c_12610,plain,
( sk_c8 = sk_c9
| inverse(sk_c1) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(copy,[status(thm)],[c_12609]) ).
cnf(c_1335,plain,
( sk_c8 = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(copy,[status(thm)],[c_12610]) ).
cnf(c_1341,plain,
( multiply(sk_c9,sk_c1) = identity
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1335,c_2]) ).
cnf(c_1344,plain,
( multiply(sk_c9,multiply(sk_c1,A)) = A
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1335,c_854]) ).
cnf(c_1345,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| inverse(sk_c4) = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1335,c_934]) ).
cnf(c_1346,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| inverse(sk_c5) = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1335,c_937]) ).
cnf(c_1356,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1341,c_854]) ).
cnf(c_12611,plain,
( inverse(sk_c4) = sk_c9
| sk_c9 = sk_c8
| inverse(sk_c4) = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1345,c_12]) ).
cnf(c_12612,plain,
( inverse(sk_c4) = sk_c9
| sk_c8 = sk_c9
| inverse(sk_c4) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12611]) ).
cnf(c_12613,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c4) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12612]) ).
cnf(c_1363,plain,
( inverse(sk_c4) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12613]) ).
cnf(c_1398,plain,
( multiply(sk_c9,sk_c4) = identity
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1363,c_2]) ).
cnf(c_1411,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1398,c_854]) ).
cnf(c_12614,plain,
( inverse(sk_c5) = sk_c9
| sk_c9 = sk_c8
| inverse(sk_c5) = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1346,c_15]) ).
cnf(c_12615,plain,
( inverse(sk_c5) = sk_c9
| sk_c8 = sk_c9
| inverse(sk_c5) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12614]) ).
cnf(c_12616,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c5) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12615]) ).
cnf(c_1418,plain,
( inverse(sk_c5) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12616]) ).
cnf(c_1419,plain,
( multiply(sk_c9,sk_c5) = identity
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1418,c_2]) ).
cnf(c_1432,plain,
( multiply(inverse(sk_c9),identity) = sk_c5
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1419,c_854]) ).
cnf(c_12617,plain,
( sk_c4 = sk_c1
| sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1411,c_1356]) ).
cnf(c_1478,plain,
( sk_c4 = sk_c1
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12617]) ).
cnf(c_1481,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1478,c_11]) ).
cnf(c_1482,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1478,c_17]) ).
cnf(c_12618,plain,
( sk_c5 = sk_c1
| sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1432,c_1356]) ).
cnf(c_1577,plain,
( sk_c5 = sk_c1
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12618]) ).
cnf(c_12619,plain,
( sk_c5 = sk_c4
| sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1432,c_1411]) ).
cnf(c_1579,plain,
( sk_c5 = sk_c4
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12619]) ).
cnf(c_1581,plain,
( multiply(sk_c1,sk_c9) = sk_c6
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1577,c_14]) ).
cnf(c_1587,plain,
( multiply(sk_c4,sk_c9) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c2
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1579,c_20]) ).
cnf(c_12620,plain,
( sk_c6 = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1581,c_1481]) ).
cnf(c_12621,plain,
( sk_c6 = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12620]) ).
cnf(c_1717,plain,
( sk_c6 = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12621]) ).
cnf(c_12622,plain,
( sk_c6 = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2
| multiply(sk_c1,sk_c9) = sk_c2
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1587,c_17]) ).
cnf(c_1842,plain,
( sk_c6 = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12622]) ).
cnf(c_12623,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_36,c_951]) ).
cnf(c_2002,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_12623]) ).
cnf(c_12624,plain,
( sk_c9 = sk_c7
| inverse(sk_c3) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_2002,c_34]) ).
cnf(c_12625,plain,
( sk_c7 = sk_c9
| inverse(sk_c3) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_12624]) ).
cnf(c_2028,plain,
( sk_c7 = sk_c9
| inverse(sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_12625]) ).
cnf(c_2042,plain,
( multiply(sk_c7,multiply(sk_c3,A)) = A
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_2028,c_854]) ).
cnf(c_2043,plain,
( multiply(sk_c7,sk_c9) = sk_c7
| inverse(sk_c4) = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_2028,c_946]) ).
cnf(c_2044,plain,
( multiply(sk_c7,sk_c9) = sk_c7
| inverse(sk_c5) = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_2028,c_949]) ).
cnf(c_2150,plain,
( multiply(identity,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_264]) ).
cnf(c_12626,plain,
( sk_c9 != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_2150]) ).
