TSTP Solution File: NUM531+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM531+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 14:32:22 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 122 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 134 ( 55 ~; 36 |; 30 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 40 ( 30 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f73,plain,
$false,
inference(avatar_sat_refutation,[],[f47,f52,f57,f61,f65,f70,f72]) ).
fof(f72,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_2
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f71,f68,f49,f54,f44]) ).
fof(f44,plain,
( spl2_1
<=> aSet0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f54,plain,
( spl2_3
<=> isFinite0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f49,plain,
( spl2_2
<=> isCountable0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f68,plain,
( spl2_6
<=> ! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f71,plain,
( ~ isFinite0(sK0)
| ~ aSet0(sK0)
| ~ spl2_2
| ~ spl2_6 ),
inference(resolution,[],[f69,f51]) ).
fof(f51,plain,
( isCountable0(sK0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f69,plain,
( ! [X0] :
( ~ isCountable0(X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f70,plain,
spl2_6,
inference(avatar_split_clause,[],[f33,f68]) ).
fof(f33,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> ~ isFinite0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(f65,plain,
spl2_5,
inference(avatar_split_clause,[],[f38,f63]) ).
fof(f63,plain,
( spl2_5
<=> ! [X0] :
( sK0 = X0
| aElementOf0(sK1(X0),X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f38,plain,
! [X0] :
( sK0 = X0
| aElementOf0(sK1(X0),X0)
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f36,f31]) ).
fof(f31,plain,
slcrc0 = sK0,
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( slcrc0 = sK0
& ! [X1] : ~ aElementOf0(X1,sK0)
& isCountable0(sK0)
& aSet0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f21]) ).
fof(f21,plain,
( ? [X0] :
( slcrc0 = X0
& ! [X1] : ~ aElementOf0(X1,X0)
& isCountable0(X0)
& aSet0(X0) )
=> ( slcrc0 = sK0
& ! [X1] : ~ aElementOf0(X1,sK0)
& isCountable0(sK0)
& aSet0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0] :
( slcrc0 = X0
& ! [X1] : ~ aElementOf0(X1,X0)
& isCountable0(X0)
& aSet0(X0) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0] :
( slcrc0 = X0
& ! [X1] : ~ aElementOf0(X1,X0)
& isCountable0(X0)
& aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> ~ ( slcrc0 = X0
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> ~ ( slcrc0 = X0
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f36,plain,
! [X0] :
( slcrc0 = X0
| aElementOf0(sK1(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ( slcrc0 = X0
| aElementOf0(sK1(X0),X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26]) ).
fof(f26,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0] :
( slcrc0 = X0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( slcrc0 = X0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f61,plain,
spl2_4,
inference(avatar_split_clause,[],[f30,f59]) ).
fof(f59,plain,
( spl2_4
<=> ! [X1] : ~ aElementOf0(X1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f30,plain,
! [X1] : ~ aElementOf0(X1,sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
spl2_3,
inference(avatar_split_clause,[],[f37,f54]) ).
fof(f37,plain,
isFinite0(sK0),
inference(definition_unfolding,[],[f32,f31]) ).
fof(f32,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
fof(f52,plain,
spl2_2,
inference(avatar_split_clause,[],[f29,f49]) ).
fof(f29,plain,
isCountable0(sK0),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
spl2_1,
inference(avatar_split_clause,[],[f28,f44]) ).
fof(f28,plain,
aSet0(sK0),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM531+2 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Tue Apr 30 00:18:02 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % (7109)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (7112)WARNING: value z3 for option sas not known
% 0.15/0.39 % (7114)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)
% 0.15/0.39 % (7113)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (7110)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (7111)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (7116)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)
% 0.15/0.39 % (7112)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)
% 0.15/0.39 % (7115)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)
% 0.15/0.39 % (7114)First to succeed.
% 0.15/0.39 Detected minimum model sizes of [1]
% 0.15/0.39 Detected maximum model sizes of [1]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (7113)Also succeeded, but the first one will report.
% 0.15/0.39 % (7110)Also succeeded, but the first one will report.
% 0.15/0.39 % (7114)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (7114)------------------------------
% 0.15/0.39 % (7114)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (7114)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (7114)Memory used [KB]: 755
% 0.15/0.39 % (7114)Time elapsed: 0.004 s
% 0.15/0.39 % (7114)Instructions burned: 3 (million)
% 0.15/0.39 % (7114)------------------------------
% 0.15/0.39 % (7114)------------------------------
% 0.15/0.39 % (7109)Success in time 0.019 s
%------------------------------------------------------------------------------