TSTP Solution File: GRP039-7 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 11:50:59 EDT 2024
% Result : Unsatisfiable 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 190 ( 62 unt; 0 def)
% Number of atoms : 374 ( 122 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 255 ( 71 ~; 180 |; 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 : 117 ( 117 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f328,plain,
$false,
inference(avatar_sat_refutation,[],[f48,f180,f188,f312,f316,f319,f323,f325,f327]) ).
fof(f327,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f326,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3 ),
inference(global_subsumption,[],[f42,f13,f16,f10,f15,f9,f14,f1,f4,f6,f8,f20,f2,f25,f7,f11,f17,f39,f3,f59,f61,f62,f57,f72,f75,f56,f85,f12,f89,f94,f96,f82,f101,f100,f105,f93,f106,f108,f111,f110,f116,f98,f118,f120,f123,f88,f128,f135,f136,f131,f63,f143,f149,f151,f153,f163,f156,f162,f165,f166,f174,f91,f195,f190,f192,f197,f66,f222,f226,f228,f229,f237,f239,f242,f244,f250,f248,f227,f265,f232,f270,f274,f277,f278,f279,f280,f281,f225,f284,f236,f289,f262,f293,f294,f297,f99,f306,f300,f302,f307,f290,f317,f70,f285,f320,f321,f127,f38,f308,f275,f47]) ).
fof(f47,plain,
( ~ subgroup_member(a)
| spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f45,plain,
( spl0_2
<=> subgroup_member(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f275,plain,
( ~ subgroup_member(c)
| spl0_2 ),
inference(resolution,[],[f274,f4]) ).
fof(f308,plain,
( subgroup_member(c)
| spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f174,f307]) ).
fof(f38,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(subsumption_resolution,[],[f36,f13]) ).
fof(f36,plain,
( subgroup_member(c)
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(a)) ),
inference(superposition,[],[f17,f14]) ).
fof(f127,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(X0) ),
inference(resolution,[],[f88,f17]) ).
fof(f321,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_demodulation,[],[f133,f6]) ).
fof(f133,plain,
( ~ subgroup_member(inverse(a))
| subgroup_member(multiply(c,identity)) ),
inference(superposition,[],[f88,f6]) ).
fof(f320,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a)) ),
inference(forward_demodulation,[],[f168,f6]) ).
fof(f168,plain,
( subgroup_member(multiply(c,identity))
| ~ subgroup_member(inverse(a)) ),
inference(superposition,[],[f162,f7]) ).
fof(f285,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(c) ),
inference(superposition,[],[f17,f225]) ).
fof(f70,plain,
! [X0] :
( subgroup_member(multiply(d,X0))
| ~ subgroup_member(a)
| ~ subgroup_member(multiply(c,X0)) ),
inference(superposition,[],[f17,f57]) ).
fof(f317,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c)) ),
inference(subsumption_resolution,[],[f271,f13]) ).
fof(f271,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(b) ),
inference(superposition,[],[f17,f232]) ).
fof(f290,plain,
( subgroup_member(inverse(c))
| ~ subgroup_member(inverse(d))
| ~ subgroup_member(a) ),
inference(superposition,[],[f17,f236]) ).
fof(f307,plain,
( c = element_in_O2(a,d)
| spl0_2 ),
inference(forward_demodulation,[],[f229,f227]) ).
fof(f302,plain,
( inverse(c) = multiply(inverse(c),element_in_O2(inverse(c),inverse(c)))
| spl0_2 ),
inference(resolution,[],[f99,f274]) ).
fof(f300,plain,
! [X0] :
( inverse(X0) = multiply(inverse(X0),element_in_O2(inverse(X0),inverse(X0)))
| subgroup_member(X0) ),
inference(resolution,[],[f99,f20]) ).
fof(f306,plain,
! [X0] :
( multiply(inverse(a),X0) = multiply(inverse(a),multiply(X0,element_in_O2(multiply(inverse(a),X0),multiply(inverse(a),X0))))
| subgroup_member(multiply(c,X0)) ),
inference(forward_demodulation,[],[f299,f3]) ).
fof(f299,plain,
! [X0] :
( multiply(inverse(a),X0) = multiply(multiply(inverse(a),X0),element_in_O2(multiply(inverse(a),X0),multiply(inverse(a),X0)))
| subgroup_member(multiply(c,X0)) ),
inference(resolution,[],[f99,f88]) ).
