TSTP Solution File: GRP039-2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:50:47 EDT 2024
% Result : Unsatisfiable 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 156 ( 62 unt; 0 def)
% Number of atoms : 286 ( 98 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 194 ( 64 ~; 126 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f353,plain,
$false,
inference(avatar_sat_refutation,[],[f56,f66,f71,f74,f345,f352]) ).
fof(f352,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f351]) ).
fof(f351,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(global_subsumption,[],[f10,f13,f12,f11,f1,f4,f6,f2,f16,f15,f7,f8,f14,f29,f3,f40,f42,f43,f31,f55,f28,f38,f80,f83,f9,f93,f88,f95,f98,f97,f103,f92,f106,f109,f86,f114,f117,f37,f131,f138,f133,f140,f141,f137,f151,f90,f136,f180,f169,f181,f183,f173,f175,f44,f193,f195,f197,f199,f200,f201,f202,f204,f210,f213,f215,f216,f217,f219,f220,f222,f47,f262,f270,f271,f273,f274,f303,f282,f284,f289,f290,f291,f293,f304,f301,f272,f318,f321,f280,f326,f330,f332,f333,f334,f336,f337,f339,f331,f317,f346,f347,f348,f167,f349,f30,f350,f50]) ).
fof(f50,plain,
( subgroup_member(c)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f49,plain,
( spl0_1
<=> subgroup_member(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f350,plain,
( ~ subgroup_member(inverse(a))
| spl0_2 ),
inference(global_subsumption,[],[f10,f13,f12,f11,f1,f4,f6,f2,f16,f15,f7,f8,f14,f29,f3,f40,f42,f43,f31,f55,f28,f38,f80,f83,f9,f93,f88,f95,f98,f97,f103,f92,f106,f109,f86,f114,f117,f37,f131,f138,f133,f140,f141,f137,f151,f90,f136,f180,f169,f181,f183,f173,f175,f44,f193,f195,f197,f199,f200,f201,f202,f204,f210,f213,f215,f216,f217,f219,f220,f222,f47,f262,f270,f271,f273,f274,f303,f282,f284,f289,f290,f291,f293,f304,f301,f272,f318,f321,f280,f326,f330,f332,f333,f334,f336,f337,f339,f331,f317,f346,f347,f348,f167,f349,f30]) ).
fof(f30,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(subsumption_resolution,[],[f26,f10]) ).
fof(f26,plain,
( subgroup_member(c)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(a)) ),
inference(superposition,[],[f14,f11]) ).
fof(f349,plain,
( ~ subgroup_member(inverse(a))
| spl0_2 ),
inference(global_subsumption,[],[f10,f13,f12,f11,f1,f4,f6,f2,f16,f15,f7,f8,f14,f29,f30,f3,f40,f42,f43,f31,f55,f28,f38,f80,f83,f9,f93,f88,f95,f98,f97,f103,f92,f106,f109,f86,f114,f117,f37,f131,f138,f133,f140,f141,f137,f151,f90,f136,f180,f169,f181,f183,f173,f175,f44,f193,f195,f197,f199,f200,f201,f202,f204,f210,f213,f215,f216,f217,f219,f220,f222,f47,f262,f270,f271,f273,f274,f303,f282,f284,f289,f290,f291,f293,f304,f301,f272,f318,f321,f280,f326,f330,f332,f333,f334,f336,f337,f339,f331,f317,f346,f347,f348,f167]) ).
fof(f167,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(X0) ),
inference(resolution,[],[f136,f14]) ).
fof(f348,plain,
( ~ subgroup_member(inverse(a))
| spl0_2 ),
inference(global_subsumption,[],[f10,f13,f12,f11,f1,f4,f6,f2,f16,f15,f7,f8,f14,f29,f30,f3,f40,f42,f43,f31,f55,f28,f38,f80,f83,f9,f93,f88,f95,f98,f97,f103,f92,f106,f109,f86,f114,f117,f37,f131,f138,f133,f140,f141,f137,f151,f90,f136,f180,f169,f181,f183,f173,f175,f44,f193,f195,f197,f199,f200,f201,f202,f204,f210,f213,f215,f216,f217,f219,f220,f222,f47,f262,f270,f271,f273,f274,f303,f282,f284,f289,f290,f291,f293,f304,f301,f272,f318,f321,f280,f326,f330,f332,f333,f334,f336,f337,f339,f331,f317,f346,f347]) ).