cnf(c_2231,plain,
( sk_c8 != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_12626]) ).
cnf(c_3362,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_1344]) ).
cnf(c_12627,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1482,c_1344]) ).
cnf(c_3377,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12627]) ).
cnf(c_12628,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1581,c_1344]) ).
cnf(c_3379,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12628]) ).
cnf(c_12629,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c8 = sk_c9
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_1842,c_1344]) ).
cnf(c_3381,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12629]) ).
cnf(c_12630,plain,
( sk_c6 = sk_c8
| sk_c9 = sk_c8
| sk_c8 = sk_c9
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3381,c_1717]) ).
cnf(c_12631,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c9
| sk_c8 = sk_c9
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12630]) ).
cnf(c_12632,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c9
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12631]) ).
cnf(c_12633,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12632]) ).
cnf(c_3397,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12633]) ).
cnf(c_12634,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3397,c_3362]) ).
cnf(c_3457,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12634]) ).
cnf(c_12635,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c2) = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3377,c_1344]) ).
cnf(c_3556,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12635]) ).
cnf(c_12636,plain,
( sk_c9 = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3379,c_13]) ).
cnf(c_12637,plain,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12636]) ).
cnf(c_12638,plain,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12637]) ).
cnf(c_3704,plain,
( multiply(sk_c9,sk_c2) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12638]) ).
cnf(c_12639,plain,
( sk_c9 = sk_c8
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3457,c_3704]) ).
cnf(c_12640,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12639]) ).
cnf(c_12641,plain,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12640]) ).
cnf(c_3842,plain,
( multiply(sk_c9,sk_c8) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12641]) ).
cnf(c_12642,plain,
( sk_c9 = sk_c8
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3556,c_3704]) ).
cnf(c_12643,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12642]) ).
cnf(c_12644,plain,
( sk_c8 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12643]) ).
cnf(c_4032,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12644]) ).
cnf(c_12645,plain,
( sk_c9 = sk_c8
| sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_4032,c_3842]) ).
cnf(c_12646,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12645]) ).
cnf(c_12647,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_12646]) ).
cnf(c_4041,plain,
sk_c8 = sk_c9,
inference(copy,[status(thm)],[c_12647]) ).
cnf(c_4221,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_4041,c_2231]) ).
cnf(c_4334,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_4]) ).
cnf(c_4336,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_6]) ).
cnf(c_4337,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_7]) ).
cnf(c_4338,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_9]) ).
cnf(c_12648,plain,
( sk_c9 = sk_c7
| inverse(sk_c4) = sk_c9
| sk_c7 = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_4336,c_2043]) ).
cnf(c_12649,plain,
( sk_c7 = sk_c9
| inverse(sk_c4) = sk_c9
| sk_c7 = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_12648]) ).
cnf(c_12650,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_12649]) ).
cnf(c_4466,plain,
( sk_c7 = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_12650]) ).
cnf(c_4471,plain,
( multiply(sk_c9,sk_c4) = identity
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4466,c_2]) ).
cnf(c_4483,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4471,c_854]) ).
cnf(c_12651,plain,
( sk_c9 = sk_c7
| inverse(sk_c5) = sk_c9
| sk_c7 = sk_c9
| inverse(sk_c5) = sk_c9 ),
inference(paramod,[status(thm)],[c_4338,c_2044]) ).
cnf(c_12652,plain,
( sk_c7 = sk_c9
| inverse(sk_c5) = sk_c9
| sk_c7 = sk_c9
| inverse(sk_c5) = sk_c9 ),
inference(copy,[status(thm)],[c_12651]) ).
cnf(c_12653,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9
| inverse(sk_c5) = sk_c9 ),
inference(copy,[status(thm)],[c_12652]) ).
cnf(c_4504,plain,
( sk_c7 = sk_c9
| inverse(sk_c5) = sk_c9 ),
inference(copy,[status(thm)],[c_12653]) ).
cnf(c_4509,plain,
( multiply(sk_c9,sk_c5) = identity
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4504,c_2]) ).
cnf(c_4521,plain,
( multiply(inverse(sk_c9),identity) = sk_c5
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4509,c_854]) ).
cnf(c_12654,plain,
( sk_c4 = sk_c1
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4483,c_1147]) ).
cnf(c_4764,plain,
( sk_c4 = sk_c1
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12654]) ).
cnf(c_4766,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4764,c_5]) ).
cnf(c_4966,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != A
| multiply(sk_c9,A) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4041,c_4221]) ).
