%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP297-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:28:35 AM UTC 2026
% Result : Unsatisfiable 2.40s 0.68s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 12
% Syntax : Number of formulae : 107 ( 24 unt; 0 def)
% Number of atoms : 289 ( 288 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 322 ( 140 ~; 182 |; 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 : 37 ( 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_1,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_16,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_20,axiom,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
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_c7,sk_c5) != sk_c6
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
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_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
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_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_35,plain,
( inverse(B) != A
| multiply(B,A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_39,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_35]) ).
cnf(c_1023,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1024,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1023]) ).
cnf(c_40,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1024]) ).
cnf(c_1025,plain,
( multiply(multiply(A,sk_c7),sk_c6) = multiply(A,sk_c5)
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_49,plain,
( multiply(A,multiply(sk_c7,sk_c6)) = multiply(A,sk_c5)
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_1025]) ).
cnf(c_96,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_105,plain,
( multiply(sk_c7,sk_c2) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_124,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_40]) ).
cnf(c_127,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_40]) ).
cnf(c_164,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_40]) ).
cnf(c_166,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_40]) ).
cnf(c_174,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_40,c_40]) ).
cnf(c_175,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_174,c_124]) ).
cnf(c_181,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_175,c_2]) ).
cnf(c_1026,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_96,c_40]) ).
cnf(c_250,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_175,c_1026]) ).
cnf(c_252,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_250,c_2]) ).
cnf(c_1027,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c6)) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_49]) ).
cnf(c_349,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c6)) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_1027]) ).
cnf(c_1028,plain,
( inverse(sk_c3) = sk_c4
| identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_252,c_14]) ).
cnf(c_401,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference(copy,[status(thm)],[c_1028]) ).
cnf(c_405,plain,
( multiply(sk_c4,sk_c3) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_401,c_2]) ).
cnf(c_1029,plain,
( multiply(inverse(sk_c4),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_405,c_40]) ).
cnf(c_415,plain,
( inverse(sk_c4) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_175,c_1029]) ).
cnf(c_421,plain,
( multiply(sk_c3,sk_c4) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_415,c_2]) ).
cnf(c_1030,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_421,c_13]) ).
cnf(c_446,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1030]) ).
cnf(c_1031,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_421,c_19]) ).
cnf(c_447,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1031]) ).
cnf(c_457,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_447,c_2]) ).
cnf(c_1032,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_457,c_40]) ).
cnf(c_522,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_175,c_1032]) ).
cnf(c_530,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_522,c_2]) ).
cnf(c_1033,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_530,c_446]) ).
cnf(c_1034,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1033]) ).
cnf(c_599,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_1034]) ).
cnf(c_1035,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_599,c_181]) ).
cnf(c_721,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_599,c_1035]) ).
cnf(c_722,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_599,c_175]) ).
cnf(c_724,plain,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_599,c_105]) ).
cnf(c_732,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_599,c_1]) ).
cnf(c_1036,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_722,c_127]) ).
cnf(c_1037,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_721,c_1036]) ).
cnf(c_1038,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_732,c_1037]) ).
cnf(c_1039,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_1038]) ).
cnf(c_739,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_1039]) ).
cnf(c_1040,plain,
( multiply(sk_c7,multiply(sk_c7,sk_c6)) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_722,c_349]) ).
cnf(c_747,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_722,c_1040]) ).
cnf(c_1041,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_722,c_166]) ).
cnf(c_1042,plain,
( inverse(sk_c7) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_722,c_1041]) ).
cnf(c_754,plain,
( inverse(sk_c7) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1042]) ).
cnf(c_1043,plain,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_722,c_164]) ).
cnf(c_755,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1043]) ).
cnf(c_1044,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_722,c_39]) ).
cnf(c_1045,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1044]) ).
cnf(c_1046,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1045]) ).
cnf(c_1047,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1046]) ).
cnf(c_1048,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1047]) ).
cnf(c_1049,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| sk_c7 != sk_c5
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_732,c_1048]) ).
cnf(c_1050,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != 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
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1049]) ).
cnf(c_1051,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != 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
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1050]) ).
cnf(c_1052,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
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_722,c_1051]) ).
cnf(c_1053,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
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_739,c_1052]) ).
cnf(c_1054,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(copy,[status(thm)],[c_1053]) ).
cnf(c_1055,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_1054]) ).
cnf(c_1056,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_1055]) ).
cnf(c_1057,plain,
( inverse(sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1056]) ).
cnf(c_779,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1057]) ).
cnf(c_798,plain,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_739,c_724]) ).
cnf(c_977,plain,
( inverse(sk_c7) != sk_c7
| sk_c2 = sk_c7 ),
inference(resolve,[status(thm)],[c_747,c_779]) ).
cnf(c_1058,plain,
( sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(resolve,[status(thm)],[c_977,c_754]) ).
cnf(c_979,plain,
sk_c2 = sk_c7,
inference(copy,[status(thm)],[c_1058]) ).
cnf(c_1059,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_979,c_798]) ).
cnf(c_1007,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(copy,[status(thm)],[c_1059]) ).
cnf(c_1060,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_979,c_755]) ).
cnf(c_1009,plain,
inverse(sk_c7) = sk_c7,
inference(copy,[status(thm)],[c_1060]) ).
cnf(c_1061,plain,
( inverse(sk_c7) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_1007,c_779]) ).
cnf(c_1062,plain,
( sk_c7 != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_1009,c_1061]) ).
cnf(c_1063,plain,
sk_c7 != sk_c7,
inference(copy,[status(thm)],[c_1062]) ).
cnf(c_1022,plain,
$false,
inference(copy,[status(thm)],[c_1063]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP297-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:43:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2342518 was started by sandbox on n012,
% 0.08/0.35 % Fri Sep 25 14:43:50 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.35
% 0.11/0.35 % From the command line: assign(max_seconds, 300).
% 2.40/0.68
% 2.40/0.68 % SZS status Unsatisfiable for theBenchmark
% 2.40/0.68
% 2.40/0.68 % Proof 1 at 0.25 (+ 0.07) seconds.
% 2.40/0.68 % Length of proof is 54.
% 2.40/0.68 % Level of proof is 21.
% 2.40/0.68 % Maximum clause weight is 51.000.
% 2.40/0.68 % Given clauses 136.
% 2.40/0.68
% 2.40/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------