TSTP Solution File: SET921+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n001.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 : Thu Aug 31 15:46:20 EDT 2023
% Result : Theorem 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 5 unt; 0 def)
% Number of atoms : 272 ( 50 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 324 ( 127 ~; 132 |; 45 &)
% ( 16 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 140 (; 122 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f183,plain,
$false,
inference(avatar_sat_refutation,[],[f69,f72,f74,f134,f137,f182]) ).
fof(f182,plain,
( ~ spl10_1
| spl10_2 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f179,plain,
( $false
| ~ spl10_1
| spl10_2 ),
inference(resolution,[],[f178,f70]) ).
fof(f70,plain,
( in(sK3,set_difference(sK4,singleton(sK5)))
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f61,plain,
( spl10_1
<=> in(sK3,set_difference(sK4,singleton(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).
fof(f178,plain,
( ! [X0] : ~ in(sK3,set_difference(sK4,X0))
| spl10_2 ),
inference(resolution,[],[f175,f59]) ).
fof(f59,plain,
! [X0,X1] : sP2(X0,X1,set_difference(X0,X1)),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP2(X0,X1,X2) )
& ( sP2(X0,X1,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP2(X0,X1,X2) ),
inference(definition_folding,[],[f3,f13,f12]) ).
fof(f12,plain,
! [X1,X3,X0] :
( sP1(X1,X3,X0)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f13,plain,
! [X0,X1,X2] :
( sP2(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP1(X1,X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4xQC4RQBdM/Vampire---4.8_1074',d4_xboole_0) ).
fof(f175,plain,
( ! [X56,X57] :
( ~ sP2(sK4,X56,X57)
| ~ in(sK3,X57) )
| spl10_2 ),
inference(resolution,[],[f91,f65]) ).
fof(f65,plain,
( ~ in(sK3,sK4)
| spl10_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f64,plain,
( spl10_2
<=> in(sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).
fof(f91,plain,
! [X6,X7,X4,X5] :
( in(X4,X6)
| ~ sP2(X6,X7,X5)
| ~ in(X4,X5) ),
inference(resolution,[],[f46,f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| in(X1,X0)
| ~ in(X1,X2) )
& ( ( ~ in(X1,X0)
& in(X1,X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X1,X3,X0] :
( ( sP1(X1,X3,X0)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ sP1(X1,X3,X0) ) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X1,X3,X0] :
( ( sP1(X1,X3,X0)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ sP1(X1,X3,X0) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f46,plain,
! [X2,X0,X1,X4] :
( sP1(X1,X4,X0)
| ~ in(X4,X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP1(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X1,X4,X0) )
& ( sP1(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) )
=> ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP1(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X1,X4,X0) )
& ( sP1(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP1(X1,X3,X0) )
& ( sP1(X1,X3,X0)
| ~ in(X3,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f137,plain,
( ~ spl10_1
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f136]) ).
fof(f136,plain,
( $false
| ~ spl10_1
| ~ spl10_3 ),
inference(subsumption_resolution,[],[f135,f117]) ).
fof(f117,plain,
! [X0,X1] : ~ in(X0,set_difference(X1,singleton(X0))),
inference(resolution,[],[f96,f59]) ).
fof(f96,plain,
! [X2,X3,X4] :
( ~ sP2(X4,singleton(X2),X3)
| ~ in(X2,X3) ),
inference(resolution,[],[f90,f78]) ).
fof(f78,plain,
! [X0] : in(X0,singleton(X0)),
inference(resolution,[],[f57,f58]) ).
fof(f58,plain,
! [X0] : sP0(X0,singleton(X0)),
inference(equality_resolution,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( sP0(X0,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f2,f10]) ).
fof(f10,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f2,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.4xQC4RQBdM/Vampire---4.8_1074',d1_tarski) ).
fof(f57,plain,
! [X3,X1] :
( ~ sP0(X3,X1)
| in(X3,X1) ),
inference(equality_resolution,[],[f41]) ).
