TSTP Solution File: SEU144+2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU144+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n012.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 17:56:01 EDT 2023
% Result : Theorem 0.23s 0.44s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 9 unt; 0 def)
% Number of atoms : 264 ( 56 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 303 ( 112 ~; 127 |; 47 &)
% ( 10 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 116 (; 100 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f527,plain,
$false,
inference(avatar_sat_refutation,[],[f319,f322,f507,f526]) ).
fof(f526,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f525,plain,
( $false
| spl15_1
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f524,f314]) ).
fof(f314,plain,
( ~ subset(sF14,sK1)
| spl15_1 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f312,plain,
( spl15_1
<=> subset(sF14,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f524,plain,
( subset(sF14,sK1)
| spl15_1
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f523,f317]) ).
fof(f317,plain,
( in(sK0,sK1)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f316,plain,
( spl15_2
<=> in(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f523,plain,
( ~ in(sK0,sK1)
| subset(sF14,sK1)
| spl15_1 ),
inference(superposition,[],[f219,f512]) ).
fof(f512,plain,
( sK0 = sK6(sF14,sK1)
| spl15_1 ),
inference(resolution,[],[f508,f480]) ).
fof(f480,plain,
! [X0] :
( ~ in(X0,sF14)
| sK0 = X0 ),
inference(superposition,[],[f281,f296]) ).
fof(f296,plain,
unordered_pair(sK0,sK0) = sF14,
introduced(function_definition,[]) ).
fof(f281,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f269]) ).
fof(f269,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f220,f160]) ).
fof(f160,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181',t69_enumset1) ).
fof(f220,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK7(X0,X1) != X0
| ~ in(sK7(X0,X1),X1) )
& ( sK7(X0,X1) = X0
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f129,f130]) ).
fof(f130,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK7(X0,X1) != X0
| ~ in(sK7(X0,X1),X1) )
& ( sK7(X0,X1) = X0
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181',d1_tarski) ).
fof(f508,plain,
( in(sK6(sF14,sK1),sF14)
| spl15_1 ),
inference(resolution,[],[f314,f218]) ).
fof(f218,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f125,f126]) ).
fof(f126,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181',d3_tarski) ).
fof(f219,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f507,plain,
( ~ spl15_1
| spl15_2 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f506,plain,
( $false
| ~ spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f505,f318]) ).
fof(f318,plain,
( ~ in(sK0,sK1)
| spl15_2 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f505,plain,
( in(sK0,sK1)
| ~ spl15_1 ),
inference(superposition,[],[f496,f379]) ).
fof(f379,plain,
( sK1 = set_union2(sK1,sF14)
| ~ spl15_1 ),
inference(superposition,[],[f378,f202]) ).
fof(f202,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181',commutativity_k2_xboole_0) ).
fof(f378,plain,
( sK1 = set_union2(sF14,sK1)
| ~ spl15_1 ),
inference(resolution,[],[f173,f313]) ).
fof(f313,plain,
( subset(sF14,sK1)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f173,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181',t12_xboole_1) ).
fof(f496,plain,
! [X8] : in(sK0,set_union2(X8,sF14)),
inference(resolution,[],[f290,f307]) ).
fof(f307,plain,
in(sK0,sF14),
inference(superposition,[],[f280,f296]) ).
fof(f280,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f279]) ).
fof(f279,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f268]) ).
fof(f268,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f221,f160]) ).
fof(f221,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f131]) ).
fof(f290,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f240]) ).
fof(f240,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK10(X0,X1,X2),X1)
& ~ in(sK10(X0,X1,X2),X0) )
| ~ in(sK10(X0,X1,X2),X2) )
& ( in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f144,f145]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK10(X0,X1,X2),X1)
& ~ in(sK10(X0,X1,X2),X0) )
| ~ in(sK10(X0,X1,X2),X2) )
& ( in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f142]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181',d2_xboole_0) ).
fof(f322,plain,
( spl15_1
| spl15_2 ),
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f321,plain,
( $false
| spl15_1
| spl15_2 ),
inference(subsumption_resolution,[],[f320,f314]) ).
fof(f320,plain,
( subset(sF14,sK1)
| spl15_2 ),
inference(subsumption_resolution,[],[f298,f318]) ).
fof(f298,plain,
( in(sK0,sK1)
| subset(sF14,sK1) ),
inference(definition_folding,[],[f253,f296]) ).
fof(f253,plain,
( in(sK0,sK1)
| subset(unordered_pair(sK0,sK0),sK1) ),
inference(definition_unfolding,[],[f156,f160]) ).
fof(f156,plain,
( in(sK0,sK1)
| subset(singleton(sK0),sK1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( ( ~ in(sK0,sK1)
| ~ subset(singleton(sK0),sK1) )
& ( in(sK0,sK1)
| subset(singleton(sK0),sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f104,f105]) ).
fof(f105,plain,
( ? [X0,X1] :
( ( ~ in(X0,X1)
| ~ subset(singleton(X0),X1) )
& ( in(X0,X1)
| subset(singleton(X0),X1) ) )
=> ( ( ~ in(sK0,sK1)
| ~ subset(singleton(sK0),sK1) )
& ( in(sK0,sK1)
| subset(singleton(sK0),sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
? [X0,X1] :
( ( ~ in(X0,X1)
| ~ subset(singleton(X0),X1) )
& ( in(X0,X1)
| subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
? [X0,X1] :
( subset(singleton(X0),X1)
<~> in(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181',l2_zfmisc_1) ).
fof(f319,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f297,f316,f312]) ).
fof(f297,plain,
( ~ in(sK0,sK1)
| ~ subset(sF14,sK1) ),
inference(definition_folding,[],[f252,f296]) ).
fof(f252,plain,
( ~ in(sK0,sK1)
| ~ subset(unordered_pair(sK0,sK0),sK1) ),
inference(definition_unfolding,[],[f157,f160]) ).
fof(f157,plain,
( ~ in(sK0,sK1)
| ~ subset(singleton(sK0),sK1) ),
inference(cnf_transformation,[],[f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU144+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36 % Computer : n012.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 : Wed Aug 23 17:36:42 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.7PEiz1ZFVJ/Vampire---4.8_18181
% 0.16/0.37 % (18322)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41 % (18327)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.23/0.43 % (18337)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.23/0.43 % (18326)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.23/0.43 % (18334)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.23/0.43 % (18339)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.23/0.43 % (18331)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.23/0.43 % (18340)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.23/0.44 % (18339)First to succeed.
% 0.23/0.44 % (18339)Refutation found. Thanks to Tanya!
% 0.23/0.44 % SZS status Theorem for Vampire---4
% 0.23/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.44 % (18339)------------------------------
% 0.23/0.44 % (18339)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.44 % (18339)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.44 % (18339)Termination reason: Refutation
% 0.23/0.44
% 0.23/0.44 % (18339)Memory used [KB]: 5628
% 0.23/0.44 % (18339)Time elapsed: 0.013 s
% 0.23/0.44 % (18339)------------------------------
% 0.23/0.44 % (18339)------------------------------
% 0.23/0.44 % (18322)Success in time 0.072 s
% 0.23/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------