TSTP Solution File: SEU230+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU230+1 : 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 : 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 : Sat Sep 2 00:10:44 EDT 2023
% Result : Theorem 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 152 ( 36 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 186 ( 69 ~; 71 |; 36 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 84 (; 75 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f749,plain,
$false,
inference(resolution,[],[f747,f285]) ).
fof(f285,plain,
! [X0] : in(X0,singleton(X0)),
inference(equality_resolution,[],[f284]) ).
fof(f284,plain,
! [X0,X1] :
( X0 != X1
| in(X1,singleton(X0)) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) )
& ( sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f64,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) )
& ( sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f64,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,[],[f63]) ).
fof(f63,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.4tJPgaspRV/Vampire---4.8_6416',d1_tarski) ).
fof(f747,plain,
~ in(sK1,singleton(sK1)),
inference(resolution,[],[f293,f91]) ).
fof(f91,plain,
~ in(sK1,succ(sK1)),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
~ in(sK1,succ(sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f41,f59]) ).
fof(f59,plain,
( ? [X0] : ~ in(X0,succ(X0))
=> ~ in(sK1,succ(sK1)) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
? [X0] : ~ in(X0,succ(X0)),
inference(ennf_transformation,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X0] : in(X0,succ(X0)),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox/tmp/tmp.4tJPgaspRV/Vampire---4.8_6416',t10_ordinal1) ).
fof(f293,plain,
! [X8,X9] :
( in(X8,succ(X9))
| ~ in(X8,singleton(X9)) ),
inference(resolution,[],[f123,f232]) ).
fof(f232,plain,
! [X5] : sP0(X5,singleton(X5),succ(X5)),
inference(superposition,[],[f224,f100]) ).
fof(f100,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/tmp/tmp.4tJPgaspRV/Vampire---4.8_6416',d1_ordinal1) ).
fof(f224,plain,
! [X2,X1] : sP0(X2,X1,set_union2(X2,X1)),
inference(superposition,[],[f221,f109]) ).
fof(f109,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/tmp/tmp.4tJPgaspRV/Vampire---4.8_6416',commutativity_k2_xboole_0) ).
fof(f221,plain,
! [X0,X1] : sP0(X0,X1,set_union2(X1,X0)),
inference(equality_resolution,[],[f128]) ).
fof(f128,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) != X2
| sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f8,f57]) ).
fof(f57,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f8,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.4tJPgaspRV/Vampire---4.8_6416',d2_xboole_0) ).
fof(f123,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( ~ in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X1) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f69,f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X1) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,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) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,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) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU230+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 30 13:49:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % (6544)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (6548)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.19/0.41 % (6546)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.19/0.41 % (6549)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)
% 0.19/0.41 % (6545)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.19/0.41 % (6547)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)
% 0.19/0.41 % (6550)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)
% 0.19/0.41 % (6551)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)
% 0.19/0.41 TRYING [1]
% 0.19/0.41 TRYING [2]
% 0.19/0.41 TRYING [3]
% 0.19/0.41 TRYING [4]
% 0.19/0.41 TRYING [1]
% 0.19/0.41 TRYING [2]
% 0.19/0.42 TRYING [5]
% 0.19/0.42 TRYING [3]
% 0.19/0.42 % (6550)First to succeed.
% 0.19/0.43 % (6550)Refutation found. Thanks to Tanya!
% 0.19/0.43 % SZS status Theorem for Vampire---4
% 0.19/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.43 % (6550)------------------------------
% 0.19/0.43 % (6550)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.43 % (6550)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.43 % (6550)Termination reason: Refutation
% 0.19/0.43
% 0.19/0.43 % (6550)Memory used [KB]: 1407
% 0.19/0.43 % (6550)Time elapsed: 0.018 s
% 0.19/0.43 % (6550)------------------------------
% 0.19/0.43 % (6550)------------------------------
% 0.19/0.43 % (6544)Success in time 0.082 s
% 0.19/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------