fof(f347,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_demodulation,[],[f178,f6]) ).
fof(f178,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(multiply(c,identity)) ),
inference(superposition,[],[f136,f6]) ).
fof(f346,plain,
( ~ subgroup_member(c)
| spl0_2 ),
inference(global_subsumption,[],[f10,f13,f12,f11,f1,f4,f6,f2,f16,f15,f7,f8,f14,f29,f30,f3,f40,f42,f43,f31,f55,f28,f38,f80,f83,f9,f93,f88,f95,f98,f97,f103,f92,f106,f109,f86,f114,f117,f37,f131,f138,f133,f140,f141,f137,f151,f90,f136,f180,f169,f181,f183,f173,f175,f44,f193,f195,f197,f199,f200,f201,f202,f204,f210,f213,f215,f216,f217,f219,f220,f222,f47,f262,f270,f271,f273,f274,f303,f282,f284,f289,f290,f291,f293,f304,f301,f272,f318,f321,f280,f326,f330,f332,f333,f334,f336,f337,f339,f331,f317]) ).
fof(f317,plain,
( ~ subgroup_member(c)
| subgroup_member(multiply(c,d)) ),
inference(superposition,[],[f136,f272]) ).
fof(f331,plain,
( ~ subgroup_member(c)
| spl0_2 ),
inference(resolution,[],[f330,f4]) ).
fof(f339,plain,
( inverse(c) = multiply(d,element_in_O2(d,inverse(c)))
| spl0_2 ),
inference(resolution,[],[f330,f92]) ).
fof(f337,plain,
( inverse(c) = multiply(a,element_in_O2(a,inverse(c)))
| spl0_2 ),
inference(resolution,[],[f330,f90]) ).
fof(f336,plain,
( d = multiply(inverse(c),element_in_O2(inverse(c),d))
| spl0_2 ),
inference(resolution,[],[f330,f88]) ).
fof(f334,plain,
( a = multiply(inverse(c),element_in_O2(inverse(c),a))
| spl0_2 ),
inference(resolution,[],[f330,f86]) ).
fof(f333,plain,
( ! [X0] :
( subgroup_member(X0)
| inverse(c) = multiply(X0,element_in_O2(X0,inverse(c))) )
| spl0_2 ),
inference(resolution,[],[f330,f9]) ).
fof(f332,plain,
( ! [X0] :
( subgroup_member(X0)
| multiply(inverse(c),element_in_O2(inverse(c),X0)) = X0 )
| spl0_2 ),
inference(resolution,[],[f330,f9]) ).
fof(f330,plain,
( ~ subgroup_member(inverse(c))
| spl0_2 ),
inference(subsumption_resolution,[],[f329,f10]) ).
fof(f329,plain,
( ~ subgroup_member(inverse(c))
| ~ subgroup_member(b)
| spl0_2 ),
inference(subsumption_resolution,[],[f327,f55]) ).
fof(f327,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(b) ),
inference(superposition,[],[f14,f280]) ).
fof(f326,plain,
! [X0] : multiply(a,X0) = multiply(inverse(c),multiply(b,X0)),
inference(superposition,[],[f3,f280]) ).
fof(f280,plain,
a = multiply(inverse(c),b),
inference(superposition,[],[f47,f131]) ).
fof(f321,plain,
! [X0] : multiply(c,X0) = multiply(inverse(a),multiply(d,X0)),
inference(superposition,[],[f3,f272]) ).
fof(f318,plain,
multiply(b,c) = multiply(c,d),
inference(superposition,[],[f37,f272]) ).
fof(f272,plain,
c = multiply(inverse(a),d),
inference(superposition,[],[f47,f12]) ).
fof(f301,plain,
( identity = element_in_O2(a,a)
| spl0_2 ),
inference(forward_demodulation,[],[f275,f2]) ).
