%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP244-1 : 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 : n007.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 43.46s 5.96s
% Output : CNFRefutation 43.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 16
% Syntax : Number of formulae : 154 ( 28 unt; 0 def)
% Number of atoms : 446 ( 445 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 522 ( 230 ~; 292 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 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 : 92 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_21,axiom,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_30,axiom,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_41,axiom,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('theBenchmark.p',prove_this_41) ).
cnf(c_44,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_41]) ).
fof(prove_this_42,axiom,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('theBenchmark.p',prove_this_42) ).
cnf(c_45,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_42]) ).
fof(prove_this_50,axiom,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('theBenchmark.p',prove_this_50) ).
cnf(c_53,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_50]) ).
fof(prove_this_51,axiom,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('theBenchmark.p',prove_this_51) ).
cnf(c_54,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_51]) ).
fof(prove_this_55,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( multiply(VAR_7,sk_c9) != sk_c10
| inverse(VAR_6) != VAR_7
| multiply(VAR_6,VAR_7) != sk_c10
| multiply(VAR_5,sk_c10) != sk_c11
| inverse(VAR_5) != sk_c11
| inverse(VAR_4) != sk_c10
| multiply(VAR_4,sk_c10) != sk_c9
| inverse(VAR_3) != sk_c11
| multiply(VAR_3,sk_c11) != sk_c10
| multiply(VAR_2,sk_c10) != sk_c11
| inverse(VAR_2) != sk_c11
| inverse(VAR_1) != sk_c10
| multiply(VAR_1,sk_c10) != sk_c9
| inverse(VAR_0) != sk_c11
| multiply(VAR_0,sk_c11) != sk_c10 ),
file('theBenchmark.p',prove_this_55) ).
cnf(c_58,plain,
( multiply(V7,sk_c9) != sk_c10
| inverse(V6) != V7
| multiply(V6,V7) != sk_c10
| multiply(F,sk_c10) != sk_c11
| inverse(F) != sk_c11
| inverse(E) != sk_c10
| multiply(E,sk_c10) != sk_c9
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c10
| multiply(C,sk_c10) != sk_c11
| inverse(C) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(clausify,[status(thm)],[prove_this_55]) ).
cnf(c_10047,plain,
( multiply(V6,sk_c9) != sk_c10
| inverse(F) != V6
| multiply(F,V6) != sk_c10
| multiply(E,sk_c10) != sk_c11
| inverse(E) != sk_c11
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(C,sk_c10) != sk_c11
| inverse(C) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_58]) ).
cnf(c_59,plain,
( multiply(V6,sk_c9) != sk_c10
| inverse(F) != V6
| multiply(F,V6) != sk_c10
| multiply(E,sk_c10) != sk_c11
| inverse(E) != sk_c11
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(C,sk_c10) != sk_c11
| inverse(C) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10047]) ).
cnf(c_62,plain,
( multiply(F,sk_c9) != sk_c10
| inverse(E) != F
| multiply(E,F) != sk_c10
| multiply(D,sk_c10) != sk_c11
| inverse(D) != sk_c11
| inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_59]) ).
cnf(c_10048,plain,
( multiply(E,sk_c9) != sk_c10
| inverse(D) != E
| multiply(D,E) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_68,plain,
( multiply(E,sk_c9) != sk_c10
| inverse(D) != E
| multiply(D,E) != sk_c10
| inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10048]) ).
cnf(c_10049,plain,
( multiply(D,sk_c9) != sk_c10
| inverse(C) != D
| multiply(C,D) != sk_c10
| inverse(B) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_68]) ).
cnf(c_75,plain,
( multiply(D,sk_c9) != sk_c10
| inverse(C) != D
| multiply(C,D) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10049]) ).
cnf(c_79,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(B,sk_c10) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_75]) ).
cnf(c_10050,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_10051,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_10050]) ).
cnf(c_81,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_10051]) ).