fof(f99,plain,
! [X0] :
( subgroup_member(X0)
| multiply(X0,element_in_O2(X0,X0)) = X0 ),
inference(factoring,[],[f12]) ).
fof(f297,plain,
! [X0] : multiply(c,multiply(d,X0)) = multiply(b,multiply(c,X0)),
inference(forward_demodulation,[],[f295,f3]) ).
fof(f295,plain,
! [X0] : multiply(c,multiply(d,X0)) = multiply(multiply(b,c),X0),
inference(superposition,[],[f3,f262]) ).
fof(f294,plain,
d = multiply(inverse(c),multiply(b,c)),
inference(superposition,[],[f66,f262]) ).
fof(f293,plain,
multiply(d,d) = multiply(a,multiply(b,c)),
inference(superposition,[],[f57,f262]) ).
fof(f262,plain,
multiply(c,d) = multiply(b,c),
inference(superposition,[],[f56,f227]) ).
fof(f289,plain,
! [X0] : multiply(inverse(c),X0) = multiply(inverse(d),multiply(a,X0)),
inference(superposition,[],[f3,f236]) ).
fof(f236,plain,
inverse(c) = multiply(inverse(d),a),
inference(superposition,[],[f66,f72]) ).
fof(f284,plain,
! [X0] : multiply(inverse(a),X0) = multiply(inverse(b),multiply(c,X0)),
inference(superposition,[],[f3,f225]) ).
fof(f225,plain,
inverse(a) = multiply(inverse(b),c),
inference(superposition,[],[f66,f14]) ).
fof(f281,plain,
( ! [X0] :
( subgroup_member(X0)
| inverse(c) = multiply(X0,element_in_O2(X0,inverse(c))) )
| spl0_2 ),
inference(resolution,[],[f274,f12]) ).
fof(f280,plain,
( ! [X0] :
( subgroup_member(X0)
| multiply(inverse(c),element_in_O2(inverse(c),X0)) = X0 )
| spl0_2 ),
inference(resolution,[],[f274,f12]) ).
fof(f279,plain,
( d = multiply(inverse(c),element_in_O2(inverse(c),d))
| spl0_2 ),
inference(resolution,[],[f274,f93]) ).
fof(f278,plain,
( inverse(c) = multiply(d,element_in_O2(d,inverse(c)))
| spl0_2 ),
inference(resolution,[],[f274,f98]) ).
fof(f277,plain,
( a = multiply(inverse(c),element_in_O2(inverse(c),a))
| spl0_2 ),
inference(resolution,[],[f274,f91]) ).
fof(f274,plain,
( ~ subgroup_member(inverse(c))
| spl0_2 ),
inference(subsumption_resolution,[],[f273,f13]) ).
fof(f273,plain,
( ~ subgroup_member(inverse(c))
| ~ subgroup_member(b)
| spl0_2 ),
inference(subsumption_resolution,[],[f271,f47]) ).
fof(f270,plain,
! [X0] : multiply(a,X0) = multiply(inverse(c),multiply(b,X0)),
inference(superposition,[],[f3,f232]) ).
fof(f232,plain,
a = multiply(inverse(c),b),
inference(superposition,[],[f66,f82]) ).
fof(f265,plain,
! [X0] : multiply(c,X0) = multiply(inverse(a),multiply(d,X0)),
inference(superposition,[],[f3,f227]) ).
fof(f227,plain,
c = multiply(inverse(a),d),
inference(superposition,[],[f66,f15]) ).
fof(f248,plain,
( identity = element_in_O2(a,a)
| spl0_2 ),
inference(forward_demodulation,[],[f230,f2]) ).
fof(f230,plain,
( multiply(inverse(a),a) = element_in_O2(a,a)
| spl0_2 ),
inference(superposition,[],[f66,f192]) ).
fof(f250,plain,
identity = element_in_O2(d,d),
inference(forward_demodulation,[],[f238,f2]) ).
fof(f238,plain,
element_in_O2(d,d) = multiply(inverse(d),d),
inference(superposition,[],[f66,f110]) ).
fof(f244,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(multiply(X0,X1)) ),
inference(superposition,[],[f17,f66]) ).
