%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP277-1 : 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 : n011.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 07:28:32 AM UTC 2026
% Result : Unsatisfiable 5.67s 1.21s
% Output : CNFRefutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 13
% Syntax : Number of formulae : 117 ( 25 unt; 0 def)
% Number of atoms : 294 ( 293 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 292 ( 115 ~; 177 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 9 !; 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_2,axiom,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_19,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(VAR_3,sk_c7) != sk_c6
| inverse(VAR_2) != VAR_3
| multiply(VAR_2,VAR_3) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| inverse(VAR_1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(D,sk_c7) != sk_c6
| inverse(C) != D
| multiply(C,D) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
cnf(c_30,plain,
( inverse(C) != A
| multiply(C,A) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_37,plain,
( inverse(B) != A
| multiply(B,A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_1166,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_37]) ).
cnf(c_45,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1166]) ).
cnf(c_1167,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1168,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1167]) ).
cnf(c_47,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1168]) ).
cnf(c_1169,plain,
( multiply(sk_c6,A) = multiply(sk_c1,multiply(sk_c7,A))
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_53,plain,
( multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c6,A)
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_1169]) ).
cnf(c_1170,plain,
( multiply(sk_c6,A) = multiply(sk_c1,multiply(sk_c7,A))
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_55,plain,
( multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c6,A)
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_1170]) ).
cnf(c_81,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_131,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_47]) ).
cnf(c_138,plain,
( multiply(inverse(sk_c2),sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_47]) ).
cnf(c_159,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_47]) ).
cnf(c_161,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_47]) ).
cnf(c_170,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_47]) ).
cnf(c_181,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_47,c_47]) ).
cnf(c_182,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_181,c_131]) ).
cnf(c_189,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_182,c_2]) ).
cnf(c_1171,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_81,c_47]) ).
cnf(c_259,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_182,c_1171]) ).
cnf(c_262,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_259,c_2]) ).
cnf(c_1172,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c5)
| inverse(sk_c2) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_53]) ).
cnf(c_315,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c5)
| inverse(sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_1172]) ).
cnf(c_1173,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_55]) ).
cnf(c_354,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_1173]) ).
cnf(c_1174,plain,
( inverse(sk_c3) = sk_c4
| identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_262,c_8]) ).
cnf(c_416,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference(copy,[status(thm)],[c_1174]) ).
cnf(c_422,plain,
( multiply(sk_c4,sk_c3) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_416,c_2]) ).
cnf(c_1175,plain,
( multiply(inverse(sk_c4),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_422,c_47]) ).
cnf(c_432,plain,
( inverse(sk_c4) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_182,c_1175]) ).
cnf(c_438,plain,
( multiply(sk_c3,sk_c4) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_432,c_2]) ).
cnf(c_1176,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_438,c_7]) ).
cnf(c_465,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1176]) ).
cnf(c_1177,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_438,c_13]) ).
cnf(c_466,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1177]) ).
cnf(c_477,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_466,c_2]) ).
cnf(c_1178,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_477,c_47]) ).
cnf(c_546,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_182,c_1178]) ).
cnf(c_557,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_546,c_2]) ).
cnf(c_1179,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_557,c_465]) ).
cnf(c_1180,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1179]) ).
cnf(c_627,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_1180]) ).
cnf(c_1181,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_627,c_189]) ).
cnf(c_741,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_627,c_1181]) ).
cnf(c_742,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_627,c_182]) ).
cnf(c_751,plain,
multiply(inverse(A),A) = sk_c6,
inference(paramod,[status(thm)],[c_627,c_2]) ).
cnf(c_752,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_627,c_1]) ).
cnf(c_1182,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_742,c_170]) ).
cnf(c_1183,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_741,c_1182]) ).
cnf(c_1184,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_752,c_1183]) ).
cnf(c_757,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_1184]) ).
cnf(c_1185,plain,
( multiply(sk_c1,sk_c6) = multiply(sk_c6,sk_c5)
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_742,c_354]) ).
