TSTP Solution File: SET199+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET199+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Tue Apr 30 15:07:10 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 106 ( 44 ~; 29 |; 25 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 44 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f73,plain,
$false,
inference(resolution,[],[f69,f25]) ).
fof(f25,plain,
~ subset(sK0,intersection(sK1,sK2)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
( ~ subset(sK0,intersection(sK1,sK2))
& subset(sK0,sK2)
& subset(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f11]) ).
fof(f11,plain,
( ? [X0,X1,X2] :
( ~ subset(X0,intersection(X1,X2))
& subset(X0,X2)
& subset(X0,X1) )
=> ( ~ subset(sK0,intersection(sK1,sK2))
& subset(sK0,sK2)
& subset(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
? [X0,X1,X2] :
( ~ subset(X0,intersection(X1,X2))
& subset(X0,X2)
& subset(X0,X1) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
? [X0,X1,X2] :
( ~ subset(X0,intersection(X1,X2))
& subset(X0,X2)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subsets) ).
fof(f69,plain,
subset(sK0,intersection(sK1,sK2)),
inference(resolution,[],[f68,f33]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f68,plain,
~ member(sK4(sK0,intersection(sK1,sK2)),sK0),
inference(duplicate_literal_removal,[],[f65]) ).
fof(f65,plain,
( ~ member(sK4(sK0,intersection(sK1,sK2)),sK0)
| ~ member(sK4(sK0,intersection(sK1,sK2)),sK0) ),
inference(resolution,[],[f64,f23]) ).
fof(f23,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f64,plain,
! [X0] :
( ~ subset(X0,sK1)
| ~ member(sK4(sK0,intersection(sK1,sK2)),X0)
| ~ member(sK4(sK0,intersection(sK1,sK2)),sK0) ),
inference(resolution,[],[f61,f32]) ).
fof(f32,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f61,plain,
( ~ member(sK4(sK0,intersection(sK1,sK2)),sK1)
| ~ member(sK4(sK0,intersection(sK1,sK2)),sK0) ),
inference(resolution,[],[f60,f24]) ).
fof(f24,plain,
subset(sK0,sK2),
inference(cnf_transformation,[],[f12]) ).
fof(f60,plain,
! [X0] :
( ~ subset(X0,sK2)
| ~ member(sK4(sK0,intersection(sK1,sK2)),X0)
| ~ member(sK4(sK0,intersection(sK1,sK2)),sK1) ),
inference(resolution,[],[f54,f32]) ).
fof(f54,plain,
( ~ member(sK4(sK0,intersection(sK1,sK2)),sK2)
| ~ member(sK4(sK0,intersection(sK1,sK2)),sK1) ),
inference(resolution,[],[f37,f40]) ).
fof(f40,plain,
~ member(sK4(sK0,intersection(sK1,sK2)),intersection(sK1,sK2)),
inference(resolution,[],[f34,f25]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET199+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n006.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 30 01:07:50 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % (15384)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (15387)WARNING: value z3 for option sas not known
% 0.15/0.32 % (15389)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 theBenchmark for (531ds/0Mi)
% 0.15/0.32 % (15386)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.32 % (15388)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.32 % (15390)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 theBenchmark for (522ds/0Mi)
% 0.15/0.32 % (15387)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 theBenchmark for (569ds/0Mi)
% 0.15/0.32 TRYING [1]
% 0.15/0.32 TRYING [2]
% 0.15/0.32 TRYING [3]
% 0.15/0.32 % (15390)First to succeed.
% 0.15/0.32 TRYING [4]
% 0.15/0.33 % (15390)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.33 % (15390)------------------------------
% 0.15/0.33 % (15390)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.33 % (15390)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (15390)Memory used [KB]: 835
% 0.15/0.33 % (15390)Time elapsed: 0.005 s
% 0.15/0.33 % (15390)Instructions burned: 6 (million)
% 0.15/0.33 % (15390)------------------------------
% 0.15/0.33 % (15390)------------------------------
% 0.15/0.33 % (15384)Success in time 0.018 s
%------------------------------------------------------------------------------