fof(f242,plain,
! [X0] : multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(superposition,[],[f56,f66]) ).
fof(f239,plain,
( element_in_O2(d,a) = multiply(inverse(d),a)
| spl0_2 ),
inference(superposition,[],[f66,f120]) ).
fof(f237,plain,
a = multiply(inverse(d),multiply(a,b)),
inference(superposition,[],[f66,f100]) ).
fof(f229,plain,
( element_in_O2(a,d) = multiply(inverse(a),d)
| spl0_2 ),
inference(superposition,[],[f66,f108]) ).
fof(f228,plain,
! [X0] : multiply(c,X0) = multiply(inverse(a),multiply(d,X0)),
inference(superposition,[],[f66,f57]) ).
fof(f226,plain,
! [X0] : multiply(inverse(a),X0) = multiply(inverse(b),multiply(c,X0)),
inference(superposition,[],[f66,f56]) ).
fof(f222,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f66,f3]) ).
fof(f66,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f55,f1]) ).
fof(f55,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f3,f2]) ).
fof(f197,plain,
( ! [X0] : multiply(a,X0) = multiply(a,multiply(element_in_O2(a,a),X0))
| spl0_2 ),
inference(superposition,[],[f3,f192]) ).
fof(f192,plain,
( a = multiply(a,element_in_O2(a,a))
| spl0_2 ),
inference(resolution,[],[f91,f47]) ).
fof(f190,plain,
( ! [X0] :
( a = multiply(inverse(X0),element_in_O2(inverse(X0),a))
| subgroup_member(X0) )
| spl0_2 ),
inference(resolution,[],[f91,f20]) ).
fof(f195,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,[],[f189,f3]) ).
fof(f189,plain,
( ! [X0] :
( a = multiply(multiply(inverse(a),X0),element_in_O2(multiply(inverse(a),X0),a))
| subgroup_member(multiply(c,X0)) )
| spl0_2 ),
inference(resolution,[],[f91,f88]) ).
fof(f91,plain,
( ! [X0] :
( subgroup_member(X0)
| a = multiply(X0,element_in_O2(X0,a)) )
| spl0_2 ),
inference(resolution,[],[f12,f47]) ).
fof(f174,plain,
( subgroup_member(element_in_O2(a,d))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f173,plain,
( spl0_3
<=> subgroup_member(element_in_O2(a,d)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f166,plain,
( subgroup_member(multiply(c,d))
| ~ subgroup_member(element_in_O2(a,d))
| spl0_2 ),
inference(superposition,[],[f162,f108]) ).
fof(f165,plain,
! [X0] :
( subgroup_member(multiply(c,multiply(d,X0)))
| ~ subgroup_member(multiply(c,X0)) ),
inference(superposition,[],[f162,f57]) ).
fof(f162,plain,
! [X0] :
( subgroup_member(multiply(c,multiply(a,X0)))
| ~ subgroup_member(X0) ),
inference(forward_demodulation,[],[f154,f8]) ).
fof(f154,plain,
! [X0] :
( ~ subgroup_member(X0)
| subgroup_member(multiply(c,multiply(inverse(inverse(a)),X0))) ),
inference(superposition,[],[f88,f63]) ).
fof(f156,plain,
! [X0] : multiply(d,multiply(inverse(c),X0)) = multiply(a,X0),
inference(superposition,[],[f57,f63]) ).
fof(f163,plain,
! [X0] : multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(forward_demodulation,[],[f155,f8]) ).
fof(f155,plain,
! [X0] : multiply(b,X0) = multiply(c,multiply(inverse(inverse(a)),X0)),
inference(superposition,[],[f56,f63]) ).
fof(f153,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[],[f3,f63]) ).
fof(f151,plain,
! [X0,X1] :
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ subgroup_member(multiply(inverse(X0),X1)) ),
inference(superposition,[],[f17,f63]) ).
fof(f149,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[],[f63,f3]) ).
fof(f143,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[],[f63,f8]) ).
fof(f63,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f52,f1]) ).
fof(f52,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f3,f7]) ).
fof(f131,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,[],[f88,f12]) ).
fof(f136,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,[],[f130,f3]) ).
fof(f130,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,[],[f88,f12]) ).