cnf(c_114,plain,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c4,sk_c11) = sk_c10 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_117,plain,
( multiply(sk_c11,sk_c1) = identity
| inverse(sk_c4) = sk_c11 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_148,plain,
( multiply(sk_c10,sk_c5) = identity
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_174,plain,
( multiply(sk_c10,sk_c2) = identity
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_33,c_2]) ).
cnf(c_177,plain,
( multiply(sk_c10,sk_c2) = identity
| inverse(sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_34,c_2]) ).
cnf(c_203,plain,
( multiply(sk_c11,sk_c6) = identity
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_44,c_2]) ).
cnf(c_10052,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(identity) != sk_c10
| multiply(identity,sk_c10) != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(resolve,[status(thm)],[c_79,c_1]) ).
cnf(c_10053,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(identity) != sk_c10
| sk_c10 != sk_c9
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_1,c_10052]) ).
cnf(c_249,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(identity) != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10053]) ).
cnf(c_253,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_81]) ).
cnf(c_363,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_81,c_81]) ).
cnf(c_364,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_363,c_253]) ).
cnf(c_513,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_364,c_2]) ).
cnf(c_660,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(A,sk_c10) != sk_c11
| identity != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_513,c_249]) ).
cnf(c_10054,plain,
( multiply(inverse(sk_c11),identity) = sk_c1
| inverse(sk_c4) = sk_c11 ),
inference(paramod,[status(thm)],[c_117,c_81]) ).
cnf(c_666,plain,
( inverse(sk_c11) = sk_c1
| inverse(sk_c4) = sk_c11 ),
inference(paramod,[status(thm)],[c_364,c_10054]) ).
cnf(c_669,plain,
( multiply(sk_c1,sk_c11) = identity
| inverse(sk_c4) = sk_c11 ),
inference(paramod,[status(thm)],[c_666,c_2]) ).
cnf(c_10055,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(inverse(sk_c11),sk_c10) != sk_c11
| identity != sk_c10
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10 ),
inference(paramod,[status(thm)],[c_2,c_660]) ).
cnf(c_900,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(inverse(sk_c11),sk_c10) != sk_c11
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10 ),
inference(copy,[status(thm)],[c_10055]) ).
cnf(c_10056,plain,
( multiply(inverse(sk_c10),identity) = sk_c2
| inverse(sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_177,c_81]) ).
cnf(c_1177,plain,
( inverse(sk_c10) = sk_c2
| inverse(sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_364,c_10056]) ).
cnf(c_1183,plain,
( multiply(sk_c10,sk_c5) = identity
| inverse(sk_c10) = sk_c2 ),
inference(paramod,[status(thm)],[c_1177,c_2]) ).
cnf(c_10057,plain,
( multiply(inverse(sk_c11),identity) = sk_c6
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_203,c_81]) ).
cnf(c_1845,plain,
( inverse(sk_c11) = sk_c6
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_364,c_10057]) ).
cnf(c_10058,plain,
( inverse(sk_c4) = sk_c11
| identity = sk_c10
| inverse(sk_c4) = sk_c11 ),
inference(paramod,[status(thm)],[c_669,c_5]) ).
cnf(c_2073,plain,
( identity = sk_c10
| inverse(sk_c4) = sk_c11 ),
inference(copy,[status(thm)],[c_10058]) ).
cnf(c_2086,plain,
( multiply(sk_c11,sk_c4) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2073,c_2]) ).
cnf(c_10059,plain,
( multiply(inverse(sk_c11),identity) = sk_c4
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2086,c_81]) ).
cnf(c_2123,plain,
( inverse(sk_c11) = sk_c4
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_364,c_10059]) ).
cnf(c_2161,plain,
( multiply(sk_c4,sk_c11) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2123,c_2]) ).
cnf(c_10060,plain,
( identity = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2161,c_4]) ).
cnf(c_2323,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_10060]) ).
cnf(c_10061,plain,
( multiply(sk_c11,sk_c1) = identity
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2161,c_114]) ).
cnf(c_2359,plain,
( multiply(sk_c11,sk_c1) = identity
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_10061]) ).
cnf(c_10062,plain,
( multiply(inverse(sk_c11),identity) = sk_c1
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2359,c_81]) ).