fof(f41,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f20,f21]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f90,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,X1)
| ~ sP2(X2,X3,X1)
| ~ in(X0,X3) ),
inference(resolution,[],[f46,f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f135,plain,
( in(sK3,set_difference(sK4,singleton(sK3)))
| ~ spl10_1
| ~ spl10_3 ),
inference(forward_demodulation,[],[f70,f68]) ).
fof(f68,plain,
( sK3 = sK5
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl10_3
<=> sK3 = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).
fof(f134,plain,
( spl10_1
| ~ spl10_2
| spl10_3 ),
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f133,plain,
( $false
| spl10_1
| ~ spl10_2
| spl10_3 ),
inference(subsumption_resolution,[],[f126,f71]) ).
fof(f71,plain,
( sK3 != sK5
| spl10_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f126,plain,
( sK3 = sK5
| spl10_1
| ~ spl10_2 ),
inference(resolution,[],[f125,f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(resolution,[],[f40,f58]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ in(X3,X1)
| ~ sP0(X0,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f22]) ).
fof(f125,plain,
( in(sK3,singleton(sK5))
| spl10_1
| ~ spl10_2 ),
inference(subsumption_resolution,[],[f124,f73]) ).
fof(f73,plain,
( in(sK3,sK4)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f124,plain,
( in(sK3,singleton(sK5))
| ~ in(sK3,sK4)
| spl10_1 ),
inference(resolution,[],[f122,f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(X1,X0)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f122,plain,
( ~ sP1(singleton(sK5),sK3,sK4)
| spl10_1 ),
inference(resolution,[],[f110,f59]) ).
fof(f110,plain,
( ! [X40,X41] :
( ~ sP2(X41,X40,set_difference(sK4,singleton(sK5)))
| ~ sP1(X40,sK3,X41) )
| spl10_1 ),
inference(resolution,[],[f47,f62]) ).
fof(f62,plain,
( ~ in(sK3,set_difference(sK4,singleton(sK5)))
| spl10_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ sP1(X1,X4,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f74,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f36,f64,f61]) ).
fof(f36,plain,
( in(sK3,sK4)
| in(sK3,set_difference(sK4,singleton(sK5))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ( sK3 = sK5
| ~ in(sK3,sK4)
| ~ in(sK3,set_difference(sK4,singleton(sK5))) )
& ( ( sK3 != sK5
& in(sK3,sK4) )
| in(sK3,set_difference(sK4,singleton(sK5))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f16,f17]) ).
fof(f17,plain,
( ? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) )
=> ( ( sK3 = sK5
| ~ in(sK3,sK4)
| ~ in(sK3,set_difference(sK4,singleton(sK5))) )
& ( ( sK3 != sK5
& in(sK3,sK4) )
| in(sK3,set_difference(sK4,singleton(sK5))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(flattening,[],[f15]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
? [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<~> ( X0 != X2
& in(X0,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.4xQC4RQBdM/Vampire---4.8_1074',t64_zfmisc_1) ).
fof(f72,plain,
( spl10_1
| ~ spl10_3 ),
inference(avatar_split_clause,[],[f37,f67,f61]) ).
fof(f37,plain,
( sK3 != sK5
| in(sK3,set_difference(sK4,singleton(sK5))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f69,plain,
( ~ spl10_1
| ~ spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f38,f67,f64,f61]) ).
fof(f38,plain,
( sK3 = sK5
| ~ in(sK3,sK4)
| ~ in(sK3,set_difference(sK4,singleton(sK5))) ),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n001.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 14:28:00 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.4xQC4RQBdM/Vampire---4.8_1074
% 0.15/0.37 % (1192)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (1195)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.15/0.41 % (1195)First to succeed.
% 0.15/0.41 % (1195)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Theorem for Vampire---4
% 0.15/0.41 % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.41 % (1195)------------------------------
% 0.15/0.41 % (1195)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.15/0.41 % (1195)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.15/0.41 % (1195)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (1195)Memory used [KB]: 10106
% 0.15/0.41 % (1195)Time elapsed: 0.007 s
% 0.15/0.41 % (1195)------------------------------
% 0.15/0.41 % (1195)------------------------------
% 0.15/0.41 % (1192)Success in time 0.042 s
% 0.15/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------