TSTP Solution File: SET918+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET918+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 : 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 : Thu Aug 31 15:46:20 EDT 2023
% Result : Theorem 0.23s 0.43s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 239 ( 112 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 310 ( 113 ~; 115 |; 72 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 107 (; 90 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f166,plain,
$false,
inference(unit_resulting_resolution,[],[f37,f36,f78,f157]) ).
fof(f157,plain,
! [X2] :
( ~ in(X2,sF9)
| ~ in(X2,sK2)
| sK0 = X2 ),
inference(resolution,[],[f149,f103]) ).
fof(f103,plain,
! [X0] :
( ~ in(X0,sF8)
| sK0 = X0 ),
inference(superposition,[],[f62,f71]) ).
fof(f71,plain,
singleton(sK0) = sF8,
introduced(function_definition,[]) ).
fof(f62,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f42]) ).
fof(f42,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,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])],[f18,f19]) ).
fof(f19,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(f18,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,[],[f17]) ).
fof(f17,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,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.ALSEEmx1gK/Vampire---4.8_30550',d1_tarski) ).
fof(f149,plain,
! [X0] :
( in(X0,sF8)
| ~ in(X0,sK2)
| ~ in(X0,sF9) ),
inference(superposition,[],[f68,f75]) ).
fof(f75,plain,
sF8 = set_intersection2(sF9,sK2),
inference(backward_demodulation,[],[f73,f74]) ).
fof(f74,plain,
sF8 = sF10,
inference(definition_folding,[],[f35,f73,f72,f71]) ).
fof(f72,plain,
unordered_pair(sK0,sK1) = sF9,
introduced(function_definition,[]) ).
fof(f35,plain,
singleton(sK0) = set_intersection2(unordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( sK0 != sK1
& in(sK1,sK2)
& singleton(sK0) = set_intersection2(unordered_pair(sK0,sK1),sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f15]) ).
fof(f15,plain,
( ? [X0,X1,X2] :
( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) )
=> ( sK0 != sK1
& in(sK1,sK2)
& singleton(sK0) = set_intersection2(unordered_pair(sK0,sK1),sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1,X2] :
( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/tmp/tmp.ALSEEmx1gK/Vampire---4.8_30550',t59_zfmisc_1) ).
fof(f73,plain,
set_intersection2(sF9,sK2) = sF10,
introduced(function_definition,[]) ).
fof(f68,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X1)
& in(sK5(X0,X1,X2),X0) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X1)
& in(sK5(X0,X1,X2),X0) )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ALSEEmx1gK/Vampire---4.8_30550',d3_xboole_0) ).
fof(f78,plain,
in(sK1,sF9),
inference(superposition,[],[f64,f72]) ).
fof(f64,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f63]) ).
fof(f63,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f48]) ).
fof(f48,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ( ( ( sK4(X0,X1,X2) != X1
& sK4(X0,X1,X2) != X0 )
| ~ in(sK4(X0,X1,X2),X2) )
& ( sK4(X0,X1,X2) = X1
| sK4(X0,X1,X2) = X0
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) )
=> ( ( ( sK4(X0,X1,X2) != X1
& sK4(X0,X1,X2) != X0 )
| ~ in(sK4(X0,X1,X2),X2) )
& ( sK4(X0,X1,X2) = X1
| sK4(X0,X1,X2) = X0
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ALSEEmx1gK/Vampire---4.8_30550',d2_tarski) ).
fof(f36,plain,
in(sK1,sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET918+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
% 0.19/0.36 % Computer : n013.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Sat Aug 26 14:14:17 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.19/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.19/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.ALSEEmx1gK/Vampire---4.8_30550
% 0.19/0.37 % (30708)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.40 % (30710)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)
% 0.23/0.42 % (30709)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_1169 on Vampire---4 for (1169ds/0Mi)
% 0.23/0.42 % (30712)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.23/0.42 % (30711)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.23/0.42 % (30713)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.23/0.42 % (30714)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.23/0.42 % (30715)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_501 on Vampire---4 for (501ds/0Mi)
% 0.23/0.43 % (30711)First to succeed.
% 0.23/0.43 % (30712)Also succeeded, but the first one will report.
% 0.23/0.43 % (30715)Also succeeded, but the first one will report.
% 0.23/0.43 % (30711)Refutation found. Thanks to Tanya!
% 0.23/0.43 % SZS status Theorem for Vampire---4
% 0.23/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.43 % (30711)------------------------------
% 0.23/0.43 % (30711)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.43 % (30711)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.43 % (30711)Termination reason: Refutation
% 0.23/0.43
% 0.23/0.43 % (30711)Memory used [KB]: 1023
% 0.23/0.43 % (30711)Time elapsed: 0.007 s
% 0.23/0.43 % (30711)------------------------------
% 0.23/0.43 % (30711)------------------------------
% 0.23/0.43 % (30708)Success in time 0.065 s
% 0.23/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------