cnf(c_3029,plain,
( inverse(sk_c11) = sk_c1
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_364,c_10062]) ).
cnf(c_3053,plain,
( multiply(sk_c1,sk_c11) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_3029,c_2]) ).
cnf(c_10063,plain,
( multiply(inverse(sk_c10),identity) = sk_c5
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_148,c_81]) ).
cnf(c_3933,plain,
( inverse(sk_c10) = sk_c5
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_364,c_10063]) ).
cnf(c_10064,plain,
( identity = sk_c10
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_3053,c_2323]) ).
cnf(c_10065,plain,
( identity = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_10064]) ).
cnf(c_4976,plain,
identity = sk_c10,
inference(copy,[status(thm)],[c_10065]) ).
cnf(c_5704,plain,
( multiply(sk_c10,sk_c5) = sk_c10
| inverse(sk_c10) = sk_c2 ),
inference(paramod,[status(thm)],[c_4976,c_1183]) ).
cnf(c_10066,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(inverse(sk_c11),sk_c10) != sk_c11
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_4976,c_900]) ).
cnf(c_5863,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(inverse(sk_c11),sk_c10) != sk_c11
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(copy,[status(thm)],[c_10066]) ).
cnf(c_10067,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(A,sk_c10) != sk_c11
| sk_c10 != sk_c10
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_4976,c_660]) ).
cnf(c_6056,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| multiply(A,sk_c10) != sk_c11
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10067]) ).
cnf(c_10068,plain,
inverse(sk_c10) = identity,
inference(paramod,[status(thm)],[c_4976,c_513]) ).
cnf(c_6198,plain,
inverse(sk_c10) = sk_c10,
inference(paramod,[status(thm)],[c_4976,c_10068]) ).
cnf(c_6199,plain,
multiply(A,sk_c10) = A,
inference(paramod,[status(thm)],[c_4976,c_364]) ).
cnf(c_10069,plain,
( multiply(sk_c10,sk_c2) = identity
| sk_c5 = sk_c9 ),
inference(paramod,[status(thm)],[c_6199,c_174]) ).
cnf(c_6218,plain,
( multiply(sk_c10,sk_c2) = sk_c10
| sk_c5 = sk_c9 ),
inference(paramod,[status(thm)],[c_4976,c_10069]) ).
cnf(c_6230,plain,
multiply(inverse(A),A) = sk_c10,
inference(paramod,[status(thm)],[c_4976,c_2]) ).
cnf(c_6231,plain,
multiply(sk_c10,A) = A,
inference(paramod,[status(thm)],[c_4976,c_1]) ).
cnf(c_10070,plain,
( multiply(sk_c10,sk_c5) = sk_c10
| sk_c10 = sk_c2 ),
inference(paramod,[status(thm)],[c_6198,c_5704]) ).
cnf(c_10071,plain,
( sk_c5 = sk_c10
| sk_c10 = sk_c2 ),
inference(paramod,[status(thm)],[c_6231,c_10070]) ).
cnf(c_6245,plain,
( sk_c5 = sk_c10
| sk_c2 = sk_c10 ),
inference(copy,[status(thm)],[c_10071]) ).
cnf(c_10072,plain,
( inverse(sk_c10) = sk_c5
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_6199,c_3933]) ).
cnf(c_10073,plain,
( sk_c10 = sk_c5
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_6198,c_10072]) ).
cnf(c_6271,plain,
( sk_c5 = sk_c10
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_10073]) ).
cnf(c_10074,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| A != sk_c11
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_6199,c_6056]) ).
cnf(c_10075,plain,
( sk_c9 != sk_c10
| A != sk_c11
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_6231,c_10074]) ).
cnf(c_10076,plain,
( sk_c9 != sk_c10
| sk_c11 != A
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10075]) ).
cnf(c_6393,plain,
( sk_c11 != A
| sk_c9 != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10076]) ).
cnf(c_10077,plain,
( multiply(sk_c10,sk_c9) != sk_c10
| inverse(sk_c11) != sk_c11
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(paramod,[status(thm)],[c_6199,c_5863]) ).