fof(f275,plain,
( element_in_O2(a,a) = multiply(inverse(a),a)
| spl0_2 ),
inference(superposition,[],[f47,f114]) ).
fof(f304,plain,
identity = element_in_O2(d,d),
inference(forward_demodulation,[],[f286,f2]) ).
fof(f286,plain,
element_in_O2(d,d) = multiply(inverse(d),d),
inference(superposition,[],[f47,f97]) ).
fof(f293,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[],[f14,f47]) ).
fof(f291,plain,
! [X0] : multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(superposition,[],[f37,f47]) ).
fof(f290,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(multiply(c,multiply(a,X0))) ),
inference(superposition,[],[f136,f47]) ).
fof(f289,plain,
a = multiply(inverse(d),multiply(a,b)),
inference(superposition,[],[f47,f137]) ).
fof(f284,plain,
( element_in_O2(d,a) = multiply(inverse(d),a)
| spl0_2 ),
inference(superposition,[],[f47,f106]) ).
fof(f282,plain,
inverse(c) = multiply(inverse(d),a),
inference(superposition,[],[f47,f80]) ).
fof(f303,plain,
a = multiply(inverse(c),b),
inference(forward_demodulation,[],[f281,f204]) ).
fof(f281,plain,
inverse(inverse(a)) = multiply(inverse(c),b),
inference(superposition,[],[f47,f133]) ).
fof(f274,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_2 ),
inference(superposition,[],[f47,f95]) ).
fof(f273,plain,
! [X0] : multiply(c,X0) = multiply(inverse(a),multiply(d,X0)),
inference(superposition,[],[f47,f38]) ).
fof(f271,plain,
! [X0] : multiply(inverse(a),X0) = multiply(inverse(b),multiply(c,X0)),
inference(superposition,[],[f47,f37]) ).
fof(f270,plain,
inverse(a) = multiply(inverse(b),c),
inference(superposition,[],[f47,f11]) ).
fof(f262,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f47,f3]) ).
fof(f47,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f36,f1]) ).
fof(f36,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f3,f2]) ).
fof(f222,plain,
! [X0] :
( subgroup_member(X0)
| inverse(X0) = multiply(d,element_in_O2(d,inverse(X0))) ),
inference(resolution,[],[f213,f92]) ).
fof(f220,plain,
( ! [X0] :
( subgroup_member(X0)
| inverse(X0) = multiply(a,element_in_O2(a,inverse(X0))) )
| spl0_2 ),
inference(resolution,[],[f213,f90]) ).
fof(f219,plain,
! [X0] :
( subgroup_member(X0)
| d = multiply(inverse(X0),element_in_O2(inverse(X0),d)) ),
inference(resolution,[],[f213,f88]) ).
fof(f217,plain,
( ! [X0] :
( subgroup_member(X0)
| a = multiply(inverse(X0),element_in_O2(inverse(X0),a)) )
| spl0_2 ),
inference(resolution,[],[f213,f86]) ).
fof(f216,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| inverse(X0) = multiply(X1,element_in_O2(X1,inverse(X0))) ),
inference(resolution,[],[f213,f9]) ).
fof(f215,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| multiply(inverse(X0),element_in_O2(inverse(X0),X1)) = X1 ),
inference(resolution,[],[f213,f9]) ).
fof(f213,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(superposition,[],[f4,f204]) ).
fof(f210,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[],[f44,f204]) ).
fof(f204,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f192,f6]) ).
fof(f192,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[],[f44,f7]) ).
fof(f202,plain,
! [X0] : multiply(d,multiply(inverse(c),X0)) = multiply(a,X0),
inference(superposition,[],[f38,f44]) ).
fof(f201,plain,
! [X0] : multiply(b,X0) = multiply(c,multiply(inverse(inverse(a)),X0)),
inference(superposition,[],[f37,f44]) ).
fof(f200,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(multiply(c,multiply(inverse(inverse(a)),X0))) ),
inference(superposition,[],[f136,f44]) ).
fof(f199,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[],[f3,f44]) ).
fof(f197,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ subgroup_member(multiply(inverse(X0),X1)) ),
inference(superposition,[],[f14,f44]) ).