cnf(c_12655,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| sk_c9 != multiply(identity,A)
| multiply(sk_c9,A) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_480,c_4966]) ).
cnf(c_4990,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| multiply(identity,A) != sk_c9
| multiply(sk_c9,A) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_12655]) ).
cnf(c_12656,plain,
( sk_c5 = sk_c1
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4521,c_1147]) ).
cnf(c_5176,plain,
( sk_c5 = sk_c1
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12656]) ).
cnf(c_12657,plain,
( sk_c5 = sk_c4
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4521,c_4483]) ).
cnf(c_5178,plain,
( sk_c5 = sk_c4
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12657]) ).
cnf(c_5179,plain,
( multiply(sk_c1,sk_c9) = sk_c6
| multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5176,c_8]) ).
cnf(c_5230,plain,
( multiply(sk_c4,sk_c9) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5178,c_32]) ).
cnf(c_12658,plain,
( sk_c6 = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5179,c_4766]) ).
cnf(c_12659,plain,
( sk_c6 = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12658]) ).
cnf(c_5239,plain,
( sk_c6 = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12659]) ).
cnf(c_5270,plain,
( sk_c6 = sk_c8
| multiply(sk_c7,sk_c9) = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_5239]) ).
cnf(c_5678,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_4990,c_1]) ).
cnf(c_5685,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c9
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_5678]) ).
cnf(c_12660,plain,
( sk_c6 = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5230,c_29]) ).
cnf(c_5691,plain,
( sk_c6 = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12660]) ).
cnf(c_6081,plain,
( multiply(sk_c7,sk_c9) = sk_c7
| sk_c7 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_28,c_2042]) ).
cnf(c_6082,plain,
( multiply(sk_c7,sk_c9) = sk_c7
| sk_c7 = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_31,c_2042]) ).
cnf(c_12661,plain,
( multiply(sk_c7,sk_c9) = sk_c7
| sk_c7 = sk_c9
| sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5691,c_2042]) ).
cnf(c_6090,plain,
( multiply(sk_c7,sk_c9) = sk_c7
| sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12661]) ).
cnf(c_12662,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c9
| sk_c7 = sk_c9
| sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_6090,c_5270]) ).
cnf(c_12663,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c9
| sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12662]) ).
cnf(c_12664,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12663]) ).
cnf(c_6170,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12664]) ).
cnf(c_12665,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = sk_c9
| sk_c7 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_6081,c_4334]) ).
cnf(c_12666,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_12665]) ).
cnf(c_6192,plain,
( sk_c7 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_12666]) ).
cnf(c_12667,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c7 = sk_c9
| sk_c7 = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_6082,c_4337]) ).
cnf(c_12668,plain,
( multiply(sk_c9,sk_c6) = sk_c8
| sk_c7 = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_12667]) ).
cnf(c_6355,plain,
( sk_c7 = sk_c9
| multiply(sk_c9,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_12668]) ).
cnf(c_12669,plain,
( sk_c7 = sk_c9
| multiply(sk_c9,sk_c8) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_6170,c_6355]) ).
cnf(c_6371,plain,
( multiply(sk_c9,sk_c8) = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12669]) ).
cnf(c_12670,plain,
( sk_c7 = sk_c9
| sk_c8 = sk_c7
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_6371,c_6192]) ).
cnf(c_12671,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12670]) ).
cnf(c_6394,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_12671]) ).
cnf(c_12672,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_6394]) ).
cnf(c_6441,plain,
sk_c7 = sk_c9,
inference(copy,[status(thm)],[c_12672]) ).
cnf(c_6634,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c9 ),
inference(resolve,[status(thm)],[c_6441,c_5685]) ).
cnf(c_7436,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_6441,c_4334]) ).
cnf(c_12673,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(paramod,[status(thm)],[c_6441,c_6634]) ).
cnf(c_7494,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(identity) != sk_c7
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(copy,[status(thm)],[c_12673]) ).
cnf(c_7497,plain,
( multiply(sk_c9,sk_c9) != sk_c7
| inverse(identity) != sk_c7
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_7494]) ).
cnf(c_12674,plain,
( multiply(sk_c9,sk_c9) != sk_c9
| inverse(identity) != sk_c7
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(paramod,[status(thm)],[c_6441,c_7497]) ).
cnf(c_7566,plain,
( inverse(identity) != sk_c7
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(copy,[status(thm)],[c_12674]) ).
