TSTP Solution File: SWC405+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC405+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : Sun May 5 10:26:49 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 31
% Syntax : Number of formulae : 77 ( 44 unt; 0 def)
% Number of atoms : 290 ( 30 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 300 ( 87 ~; 66 |; 111 &)
% ( 16 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 17 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 69 ( 31 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f722,plain,
$false,
inference(avatar_sat_refutation,[],[f646,f651,f656,f661,f666,f670,f674,f680,f685,f690,f695,f700,f705,f710,f715,f720,f721]) ).
fof(f721,plain,
( ~ spl70_3
| spl70_4
| ~ spl70_5
| ~ spl70_6 ),
inference(avatar_split_clause,[],[f675,f668,f663,f658,f653]) ).
fof(f653,plain,
( spl70_3
<=> ssItem(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_3])]) ).
fof(f658,plain,
( spl70_4
<=> memberP(sK21,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_4])]) ).
fof(f663,plain,
( spl70_5
<=> memberP(sK20,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_5])]) ).
fof(f668,plain,
( spl70_6
<=> ! [X5] :
( ~ memberP(sK20,X5)
| memberP(sK21,X5)
| ~ ssItem(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_6])]) ).
fof(f675,plain,
( memberP(sK21,sK22)
| ~ ssItem(sK22)
| ~ spl70_5
| ~ spl70_6 ),
inference(resolution,[],[f669,f665]) ).
fof(f665,plain,
( memberP(sK20,sK22)
| ~ spl70_5 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f669,plain,
( ! [X5] :
( ~ memberP(sK20,X5)
| memberP(sK21,X5)
| ~ ssItem(X5) )
| ~ spl70_6 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f720,plain,
spl70_16,
inference(avatar_split_clause,[],[f395,f717]) ).
fof(f717,plain,
( spl70_16
<=> ssList(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_16])]) ).
fof(f395,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f715,plain,
spl70_15,
inference(avatar_split_clause,[],[f394,f712]) ).
fof(f712,plain,
( spl70_15
<=> totalorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_15])]) ).
fof(f394,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f710,plain,
spl70_14,
inference(avatar_split_clause,[],[f393,f707]) ).
fof(f707,plain,
( spl70_14
<=> strictorderedP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_14])]) ).
fof(f393,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f705,plain,
spl70_13,
inference(avatar_split_clause,[],[f392,f702]) ).
fof(f702,plain,
( spl70_13
<=> totalorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_13])]) ).
fof(f392,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f700,plain,
spl70_12,
inference(avatar_split_clause,[],[f391,f697]) ).
fof(f697,plain,
( spl70_12
<=> strictorderP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_12])]) ).
fof(f391,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f695,plain,
spl70_11,
inference(avatar_split_clause,[],[f390,f692]) ).
fof(f692,plain,
( spl70_11
<=> cyclefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_11])]) ).
fof(f390,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f690,plain,
spl70_10,
inference(avatar_split_clause,[],[f389,f687]) ).
fof(f687,plain,
( spl70_10
<=> duplicatefreeP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_10])]) ).
fof(f389,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f685,plain,
spl70_9,
inference(avatar_split_clause,[],[f388,f682]) ).
fof(f682,plain,
( spl70_9
<=> equalelemsP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_9])]) ).
fof(f388,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f680,plain,
~ spl70_8,
inference(avatar_split_clause,[],[f387,f677]) ).
fof(f677,plain,
( spl70_8
<=> singletonP(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_8])]) ).
fof(f387,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f674,plain,
spl70_7,
inference(avatar_split_clause,[],[f383,f672]) ).
fof(f672,plain,
( spl70_7
<=> ! [X5] :
( ~ memberP(sK21,X5)
| memberP(sK20,X5)
| ~ ssItem(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_7])]) ).
fof(f383,plain,
! [X5] :
( ~ memberP(sK21,X5)
| memberP(sK20,X5)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
( ~ memberP(sK19,sK22)
& memberP(sK18,sK22)
& ssItem(sK22)
& ! [X5] :
( ( ( ~ memberP(sK21,X5)
| memberP(sK20,X5) )
& ( ~ memberP(sK20,X5)
| memberP(sK21,X5) ) )
| ~ ssItem(X5) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f100,f255,f254,f253,f252,f251]) ).