fof(f135,plain,
! [X0] :
( d = multiply(inverse(a),multiply(X0,element_in_O2(multiply(inverse(a),X0),d)))
| subgroup_member(multiply(c,X0)) ),
inference(forward_demodulation,[],[f129,f3]) ).
fof(f129,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| d = multiply(multiply(inverse(a),X0),element_in_O2(multiply(inverse(a),X0),d)) ),
inference(resolution,[],[f88,f93]) ).
fof(f128,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| multiply(inverse(a),X0) = multiply(d,element_in_O2(d,multiply(inverse(a),X0))) ),
inference(resolution,[],[f88,f98]) ).
fof(f88,plain,
! [X0] :
( ~ subgroup_member(multiply(inverse(a),X0))
| subgroup_member(multiply(c,X0)) ),
inference(subsumption_resolution,[],[f81,f13]) ).
fof(f81,plain,
! [X0] :
( subgroup_member(multiply(c,X0))
| ~ subgroup_member(b)
| ~ subgroup_member(multiply(inverse(a),X0)) ),
inference(superposition,[],[f17,f56]) ).
fof(f123,plain,
( ! [X0] : multiply(a,X0) = multiply(d,multiply(element_in_O2(d,a),X0))
| spl0_2 ),
inference(superposition,[],[f3,f120]) ).
fof(f120,plain,
( a = multiply(d,element_in_O2(d,a))
| spl0_2 ),
inference(resolution,[],[f98,f47]) ).
fof(f118,plain,
! [X0] :
( inverse(X0) = multiply(d,element_in_O2(d,inverse(X0)))
| subgroup_member(X0) ),
inference(resolution,[],[f98,f20]) ).
fof(f98,plain,
! [X0] :
( subgroup_member(X0)
| multiply(d,element_in_O2(d,X0)) = X0 ),
inference(resolution,[],[f12,f16]) ).
fof(f116,plain,
! [X0] : multiply(d,X0) = multiply(d,multiply(element_in_O2(d,d),X0)),
inference(superposition,[],[f3,f110]) ).
fof(f110,plain,
d = multiply(d,element_in_O2(d,d)),
inference(resolution,[],[f93,f16]) ).
fof(f111,plain,
( ! [X0] : multiply(d,X0) = multiply(a,multiply(element_in_O2(a,d),X0))
| spl0_2 ),
inference(superposition,[],[f3,f108]) ).
fof(f108,plain,
( d = multiply(a,element_in_O2(a,d))
| spl0_2 ),
inference(resolution,[],[f93,f47]) ).
fof(f106,plain,
! [X0] :
( d = multiply(inverse(X0),element_in_O2(inverse(X0),d))
| subgroup_member(X0) ),
inference(resolution,[],[f93,f20]) ).
fof(f93,plain,
! [X0] :
( subgroup_member(X0)
| d = multiply(X0,element_in_O2(X0,d)) ),
inference(resolution,[],[f12,f16]) ).
fof(f105,plain,
! [X0] : multiply(d,multiply(a,X0)) = multiply(a,multiply(b,X0)),
inference(forward_demodulation,[],[f103,f3]) ).
fof(f103,plain,
! [X0] : multiply(d,multiply(a,X0)) = multiply(multiply(a,b),X0),
inference(superposition,[],[f3,f100]) ).
fof(f100,plain,
multiply(d,a) = multiply(a,b),
inference(superposition,[],[f57,f82]) ).
fof(f101,plain,
! [X0] : multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(superposition,[],[f3,f82]) ).
fof(f82,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f77,f6]) ).
fof(f77,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[],[f56,f2]) ).
fof(f96,plain,
( ! [X0] :
( subgroup_member(X0)
| multiply(a,element_in_O2(a,X0)) = X0 )
| spl0_2 ),
inference(resolution,[],[f12,f47]) ).
fof(f94,plain,
! [X0,X1] :
( subgroup_member(X0)
| multiply(inverse(X1),element_in_O2(inverse(X1),X0)) = X0
| subgroup_member(X1) ),
inference(resolution,[],[f12,f20]) ).
fof(f89,plain,
! [X0,X1] :
( subgroup_member(X0)
| inverse(X1) = multiply(X0,element_in_O2(X0,inverse(X1)))
| subgroup_member(X1) ),
inference(resolution,[],[f12,f20]) ).
