TSTP Solution File: SET882+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Sun May 5 09:19:36 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 97 ( 61 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 120 ( 49 ~; 42 |; 22 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 45 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f87,plain,
$false,
inference(subsumption_resolution,[],[f86,f23]) ).
fof(f23,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
( singleton(sK0) != set_difference(unordered_pair(sK0,sK1),singleton(sK1))
& sK0 != sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11]) ).
fof(f11,plain,
( ? [X0,X1] :
( singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1))
& X0 != X1 )
=> ( singleton(sK0) != set_difference(unordered_pair(sK0,sK1),singleton(sK1))
& sK0 != sK1 ) ),
introduced(choice_axiom,[]) ).
fof(f9,plain,
? [X0,X1] :
( singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1))
& X0 != X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( X0 != X1
=> singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( X0 != X1
=> singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(f86,plain,
sK0 = sK1,
inference(trivial_inequality_removal,[],[f79]) ).
fof(f79,plain,
( singleton(sK0) != singleton(sK0)
| sK0 = sK1 ),
inference(superposition,[],[f24,f71]) ).
fof(f71,plain,
! [X0,X1] :
( singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1))
| X0 = X1 ),
inference(resolution,[],[f68,f39]) ).
fof(f39,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f27]) ).
fof(f27,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK2(X0,X1) != X0
| ~ in(sK2(X0,X1),X1) )
& ( sK2(X0,X1) = X0
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f14,f15]) ).
fof(f15,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK2(X0,X1) != X0
| ~ in(sK2(X0,X1),X1) )
& ( sK2(X0,X1) = X0
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,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,[],[f13]) ).
fof(f13,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,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f68,plain,
! [X0,X1] :
( in(X0,singleton(X1))
| singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
inference(resolution,[],[f33,f38]) ).
fof(f38,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f37]) ).
fof(f37,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f28]) ).
fof(f28,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| singleton(X0) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| singleton(X0) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( singleton(X0) = set_difference(unordered_pair(X0,X1),X2)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f24,plain,
singleton(sK0) != set_difference(unordered_pair(sK0,sK1),singleton(sK1)),
inference(cnf_transformation,[],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 17:03:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (19640)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (19646)WARNING: value z3 for option sas not known
% 0.21/0.37 % (19645)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (19646)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)
% 0.21/0.37 % (19649)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)
% 0.21/0.37 % (19648)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)
% 0.21/0.37 % (19650)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 theBenchmark for (497ds/0Mi)
% 0.21/0.37 % (19644)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (19646)First to succeed.
% 0.21/0.38 TRYING [1]
% 0.21/0.38 % (19646)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19640"
% 0.21/0.38 TRYING [1]
% 0.21/0.38 % (19647)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 % (19649)Also succeeded, but the first one will report.
% 0.21/0.38 % (19646)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (19646)------------------------------
% 0.21/0.38 % (19646)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.38 % (19646)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (19646)Memory used [KB]: 832
% 0.21/0.38 % (19646)Time elapsed: 0.008 s
% 0.21/0.38 % (19646)Instructions burned: 7 (million)
% 0.21/0.38 % (19640)Success in time 0.024 s
%------------------------------------------------------------------------------