fof(f251,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(X2,X5) )
& ( ~ memberP(X2,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK18,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(X2,X5) )
& ( ~ memberP(X2,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ memberP(X1,X4)
& memberP(sK18,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(X2,X5) )
& ( ~ memberP(X2,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ memberP(sK19,X4)
& memberP(sK18,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(X2,X5) )
& ( ~ memberP(X2,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ memberP(sK19,X4)
& memberP(sK18,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(X2,X5) )
& ( ~ memberP(X2,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ? [X4] :
( ~ memberP(sK19,X4)
& memberP(sK18,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(sK20,X5) )
& ( ~ memberP(sK20,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X3] :
( ? [X4] :
( ~ memberP(sK19,X4)
& memberP(sK18,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(sK20,X5) )
& ( ~ memberP(sK20,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ? [X4] :
( ~ memberP(sK19,X4)
& memberP(sK18,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(sK21,X5)
| memberP(sK20,X5) )
& ( ~ memberP(sK20,X5)
| memberP(sK21,X5) ) )
| ~ ssItem(X5) )
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
( ? [X4] :
( ~ memberP(sK19,X4)
& memberP(sK18,X4)
& ssItem(X4) )
=> ( ~ memberP(sK19,sK22)
& memberP(sK18,sK22)
& ssItem(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(X2,X5) )
& ( ~ memberP(X2,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ memberP(X1,X4)
& memberP(X0,X4)
& ssItem(X4) )
& ! [X5] :
( ( ( ~ memberP(X3,X5)
| memberP(X2,X5) )
& ( ~ memberP(X2,X5)
| memberP(X3,X5) ) )
| ~ ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| ? [X5] :
( ( ( memberP(X3,X5)
& ~ memberP(X2,X5) )
| ( memberP(X2,X5)
& ~ memberP(X3,X5) ) )
& ssItem(X5) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X5] :
( ssItem(X5)
=> ( memberP(X1,X5)
| ~ memberP(X0,X5) ) )
| ? [X4] :
( ( ( memberP(X3,X4)
& ~ memberP(X2,X4) )
| ( memberP(X2,X4)
& ~ memberP(X3,X4) ) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X5] :
( ssItem(X5)
=> ( memberP(X1,X5)
| ~ memberP(X0,X5) ) )
| ? [X4] :
( ( ( memberP(X3,X4)
& ~ memberP(X2,X4) )
| ( memberP(X2,X4)
& ~ memberP(X3,X4) ) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f670,plain,
spl70_6,
inference(avatar_split_clause,[],[f382,f668]) ).
fof(f382,plain,
! [X5] :
( ~ memberP(sK20,X5)
| memberP(sK21,X5)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f256]) ).
fof(f666,plain,
spl70_5,
inference(avatar_split_clause,[],[f605,f663]) ).
fof(f605,plain,
memberP(sK20,sK22),
inference(definition_unfolding,[],[f385,f381]) ).
fof(f381,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f256]) ).
fof(f385,plain,
memberP(sK18,sK22),
inference(cnf_transformation,[],[f256]) ).
fof(f661,plain,
~ spl70_4,
inference(avatar_split_clause,[],[f604,f658]) ).
fof(f604,plain,
~ memberP(sK21,sK22),
inference(definition_unfolding,[],[f386,f380]) ).
fof(f380,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f256]) ).
fof(f386,plain,
~ memberP(sK19,sK22),
inference(cnf_transformation,[],[f256]) ).
fof(f656,plain,
spl70_3,
inference(avatar_split_clause,[],[f384,f653]) ).
fof(f384,plain,
ssItem(sK22),
inference(cnf_transformation,[],[f256]) ).
fof(f651,plain,
spl70_2,
inference(avatar_split_clause,[],[f379,f648]) ).
fof(f648,plain,
( spl70_2
<=> ssList(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_2])]) ).
fof(f379,plain,
ssList(sK21),
inference(cnf_transformation,[],[f256]) ).
fof(f646,plain,
spl70_1,
inference(avatar_split_clause,[],[f378,f643]) ).
fof(f643,plain,
( spl70_1
<=> ssList(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl70_1])]) ).
fof(f378,plain,
ssList(sK20),
inference(cnf_transformation,[],[f256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC405+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 20:29:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (17547)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (17550)WARNING: value z3 for option sas not known
% 0.14/0.38 % (17551)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (17549)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (17548)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (17553)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)
% 0.14/0.38 % (17550)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)
% 0.14/0.38 % (17552)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)
% 0.14/0.38 % (17554)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)
% 0.21/0.39 % (17552)First to succeed.
% 0.21/0.39 % (17553)Also succeeded, but the first one will report.
% 0.21/0.39 % (17552)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17547"
% 0.21/0.39 % (17552)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.40 % (17552)------------------------------
% 0.21/0.40 % (17552)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40 % (17552)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (17552)Memory used [KB]: 1249
% 0.21/0.40 % (17552)Time elapsed: 0.013 s
% 0.21/0.40 % (17552)Instructions burned: 18 (million)
% 0.21/0.40 % (17547)Success in time 0.02 s
%------------------------------------------------------------------------------