fof(f195,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[],[f44,f3]) ).
fof(f193,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[],[f44,f44]) ).
fof(f44,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f33,f1]) ).
fof(f33,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f3,f7]) ).
fof(f175,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| multiply(inverse(a),X0) = multiply(d,element_in_O2(d,multiply(inverse(a),X0))) ),
inference(resolution,[],[f136,f92]) ).
fof(f173,plain,
( ! [X0] :
( subgroup_member(multiply(c,X0))
| multiply(inverse(a),X0) = multiply(a,element_in_O2(a,multiply(inverse(a),X0))) )
| spl0_2 ),
inference(resolution,[],[f136,f90]) ).
fof(f183,plain,
! [X0] :
( d = multiply(inverse(a),multiply(X0,element_in_O2(multiply(inverse(a),X0),d)))
| subgroup_member(multiply(c,X0)) ),
inference(forward_demodulation,[],[f172,f3]) ).
fof(f172,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| d = multiply(multiply(inverse(a),X0),element_in_O2(multiply(inverse(a),X0),d)) ),
inference(resolution,[],[f136,f88]) ).
fof(f181,plain,
( ! [X0] :
( a = multiply(inverse(a),multiply(X0,element_in_O2(multiply(inverse(a),X0),a)))
| subgroup_member(multiply(c,X0)) )
| spl0_2 ),
inference(forward_demodulation,[],[f170,f3]) ).
fof(f170,plain,
( ! [X0] :
( subgroup_member(multiply(c,X0))
| a = multiply(multiply(inverse(a),X0),element_in_O2(multiply(inverse(a),X0),a)) )
| spl0_2 ),
inference(resolution,[],[f136,f86]) ).
fof(f169,plain,
! [X0,X1] :
( subgroup_member(multiply(c,X0))
| subgroup_member(X1)
| multiply(inverse(a),X0) = multiply(X1,element_in_O2(X1,multiply(inverse(a),X0))) ),
inference(resolution,[],[f136,f9]) ).
fof(f180,plain,
! [X0,X1] :
( multiply(inverse(a),multiply(X0,element_in_O2(multiply(inverse(a),X0),X1))) = X1
| subgroup_member(multiply(c,X0))
| subgroup_member(X1) ),
inference(forward_demodulation,[],[f168,f3]) ).
fof(f168,plain,
! [X0,X1] :
( subgroup_member(multiply(c,X0))
| subgroup_member(X1)
| multiply(multiply(inverse(a),X0),element_in_O2(multiply(inverse(a),X0),X1)) = X1 ),
inference(resolution,[],[f136,f9]) ).
fof(f136,plain,
! [X0] :
( ~ subgroup_member(multiply(inverse(a),X0))
| subgroup_member(multiply(c,X0)) ),
inference(subsumption_resolution,[],[f130,f10]) ).
fof(f130,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| ~ subgroup_member(b)
| ~ subgroup_member(multiply(inverse(a),X0)) ),
inference(superposition,[],[f14,f37]) ).
fof(f90,plain,
( ! [X0] :
( subgroup_member(X0)
| multiply(a,element_in_O2(a,X0)) = X0 )
| spl0_2 ),
inference(resolution,[],[f9,f55]) ).
fof(f151,plain,
! [X0] : multiply(d,multiply(a,X0)) = multiply(a,multiply(b,X0)),
inference(forward_demodulation,[],[f149,f3]) ).
fof(f149,plain,
! [X0] : multiply(d,multiply(a,X0)) = multiply(multiply(a,b),X0),
inference(superposition,[],[f3,f137]) ).
fof(f137,plain,
multiply(d,a) = multiply(a,b),
inference(superposition,[],[f38,f131]) ).
fof(f141,plain,
! [X0] : multiply(b,X0) = multiply(c,multiply(inverse(inverse(a)),X0)),
inference(superposition,[],[f3,f133]) ).
fof(f140,plain,
multiply(a,b) = multiply(d,inverse(inverse(a))),
inference(superposition,[],[f38,f133]) ).