cnf(c_1186,plain,
( sk_c1 = multiply(sk_c6,sk_c5)
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_742,c_1185]) ).
cnf(c_1187,plain,
( sk_c1 = multiply(sk_c6,sk_c7)
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_757,c_1186]) ).
cnf(c_798,plain,
( sk_c1 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_752,c_1187]) ).
cnf(c_1188,plain,
( sk_c1 = multiply(sk_c6,sk_c5)
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_742,c_315]) ).
cnf(c_1189,plain,
( sk_c1 = multiply(sk_c6,sk_c7)
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_757,c_1188]) ).
cnf(c_802,plain,
( sk_c1 = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_752,c_1189]) ).
cnf(c_1190,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_742,c_161]) ).
cnf(c_1191,plain,
( inverse(sk_c7) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_742,c_1190]) ).
cnf(c_808,plain,
( inverse(sk_c7) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_757,c_1191]) ).
cnf(c_1192,plain,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_742,c_159]) ).
cnf(c_809,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_757,c_1192]) ).
cnf(c_1193,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_757,c_45]) ).
cnf(c_1194,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_757,c_1193]) ).
cnf(c_1195,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_757,c_1194]) ).
cnf(c_1196,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_757,c_1195]) ).
cnf(c_1197,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_742,c_1196]) ).
cnf(c_1198,plain,
( inverse(sk_c7) != sk_c5
| sk_c7 != sk_c5
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_752,c_1197]) ).
cnf(c_1199,plain,
( inverse(sk_c7) != sk_c5
| sk_c7 != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_757,c_1198]) ).
cnf(c_1200,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_757,c_1199]) ).
cnf(c_1201,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1200]) ).
cnf(c_1202,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1201]) ).
cnf(c_1203,plain,
( inverse(sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1202]) ).
cnf(c_832,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1203]) ).
cnf(c_1204,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_138]) ).
cnf(c_953,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_1204]) ).
cnf(c_1205,plain,
( sk_c1 = sk_c7
| inverse(sk_c7) = sk_c7
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_798,c_802]) ).
cnf(c_991,plain,
( inverse(sk_c7) = sk_c7
| sk_c1 = sk_c7 ),
inference(copy,[status(thm)],[c_1205]) ).
cnf(c_1058,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_991,c_751]) ).
cnf(c_1206,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c7) = sk_c7
| inverse(sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_808,c_809]) ).
cnf(c_1207,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c7) = sk_c7 ),
inference(copy,[status(thm)],[c_1206]) ).
cnf(c_1153,plain,
inverse(sk_c7) = sk_c7,
inference(copy,[status(thm)],[c_1207]) ).
cnf(c_1208,plain,
( sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1153,c_832]) ).
cnf(c_1160,plain,
multiply(sk_c7,sk_c7) != sk_c6,
inference(copy,[status(thm)],[c_1208]) ).
cnf(c_1164,plain,
sk_c1 = sk_c7,
inference(resolve,[status(thm)],[c_1160,c_1058]) ).
cnf(c_1209,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1164,c_953]) ).
cnf(c_1210,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(copy,[status(thm)],[c_1209]) ).
cnf(c_1165,plain,
$false,
inference(resolve,[status(thm)],[c_1160,c_1210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP277-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:42:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2248891 was started by sandbox2 on n011,
% 0.10/0.37 % Fri Sep 25 14:42:43 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 5.67/1.21
% 5.67/1.21 % SZS status Unsatisfiable for theBenchmark
% 5.67/1.21
% 5.67/1.21 % Proof 1 at 0.56 (+ 0.22) seconds.
% 5.67/1.21 % Length of proof is 59.
% 5.67/1.21 % Level of proof is 21.
% 5.67/1.21 % Maximum clause weight is 51.000.
% 5.67/1.21 % Given clauses 156.
% 5.67/1.21
% 5.67/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------