TSTP Solution File: SET891+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET891+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 : n015.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 : Sat Sep 2 00:03:27 EDT 2023
% Result : Theorem 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 24
% Syntax : Number of formulae : 62 ( 33 unt; 0 def)
% Number of atoms : 97 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 35 ~; 19 |; 0 &)
% ( 11 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 61 (; 53 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f100,plain,
$false,
inference(avatar_sat_refutation,[],[f36,f41,f46,f50,f54,f58,f64,f68,f76,f83,f96,f99]) ).
fof(f99,plain,
( ~ spl4_10
| spl4_11 ),
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f98,plain,
( $false
| ~ spl4_10
| spl4_11 ),
inference(trivial_inequality_removal,[],[f97]) ).
fof(f97,plain,
( unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1)
| ~ spl4_10
| spl4_11 ),
inference(superposition,[],[f95,f82]) ).
fof(f82,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1))
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f81,plain,
( spl4_10
<=> ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
fof(f95,plain,
( unordered_pair(sK0,sK1) != set_union2(singleton(sK0),singleton(sK1))
| spl4_11 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f93,plain,
( spl4_11
<=> unordered_pair(sK0,sK1) = set_union2(singleton(sK0),singleton(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
fof(f96,plain,
( ~ spl4_11
| spl4_3
| ~ spl4_9 ),
inference(avatar_split_clause,[],[f79,f74,f43,f93]) ).
fof(f43,plain,
( spl4_3
<=> unordered_pair(sK0,sK1) = union(unordered_pair(singleton(sK0),singleton(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f74,plain,
( spl4_9
<=> ! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
fof(f79,plain,
( unordered_pair(sK0,sK1) != set_union2(singleton(sK0),singleton(sK1))
| spl4_3
| ~ spl4_9 ),
inference(superposition,[],[f45,f75]) ).
fof(f75,plain,
( ! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1))
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f45,plain,
( unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1)))
| spl4_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f83,plain,
spl4_10,
inference(avatar_split_clause,[],[f27,f81]) ).
fof(f27,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',t41_enumset1) ).
fof(f76,plain,
spl4_9,
inference(avatar_split_clause,[],[f26,f74]) ).
fof(f26,plain,
! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',l52_zfmisc_1) ).
fof(f68,plain,
spl4_8,
inference(avatar_split_clause,[],[f25,f66]) ).
fof(f66,plain,
( spl4_8
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
fof(f25,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',commutativity_k2_xboole_0) ).
fof(f64,plain,
spl4_7,
inference(avatar_split_clause,[],[f24,f62]) ).
fof(f62,plain,
( spl4_7
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',commutativity_k2_tarski) ).
fof(f58,plain,
spl4_6,
inference(avatar_split_clause,[],[f29,f56]) ).
fof(f56,plain,
( spl4_6
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
fof(f29,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',fc2_xboole_0) ).
fof(f54,plain,
spl4_5,
inference(avatar_split_clause,[],[f28,f52]) ).
fof(f52,plain,
( spl4_5
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
fof(f28,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',fc3_xboole_0) ).
fof(f50,plain,
spl4_4,
inference(avatar_split_clause,[],[f23,f48]) ).
fof(f48,plain,
( spl4_4
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
fof(f23,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',idempotence_k2_xboole_0) ).
fof(f46,plain,
~ spl4_3,
inference(avatar_split_clause,[],[f22,f43]) ).
fof(f22,plain,
unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16]) ).
fof(f16,plain,
( ? [X0,X1] : unordered_pair(X0,X1) != union(unordered_pair(singleton(X0),singleton(X1)))
=> unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1] : unordered_pair(X0,X1) != union(unordered_pair(singleton(X0),singleton(X1))),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : unordered_pair(X0,X1) = union(unordered_pair(singleton(X0),singleton(X1))),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1] : unordered_pair(X0,X1) = union(unordered_pair(singleton(X0),singleton(X1))),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',t32_zfmisc_1) ).
fof(f41,plain,
spl4_2,
inference(avatar_split_clause,[],[f31,f38]) ).
fof(f38,plain,
( spl4_2
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f31,plain,
empty(sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
empty(sK3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f7,f20]) ).
fof(f20,plain,
( ? [X0] : empty(X0)
=> empty(sK3) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',rc1_xboole_0) ).
fof(f36,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f30,f33]) ).
fof(f33,plain,
( spl4_1
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f30,plain,
~ empty(sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
~ empty(sK2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f8,f18]) ).
fof(f18,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK2) ),
introduced(choice_axiom,[]) ).
fof(f8,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',rc2_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET891+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
% 0.16/0.35 % Computer : n015.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Wed Aug 30 16:02:12 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.21/0.41 % (2932)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (2947)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 Vampire---4 for (531ds/0Mi)
% 0.21/0.41 % (2939)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.41 % (2941)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.41 % (2942)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 Vampire---4 for (569ds/0Mi)
% 0.21/0.41 % (2946)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.41 % (2949)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 Vampire---4 for (522ds/0Mi)
% 0.21/0.41 % (2950)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 Vampire---4 for (497ds/0Mi)
% 0.21/0.41 % (2947)First to succeed.
% 0.21/0.41 TRYING [1]
% 0.21/0.41 TRYING [2]
% 0.21/0.41 % (2947)Refutation found. Thanks to Tanya!
% 0.21/0.41 % SZS status Theorem for Vampire---4
% 0.21/0.41 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.41 % (2947)------------------------------
% 0.21/0.41 % (2947)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.41 % (2947)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.41 % (2947)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (2947)Memory used [KB]: 5373
% 0.21/0.41 % (2947)Time elapsed: 0.003 s
% 0.21/0.41 % (2947)------------------------------
% 0.21/0.41 % (2947)------------------------------
% 0.21/0.41 % (2932)Success in time 0.06 s
% 0.21/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------