fof(f12,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(f85,plain,
b = multiply(c,a),
inference(forward_demodulation,[],[f84,f6]) ).
fof(f84,plain,
multiply(c,a) = multiply(b,identity),
inference(forward_demodulation,[],[f79,f8]) ).
fof(f79,plain,
multiply(b,identity) = multiply(c,inverse(inverse(a))),
inference(superposition,[],[f56,f7]) ).
fof(f56,plain,
! [X0] : multiply(b,multiply(inverse(a),X0)) = multiply(c,X0),
inference(superposition,[],[f3,f14]) ).
fof(f75,plain,
! [X0] : multiply(d,multiply(inverse(c),X0)) = multiply(a,X0),
inference(superposition,[],[f3,f72]) ).
fof(f72,plain,
a = multiply(d,inverse(c)),
inference(forward_demodulation,[],[f68,f6]) ).
fof(f68,plain,
multiply(d,inverse(c)) = multiply(a,identity),
inference(superposition,[],[f57,f7]) ).
fof(f57,plain,
! [X0] : multiply(a,multiply(c,X0)) = multiply(d,X0),
inference(superposition,[],[f3,f15]) ).
fof(f62,plain,
! [X2,X0,X1] :
( subgroup_member(multiply(X0,multiply(X1,X2)))
| ~ subgroup_member(multiply(X0,X1))
| ~ subgroup_member(X2) ),
inference(superposition,[],[f17,f3]) ).
fof(f61,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f7,f3]) ).
fof(f59,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(f39,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(subsumption_resolution,[],[f37,f16]) ).
fof(f37,plain,
( subgroup_member(d)
| ~ subgroup_member(a)
| ~ subgroup_member(c) ),
inference(superposition,[],[f17,f15]) ).
fof(f17,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(f11,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(f25,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f2,f8]) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f20,plain,
! [X0] :
( ~ subgroup_member(inverse(X0))
| subgroup_member(X0) ),
inference(superposition,[],[f4,f8]) ).
fof(f8,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_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(f14,axiom,
multiply(b,inverse(a)) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f9,axiom,
identity = inverse(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_of_identity) ).
fof(f15,axiom,
multiply(a,c) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f10,axiom,
subgroup_member(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_in_O2) ).
fof(f16,axiom,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_in_O2) ).
fof(f13,axiom,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_in_O2) ).
fof(f42,plain,
( subgroup_member(c)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f41,plain,
( spl0_1
<=> subgroup_member(c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f325,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f324,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(global_subsumption,[],[f13,f16,f10,f15,f9,f14,f1,f4,f6,f8,f20,f2,f25,f7,f11,f17,f39,f3,f59,f61,f62,f57,f72,f75,f56,f85,f12,f89,f94,f96,f82,f101,f100,f105,f93,f106,f108,f111,f110,f116,f98,f118,f120,f123,f88,f128,f135,f136,f131,f63,f143,f149,f151,f153,f163,f156,f162,f165,f166,f174,f91,f195,f190,f192,f197,f66,f222,f226,f228,f229,f237,f239,f242,f244,f250,f248,f227,f265,f232,f270,f274,f277,f278,f279,f280,f281,f225,f284,f236,f289,f262,f293,f294,f297,f99,f306,f300,f302,f307,f290,f317,f70,f285,f320,f321,f127,f38,f308,f275,f47]) ).
fof(f323,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f322,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(global_subsumption,[],[f13,f16,f10,f15,f9,f14,f1,f4,f6,f8,f20,f2,f25,f7,f11,f17,f39,f47,f3,f59,f61,f62,f57,f72,f75,f56,f85,f12,f89,f94,f96,f82,f101,f100,f105,f93,f106,f108,f111,f110,f116,f98,f118,f120,f123,f88,f128,f135,f136,f131,f63,f143,f149,f151,f153,f163,f156,f162,f165,f166,f174,f91,f195,f190,f192,f197,f66,f222,f226,f228,f229,f237,f239,f242,f244,f250,f248,f227,f265,f232,f270,f274,f277,f278,f279,f280,f281,f225,f284,f236,f289,f262,f293,f294,f297,f99,f306,f300,f302,f307,f290,f317,f70,f285,f320,f321,f127,f38,f308,f275]) ).