cnf(c_10078,plain,
( sk_c9 != sk_c10
| inverse(sk_c11) != sk_c11
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(paramod,[status(thm)],[c_6231,c_10077]) ).
cnf(c_6544,plain,
( inverse(sk_c11) != sk_c11
| sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(copy,[status(thm)],[c_10078]) ).
cnf(c_10079,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| sk_c3 = sk_c11 ),
inference(paramod,[status(thm)],[c_6199,c_54]) ).
cnf(c_7425,plain,
( sk_c6 = sk_c11
| sk_c3 = sk_c11 ),
inference(paramod,[status(thm)],[c_6199,c_10079]) ).
cnf(c_7426,plain,
( inverse(sk_c6) = sk_c11
| sk_c3 = sk_c11 ),
inference(paramod,[status(thm)],[c_6199,c_53]) ).
cnf(c_7430,plain,
( sk_c6 = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_6199,c_45]) ).
cnf(c_10080,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_6199,c_24]) ).
cnf(c_7439,plain,
( sk_c5 = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_6199,c_10080]) ).
cnf(c_7440,plain,
( sk_c2 = sk_c10
| sk_c5 = sk_c9 ),
inference(paramod,[status(thm)],[c_6231,c_6218]) ).
cnf(c_10081,plain,
( inverse(sk_c11) = sk_c6
| sk_c11 = inverse(sk_c3) ),
inference(copy,[status(thm)],[c_1845]) ).
cnf(c_7655,plain,
( inverse(sk_c11) = sk_c6
| sk_c9 != sk_c10
| inverse(inverse(sk_c3)) != sk_c11
| multiply(inverse(sk_c3),sk_c11) != sk_c10 ),
inference(resolve,[status(thm)],[c_6393,c_10081]) ).
cnf(c_10082,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_7439,c_6271]) ).
cnf(c_7981,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_10082]) ).
cnf(c_10083,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c10
| sk_c2 = sk_c10 ),
inference(paramod,[status(thm)],[c_7440,c_6245]) ).
cnf(c_7994,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c10 ),
inference(copy,[status(thm)],[c_10083]) ).
cnf(c_10084,plain,
( sk_c9 = sk_c10
| sk_c10 = sk_c9
| sk_c9 = sk_c10 ),
inference(paramod,[status(thm)],[c_7994,c_7981]) ).
cnf(c_10085,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_10084]) ).
cnf(c_10086,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_10085]) ).
cnf(c_8409,plain,
sk_c9 = sk_c10,
inference(copy,[status(thm)],[c_10086]) ).
cnf(c_10087,plain,
( inverse(sk_c11) = sk_c6
| sk_c10 != sk_c10
| inverse(inverse(sk_c3)) != sk_c11
| multiply(inverse(sk_c3),sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_8409,c_7655]) ).
cnf(c_8709,plain,
( inverse(sk_c11) = sk_c6
| inverse(inverse(sk_c3)) != sk_c11
| multiply(inverse(sk_c3),sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_10087]) ).
cnf(c_10088,plain,
( inverse(sk_c11) != sk_c11
| sk_c10 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(paramod,[status(thm)],[c_8409,c_6544]) ).
cnf(c_9018,plain,
( inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(copy,[status(thm)],[c_10088]) ).
cnf(c_10089,plain,
( inverse(sk_c11) = sk_c11
| sk_c3 = sk_c11
| sk_c3 = sk_c11 ),
inference(paramod,[status(thm)],[c_7425,c_7426]) ).
cnf(c_9416,plain,
( inverse(sk_c11) = sk_c11
| sk_c3 = sk_c11 ),
inference(copy,[status(thm)],[c_10089]) ).
cnf(c_10090,plain,
( sk_c6 = sk_c11
| inverse(sk_c11) = sk_c11
| sk_c6 = sk_c11 ),
inference(paramod,[status(thm)],[c_7425,c_7430]) ).
cnf(c_9418,plain,
( inverse(sk_c11) = sk_c11
| sk_c6 = sk_c11 ),
inference(copy,[status(thm)],[c_10090]) ).