cnf(c_7713,plain,
( multiply(sk_c9,sk_c9) = sk_c7
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_4041,c_7436]) ).
cnf(c_12675,plain,
( multiply(sk_c9,sk_c9) = sk_c9
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_6441,c_7713]) ).
cnf(c_7787,plain,
multiply(sk_c9,sk_c9) = sk_c9,
inference(copy,[status(thm)],[c_12675]) ).
cnf(c_7789,plain,
( inverse(identity) != sk_c7
| inverse(identity) != sk_c9 ),
inference(resolve,[status(thm)],[c_7787,c_7566]) ).
cnf(c_12676,plain,
( inverse(identity) != sk_c9
| inverse(identity) != sk_c9 ),
inference(paramod,[status(thm)],[c_6441,c_7789]) ).
cnf(c_7817,plain,
inverse(identity) != sk_c9,
inference(copy,[status(thm)],[c_12676]) ).
cnf(c_7835,plain,
multiply(inverse(sk_c9),sk_c9) = sk_c9,
inference(paramod,[status(thm)],[c_7787,c_854]) ).
cnf(c_12677,plain,
sk_c9 = identity,
inference(paramod,[status(thm)],[c_7835,c_2]) ).
cnf(c_7880,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_12677]) ).
cnf(c_8040,plain,
multiply(sk_c9,A) = A,
inference(paramod,[status(thm)],[c_7880,c_1]) ).
cnf(c_8103,plain,
inverse(sk_c9) != sk_c9,
inference(paramod,[status(thm)],[c_7880,c_7817]) ).
cnf(c_12678,plain,
( sk_c4 = identity
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_8040,c_105]) ).
cnf(c_8462,plain,
( identity = sk_c4
| inverse(sk_c1) = sk_c9 ),
inference(copy,[status(thm)],[c_12678]) ).
cnf(c_10242,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_8462,c_2]) ).
cnf(c_11586,plain,
( identity = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10242,c_8040]) ).
cnf(c_11623,plain,
( sk_c4 = sk_c9
| identity = sk_c1 ),
inference(paramod,[status(thm)],[c_11586,c_7880]) ).
cnf(c_11720,plain,
( inverse(sk_c1) != sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_11623,c_7817]) ).
cnf(c_12150,plain,
( identity = sk_c4
| sk_c4 = sk_c9 ),
inference(resolve,[status(thm)],[c_11720,c_8462]) ).
cnf(c_12679,plain,
( sk_c4 = sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_12150,c_7880]) ).
cnf(c_12254,plain,
sk_c4 = sk_c9,
inference(copy,[status(thm)],[c_12679]) ).
cnf(c_12680,plain,
( inverse(sk_c9) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_12254,c_24]) ).
cnf(c_12320,plain,
inverse(sk_c1) = sk_c9,
inference(resolve,[status(thm)],[c_8103,c_12680]) ).
cnf(c_12369,plain,
multiply(sk_c9,sk_c1) = identity,
inference(paramod,[status(thm)],[c_12320,c_2]) ).
cnf(c_12566,plain,
identity = sk_c1,
inference(paramod,[status(thm)],[c_12369,c_8040]) ).
cnf(c_12681,plain,
inverse(sk_c1) != sk_c9,
inference(paramod,[status(thm)],[c_12566,c_7817]) ).
cnf(c_12600,plain,
$false,
inference(resolve,[status(thm)],[c_12320,c_12681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP364-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n012.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:48:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2350960 was started by sandbox2 on n012,
% 0.09/0.36 % Fri Sep 25 14:48:35 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 144.87/18.96
% 144.87/18.96 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 144.87/18.96
% 144.87/18.96 % given #500 (F,wt=33): 6634 multiply(sk_c7,sk_c9) != sk_c9 | multiply(sk_c9,sk_c9) != sk_c9 | inverse(identity) != sk_c9 | inverse(identity) != sk_c7 | multiply(sk_c9,sk_c8) != sk_c7. [back_unit_del(5685),unit_del(d,6441)].
% 144.87/18.96
% 144.87/18.96 % SZS status Unsatisfiable for theBenchmark
% 144.87/18.96
% 144.87/18.96 % Proof 1 at 2.14 (+ 0.36) seconds.
% 144.87/18.96 % Length of proof is 151.
% 144.87/18.96 % Level of proof is 46.
% 144.87/18.96 % Maximum clause weight is 66.000.
% 144.87/18.96 % Given clauses 794.
% 144.87/18.96
% 144.87/18.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------