fof(f133,plain,
b = multiply(c,inverse(inverse(a))),
inference(forward_demodulation,[],[f128,f6]) ).
fof(f128,plain,
multiply(b,identity) = multiply(c,inverse(inverse(a))),
inference(superposition,[],[f37,f7]) ).
fof(f138,plain,
! [X0] : multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(superposition,[],[f3,f131]) ).
fof(f131,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f126,f6]) ).
fof(f126,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[],[f37,f2]) ).
fof(f37,plain,
! [X0] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[],[f3,f11]) ).
fof(f117,plain,
( ! [X0] : multiply(a,X0) = multiply(a,multiply(element_in_O2(a,a),X0))
| spl0_2 ),
inference(superposition,[],[f3,f114]) ).
fof(f114,plain,
( a = multiply(a,element_in_O2(a,a))
| spl0_2 ),
inference(resolution,[],[f86,f55]) ).
fof(f86,plain,
( ! [X0] :
( subgroup_member(X0)
| a = multiply(X0,element_in_O2(X0,a)) )
| spl0_2 ),
inference(resolution,[],[f9,f55]) ).
fof(f109,plain,
( ! [X0] : multiply(a,X0) = multiply(d,multiply(element_in_O2(d,a),X0))
| spl0_2 ),
inference(superposition,[],[f3,f106]) ).
fof(f106,plain,
( a = multiply(d,element_in_O2(d,a))
| spl0_2 ),
inference(resolution,[],[f92,f55]) ).
fof(f92,plain,
! [X0] :
( subgroup_member(X0)
| multiply(d,element_in_O2(d,X0)) = X0 ),
inference(resolution,[],[f9,f13]) ).
fof(f103,plain,
! [X0] : multiply(d,X0) = multiply(d,multiply(element_in_O2(d,d),X0)),
inference(superposition,[],[f3,f97]) ).
fof(f97,plain,
d = multiply(d,element_in_O2(d,d)),
inference(resolution,[],[f88,f13]) ).
fof(f98,plain,
( ! [X0] : multiply(d,X0) = multiply(a,multiply(element_in_O2(a,d),X0))
| spl0_2 ),
inference(superposition,[],[f3,f95]) ).
fof(f95,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_2 ),
inference(resolution,[],[f88,f55]) ).
fof(f88,plain,
! [X0] :
( subgroup_member(X0)
| d = multiply(X0,element_in_O2(X0,d)) ),
inference(resolution,[],[f9,f13]) ).
fof(f93,plain,
! [X0] :
( subgroup_member(X0)
| multiply(X0,element_in_O2(X0,X0)) = X0 ),
inference(factoring,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( subgroup_member(X1)
| subgroup_member(X0)
| multiply(X0,element_in_O2(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f83,plain,
! [X0] : multiply(d,multiply(inverse(c),X0)) = multiply(a,X0),
inference(superposition,[],[f3,f80]) ).
fof(f80,plain,
a = multiply(d,inverse(c)),
inference(forward_demodulation,[],[f76,f6]) ).
fof(f76,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(superposition,[],[f38,f7]) ).
fof(f38,plain,
! [X0] : multiply(a,multiply(c,X0)) = multiply(d,X0),
inference(superposition,[],[f3,f12]) ).
fof(f28,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(subsumption_resolution,[],[f23,f4]) ).
fof(f23,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(superposition,[],[f14,f7]) ).
fof(f55,plain,
( ~ subgroup_member(a)
| spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl0_2
<=> subgroup_member(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f31,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(subsumption_resolution,[],[f27,f13]) ).
fof(f27,plain,
( subgroup_member(d)
| ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(superposition,[],[f14,f12]) ).
fof(f43,plain,
! [X2,X0,X1] :
( subgroup_member(multiply(X0,multiply(X1,X2)))
| ~ subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X2) ),
inference(superposition,[],[f14,f3]) ).
fof(f42,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f7,f3]) ).
fof(f40,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f3,f7]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f29,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0) ),
inference(subsumption_resolution,[],[f25,f4]) ).
fof(f25,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(superposition,[],[f14,f2]) ).