cnf(c_9716,plain,
( inverse(inverse(sk_c11)) != sk_c11
| sk_c3 = sk_c11 ),
inference(resolve,[status(thm)],[c_9416,c_9018]) ).
cnf(c_9806,plain,
( inverse(inverse(sk_c11)) != sk_c11
| sk_c6 = sk_c11 ),
inference(resolve,[status(thm)],[c_9418,c_9018]) ).
cnf(c_10091,plain,
multiply(A,sk_c10) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_363,c_6199]) ).
cnf(c_10092,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_6199,c_10091]) ).
cnf(c_9990,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_10092]) ).
cnf(c_10093,plain,
( sk_c11 != sk_c11
| sk_c6 = sk_c11 ),
inference(paramod,[status(thm)],[c_9990,c_9806]) ).
cnf(c_10031,plain,
sk_c6 = sk_c11,
inference(copy,[status(thm)],[c_10093]) ).
cnf(c_10094,plain,
( sk_c11 != sk_c11
| sk_c3 = sk_c11 ),
inference(paramod,[status(thm)],[c_9990,c_9716]) ).
cnf(c_10035,plain,
sk_c3 = sk_c11,
inference(copy,[status(thm)],[c_10094]) ).
cnf(c_10095,plain,
( inverse(sk_c11) != sk_c11
| sk_c11 != sk_c11 ),
inference(paramod,[status(thm)],[c_9990,c_9018]) ).
cnf(c_10044,plain,
inverse(sk_c11) != sk_c11,
inference(copy,[status(thm)],[c_10095]) ).
cnf(c_10096,plain,
( inverse(sk_c11) = sk_c6
| inverse(inverse(sk_c3)) != sk_c11
| multiply(inverse(sk_c11),sk_c11) != sk_c10 ),
inference(paramod,[status(thm)],[c_10035,c_8709]) ).
cnf(c_10097,plain,
( inverse(sk_c11) = sk_c6
| inverse(inverse(sk_c3)) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_6230,c_10096]) ).
cnf(c_10098,plain,
( inverse(sk_c11) = sk_c6
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_10035,c_10097]) ).
cnf(c_10099,plain,
( inverse(sk_c11) = sk_c6
| sk_c11 != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_9990,c_10098]) ).
cnf(c_10100,plain,
( inverse(sk_c11) = sk_c11
| sk_c11 != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_10031,c_10099]) ).
cnf(c_10101,plain,
( inverse(sk_c11) = sk_c11
| sk_c11 != sk_c11 ),
inference(copy,[status(thm)],[c_10100]) ).
cnf(c_10102,plain,
inverse(sk_c11) = sk_c11,
inference(copy,[status(thm)],[c_10101]) ).
cnf(c_10046,plain,
$false,
inference(resolve,[status(thm)],[c_10044,c_10102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP244-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 % Computer : n007.cluster.edu
% 0.19/0.41 % Model : x86_64 x86_64
% 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.41 % Memory : 8046.5625MB
% 0.19/0.41 % OS : Linux 6.8.0-71-generic
% 0.19/0.41 % CPULimit : 300
% 0.19/0.41 % WCLimit : 300
% 0.19/0.41 % DateTime : Fri Sep 25 14:38:23 UTC 2026
% 0.19/0.41 % CPUTime :
% 0.19/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.42 % Process 1235836 was started by sandbox2 on n007,
% 0.19/0.42 % Fri Sep 25 14:38:23 2026
% 0.19/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.42
% 0.19/0.42 % From the command line: assign(max_seconds, 300).
% 43.46/5.96
% 43.46/5.96 % SZS status Unsatisfiable for theBenchmark
% 43.46/5.96
% 43.46/5.96 % Proof 1 at 4.28 (+ 1.19) seconds.
% 43.46/5.96 % Length of proof is 82.
% 43.46/5.96 % Level of proof is 22.
% 43.46/5.96 % Maximum clause weight is 72.000.
% 43.46/5.96 % Given clauses 477.
% 43.46/5.96
% 43.46/5.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------