fof(f319,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f318,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(global_subsumption,[],[f13,f16,f10,f15,f9,f14,f1,f4,f6,f8,f20,f2,f25,f7,f11,f17,f38,f39,f43,f49,f3,f59,f61,f62,f57,f72,f75,f56,f85,f12,f89,f90,f94,f95,f97,f82,f101,f100,f105,f93,f106,f107,f109,f113,f114,f110,f116,f98,f118,f119,f121,f125,f88,f128,f135,f136,f131,f63,f143,f149,f151,f153,f163,f156,f162,f165,f92,f209,f204,f205,f207,f216,f214,f66,f222,f226,f228,f233,f237,f240,f242,f244,f250,f249,f227,f265,f232,f270,f225,f284,f236,f289,f262,f293,f294,f297,f99,f306,f300,f301,f290,f317,f70,f50,f46]) ).
fof(f46,plain,
( subgroup_member(a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f50,plain,
( ~ subgroup_member(a)
| spl0_1 ),
inference(resolution,[],[f49,f4]) ).
fof(f301,plain,
( inverse(a) = multiply(inverse(a),element_in_O2(inverse(a),inverse(a)))
| spl0_1 ),
inference(resolution,[],[f99,f49]) ).
fof(f249,plain,
( identity = element_in_O2(c,c)
| spl0_1 ),
inference(forward_demodulation,[],[f235,f2]) ).
fof(f235,plain,
( element_in_O2(c,c) = multiply(inverse(c),c)
| spl0_1 ),
inference(superposition,[],[f66,f207]) ).
fof(f240,plain,
( element_in_O2(d,c) = multiply(inverse(d),c)
| spl0_1 ),
inference(superposition,[],[f66,f121]) ).
fof(f233,plain,
( element_in_O2(c,d) = multiply(inverse(c),d)
| spl0_1 ),
inference(superposition,[],[f66,f109]) ).
fof(f214,plain,
( ! [X0] : multiply(c,X0) = multiply(c,multiply(element_in_O2(c,c),X0))
| spl0_1 ),
inference(superposition,[],[f3,f207]) ).
fof(f216,plain,
( d = multiply(d,element_in_O2(c,c))
| spl0_1 ),
inference(forward_demodulation,[],[f213,f15]) ).
fof(f213,plain,
( multiply(a,c) = multiply(d,element_in_O2(c,c))
| spl0_1 ),
inference(superposition,[],[f57,f207]) ).
fof(f207,plain,
( c = multiply(c,element_in_O2(c,c))
| spl0_1 ),
inference(resolution,[],[f92,f43]) ).
fof(f205,plain,
( c = multiply(inverse(a),element_in_O2(inverse(a),c))
| spl0_1 ),
inference(resolution,[],[f92,f49]) ).
fof(f204,plain,
( ! [X0] :
( c = multiply(inverse(X0),element_in_O2(inverse(X0),c))
| subgroup_member(X0) )
| spl0_1 ),
inference(resolution,[],[f92,f20]) ).
fof(f209,plain,
( ! [X0] :
( c = multiply(inverse(a),multiply(X0,element_in_O2(multiply(inverse(a),X0),c)))
| subgroup_member(multiply(c,X0)) )
| spl0_1 ),
inference(forward_demodulation,[],[f203,f3]) ).
fof(f203,plain,
( ! [X0] :
( c = multiply(multiply(inverse(a),X0),element_in_O2(multiply(inverse(a),X0),c))
| subgroup_member(multiply(c,X0)) )
| spl0_1 ),
inference(resolution,[],[f92,f88]) ).
fof(f92,plain,
( ! [X0] :
( subgroup_member(X0)
| c = multiply(X0,element_in_O2(X0,c)) )
| spl0_1 ),
inference(resolution,[],[f12,f43]) ).
fof(f125,plain,
( ! [X0] : multiply(c,X0) = multiply(d,multiply(element_in_O2(d,c),X0))
| spl0_1 ),
inference(superposition,[],[f3,f121]) ).
fof(f121,plain,
( c = multiply(d,element_in_O2(d,c))
| spl0_1 ),
inference(resolution,[],[f98,f43]) ).
fof(f119,plain,
( inverse(a) = multiply(d,element_in_O2(d,inverse(a)))
| spl0_1 ),
inference(resolution,[],[f98,f49]) ).
