TSTP Solution File: NUM385+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM385+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 : n026.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 14:21:56 EDT 2024
% Result : Theorem 0.10s 0.37s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 19 unt; 0 def)
% Number of atoms : 172 ( 45 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 193 ( 73 ~; 69 |; 34 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 105 ( 95 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2250,plain,
$false,
inference(subsumption_resolution,[],[f2244,f2158]) ).
fof(f2158,plain,
sP1(singleton(sK4),sK3,sK4),
inference(unit_resulting_resolution,[],[f110,f309,f135]) ).
fof(f135,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| sP1(X1,X4,X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP1(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X1,X4,X0) )
& ( sP1(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f75,f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) )
=> ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP1(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X1,X4,X0) )
& ( sP1(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP1(X1,X3,X0) )
& ( sP1(X1,X3,X0)
| ~ in(X3,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sP2(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP1(X1,X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f309,plain,
sP2(sK4,singleton(sK4),succ(sK3)),
inference(superposition,[],[f294,f102]) ).
fof(f102,plain,
succ(sK3) = succ(sK4),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( sK3 != sK4
& succ(sK3) = succ(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f44,f65]) ).
fof(f65,plain,
( ? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) )
=> ( sK3 != sK4
& succ(sK3) = succ(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X1] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(f294,plain,
! [X0] : sP2(X0,singleton(X0),succ(X0)),
inference(superposition,[],[f164,f112]) ).
fof(f112,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/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f164,plain,
! [X0,X1] : sP2(X0,X1,set_union2(X0,X1)),
inference(equality_resolution,[],[f142]) ).
fof(f142,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP2(X0,X1,X2) )
& ( sP2(X0,X1,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP2(X0,X1,X2) ),
inference(definition_folding,[],[f8,f63,f62]) ).
fof(f62,plain,
! [X1,X3,X0] :
( sP1(X1,X3,X0)
<=> ( in(X3,X1)
| in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f110,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f2244,plain,
~ sP1(singleton(sK4),sK3,sK4),
inference(unit_resulting_resolution,[],[f1066,f2215,f139]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| in(X1,X2)
| in(X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ~ in(X1,X0)
& ~ in(X1,X2) ) )
& ( in(X1,X0)
| in(X1,X2)
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f79]) ).
fof(f79,plain,
! [X1,X3,X0] :
( ( sP1(X1,X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ sP1(X1,X3,X0) ) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X1,X3,X0] :
( ( sP1(X1,X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ sP1(X1,X3,X0) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f2215,plain,
~ in(sK3,sK4),
inference(unit_resulting_resolution,[],[f2212,f124]) ).
fof(f124,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2212,plain,
in(sK4,sK3),
inference(unit_resulting_resolution,[],[f1067,f2126,f139]) ).
fof(f2126,plain,
sP1(singleton(sK3),sK4,sK3),
inference(unit_resulting_resolution,[],[f166,f294,f135]) ).
fof(f166,plain,
in(sK4,succ(sK3)),
inference(superposition,[],[f110,f102]) ).
fof(f1067,plain,
~ in(sK4,singleton(sK3)),
inference(unit_resulting_resolution,[],[f103,f163,f127]) ).
fof(f127,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f70,f71]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f163,plain,
! [X0] : sP0(X0,singleton(X0)),
inference(equality_resolution,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( sP0(X0,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f7,f60]) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f103,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f66]) ).
fof(f1066,plain,
~ in(sK3,singleton(sK4)),
inference(unit_resulting_resolution,[],[f103,f163,f127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:31:19 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (13425)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (13428)WARNING: value z3 for option sas not known
% 0.10/0.33 % (13427)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.33 % (13432)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)
% 0.10/0.33 % (13429)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.33 % (13430)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)
% 0.10/0.34 % (13431)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)
% 0.10/0.34 % (13428)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)
% 0.10/0.34 % (13426)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [3]
% 0.10/0.34 TRYING [4]
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.35 TRYING [5]
% 0.10/0.35 TRYING [3]
% 0.10/0.37 % (13432)First to succeed.
% 0.10/0.37 % (13432)Refutation found. Thanks to Tanya!
% 0.10/0.37 % SZS status Theorem for theBenchmark
% 0.10/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.37 % (13432)------------------------------
% 0.10/0.37 % (13432)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.37 % (13432)Termination reason: Refutation
% 0.10/0.37
% 0.10/0.37 % (13432)Memory used [KB]: 1368
% 0.10/0.37 % (13432)Time elapsed: 0.037 s
% 0.10/0.37 % (13432)Instructions burned: 71 (million)
% 0.10/0.37 % (13432)------------------------------
% 0.10/0.37 % (13432)------------------------------
% 0.10/0.37 % (13425)Success in time 0.052 s
%------------------------------------------------------------------------------