fof(f14,plain,
! [X0,X1] :
( subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X0)
| ~ subgroup_member(X1) ),
inference(equality_resolution,[],[f5]) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ subgroup_member(X1)
| ~ subgroup_member(X0)
| subgroup_member(X2)
| multiply(X0,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiply) ).
fof(f8,axiom,
! [X0,X1] :
( subgroup_member(element_in_O2(X0,X1))
| subgroup_member(X1)
| subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f7,axiom,
! [X0] : identity = multiply(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f15,plain,
identity = inverse(identity),
inference(superposition,[],[f2,f6]) ).
fof(f16,plain,
identity = inverse(identity),
inference(superposition,[],[f6,f2]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f6,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f4,axiom,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f11,axiom,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f12,axiom,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f13,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f10,axiom,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).
fof(f345,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f344]) ).
fof(f344,plain,
( $false
| spl0_1 ),
inference(subsumption_resolution,[],[f343,f57]) ).
fof(f57,plain,
( ~ subgroup_member(inverse(a))
| spl0_1 ),
inference(subsumption_resolution,[],[f30,f51]) ).
fof(f51,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f343,plain,
( subgroup_member(inverse(a))
| spl0_1 ),
inference(subsumption_resolution,[],[f342,f51]) ).
fof(f342,plain,
( subgroup_member(c)
| subgroup_member(inverse(a))
| spl0_1 ),
inference(subsumption_resolution,[],[f341,f13]) ).
fof(f341,plain,
( subgroup_member(d)
| subgroup_member(c)
| subgroup_member(inverse(a))
| spl0_1 ),
inference(superposition,[],[f8,f256]) ).
fof(f256,plain,
( d = element_in_O2(inverse(a),c)
| spl0_1 ),
inference(forward_demodulation,[],[f253,f12]) ).
fof(f253,plain,
( multiply(a,c) = element_in_O2(inverse(a),c)
| spl0_1 ),
inference(superposition,[],[f44,f122]) ).
fof(f122,plain,
( c = multiply(inverse(a),element_in_O2(inverse(a),c))
| spl0_1 ),
inference(resolution,[],[f87,f57]) ).
fof(f87,plain,
( ! [X0] :
( subgroup_member(X0)
| c = multiply(X0,element_in_O2(X0,c)) )
| spl0_1 ),
inference(resolution,[],[f9,f51]) ).
fof(f74,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f73]) ).
fof(f73,plain,
( $false
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f72,f61]) ).
fof(f61,plain,
( ! [X0] : ~ subgroup_member(X0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f60,plain,
( spl0_3
<=> ! [X0] : ~ subgroup_member(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f72,plain,
( ! [X1] : subgroup_member(X1)
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f69,f61]) ).
fof(f69,plain,
( ! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1) )
| ~ spl0_3 ),
inference(resolution,[],[f61,f8]) ).
fof(f71,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f70]) ).
fof(f70,plain,
( $false
| ~ spl0_3 ),
inference(resolution,[],[f61,f10]) ).
fof(f66,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f28,f63,f60]) ).
fof(f63,plain,
( spl0_4
<=> subgroup_member(identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f56,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f31,f53,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 04:28:56 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (15936)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (15939)WARNING: value z3 for option sas not known
% 0.15/0.37 % (15938)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (15940)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (15937)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (15939)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37 % (15941)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.37 % (15943)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.37 % (15942)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [4]
% 0.15/0.38 TRYING [3]
% 0.22/0.39 % (15939)First to succeed.
% 0.22/0.39 TRYING [5]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 % (15942)Also succeeded, but the first one will report.
% 0.22/0.39 TRYING [3]
% 0.22/0.39 % (15939)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (15939)------------------------------
% 0.22/0.39 % (15939)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.39 % (15939)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (15939)Memory used [KB]: 958
% 0.22/0.39 % (15939)Time elapsed: 0.016 s
% 0.22/0.39 % (15939)Instructions burned: 22 (million)
% 0.22/0.39 % (15939)------------------------------
% 0.22/0.39 % (15939)------------------------------
% 0.22/0.39 % (15936)Success in time 0.032 s
%------------------------------------------------------------------------------