fof(f114,plain,
( ! [X0] : multiply(d,X0) = multiply(c,multiply(element_in_O2(c,d),X0))
| spl0_1 ),
inference(superposition,[],[f3,f109]) ).
fof(f113,plain,
( multiply(d,element_in_O2(c,d)) = multiply(a,d)
| spl0_1 ),
inference(superposition,[],[f57,f109]) ).
fof(f109,plain,
( d = multiply(c,element_in_O2(c,d))
| spl0_1 ),
inference(resolution,[],[f93,f43]) ).
fof(f107,plain,
( d = multiply(inverse(a),element_in_O2(inverse(a),d))
| spl0_1 ),
inference(resolution,[],[f93,f49]) ).
fof(f97,plain,
( ! [X0] :
( subgroup_member(X0)
| multiply(c,element_in_O2(c,X0)) = X0 )
| spl0_1 ),
inference(resolution,[],[f12,f43]) ).
fof(f95,plain,
( ! [X0] :
( subgroup_member(X0)
| multiply(inverse(a),element_in_O2(inverse(a),X0)) = X0 )
| spl0_1 ),
inference(resolution,[],[f12,f49]) ).
fof(f90,plain,
( ! [X0] :
( subgroup_member(X0)
| inverse(a) = multiply(X0,element_in_O2(X0,inverse(a))) )
| spl0_1 ),
inference(resolution,[],[f12,f49]) ).
fof(f49,plain,
( ~ subgroup_member(inverse(a))
| spl0_1 ),
inference(subsumption_resolution,[],[f38,f43]) ).
fof(f43,plain,
( ~ subgroup_member(c)
| spl0_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f316,plain,
( spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f315,plain,
( $false
| spl0_1
| spl0_2 ),
inference(subsumption_resolution,[],[f314,f47]) ).
fof(f314,plain,
( subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(subsumption_resolution,[],[f313,f16]) ).
fof(f313,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_1
| spl0_2 ),
inference(subsumption_resolution,[],[f310,f43]) ).
fof(f310,plain,
( subgroup_member(c)
| subgroup_member(d)
| subgroup_member(a)
| spl0_2 ),
inference(superposition,[],[f11,f307]) ).
fof(f312,plain,
( spl0_1
| spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f311]) ).
fof(f311,plain,
( $false
| spl0_1
| spl0_2
| ~ spl0_3 ),
inference(subsumption_resolution,[],[f308,f43]) ).
fof(f188,plain,
( spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f187,plain,
( $false
| spl0_2
| spl0_3 ),
inference(subsumption_resolution,[],[f186,f47]) ).
fof(f186,plain,
( subgroup_member(a)
| spl0_3 ),
inference(subsumption_resolution,[],[f181,f16]) ).
fof(f181,plain,
( subgroup_member(d)
| subgroup_member(a)
| spl0_3 ),
inference(resolution,[],[f175,f11]) ).
fof(f175,plain,
( ~ subgroup_member(element_in_O2(a,d))
| spl0_3 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f180,plain,
( ~ spl0_3
| spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f166,f45,f177,f173]) ).
fof(f177,plain,
( spl0_4
<=> subgroup_member(multiply(c,d)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f48,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f39,f45,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Tue Apr 30 04:17:04 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (24125)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (24128)WARNING: value z3 for option sas not known
% 0.22/0.38 % (24126)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (24129)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (24131)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)
% 0.22/0.38 % (24130)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)
% 0.22/0.38 % (24128)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)
% 0.22/0.38 % (24127)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (24132)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)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [3]
% 0.22/0.38 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [4]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 % (24128)First to succeed.
% 0.22/0.40 TRYING [5]
% 0.22/0.40 % (24131)Also succeeded, but the first one will report.
% 0.22/0.40 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.40 TRYING [3]
% 0.22/0.40 % (24128)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (24128)------------------------------
% 0.22/0.40 % (24128)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40 % (24128)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (24128)Memory used [KB]: 938
% 0.22/0.40 % (24128)Time elapsed: 0.016 s
% 0.22/0.40 % (24128)Instructions burned: 21 (million)
% 0.22/0.40 % (24128)------------------------------
% 0.22/0.40 % (24128)------------------------------
% 0.22/0.40 % (24125)Success in time 0.032 s
%------------------------------------------------------------------------------