%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT381+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:47:32 AM UTC 2026
% Result : Theorem 2.56s 1.33s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 23 unt; 5 def)
% Number of atoms : 197 ( 9 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 204 ( 64 ~; 61 |; 58 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 42 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f8,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
fof(f14,axiom,
aSet0(xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__725) ).
fof(f16,axiom,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(X0,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X0] :
( ( ( aElementOf0(X0,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,X0) ) )
| aUpperBoundOfIn0(X0,xS,xT) )
=> sdtlseqdt0(xu,X0) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(X0,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X0] :
( ( ( aElementOf0(X0,xT)
& ! [X1] :
( aElementOf0(X1,xS)
=> sdtlseqdt0(X1,X0) ) )
| aUpperBoundOfIn0(X0,xS,xT) )
=> sdtlseqdt0(xv,X0) )
& aSupremumOfIn0(xv,xS,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__744) ).
fof(f17,conjecture,
xu = xv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f18,negated_conjecture,
xu != xv,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f22,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [X0] :
( aElementOf0(X0,xS)
=> sdtlseqdt0(X0,xu) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X1] :
( ( ( aElementOf0(X1,xT)
& ! [X2] :
( aElementOf0(X2,xS)
=> sdtlseqdt0(X2,X1) ) )
| aUpperBoundOfIn0(X1,xS,xT) )
=> sdtlseqdt0(xu,X1) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X3] :
( aElementOf0(X3,xS)
=> sdtlseqdt0(X3,xv) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X4] :
( ( ( aElementOf0(X4,xT)
& ! [X5] :
( aElementOf0(X5,xS)
=> sdtlseqdt0(X5,X4) ) )
| aUpperBoundOfIn0(X4,xS,xT) )
=> sdtlseqdt0(xv,X4) )
& aSupremumOfIn0(xv,xS,xT) ),
inference(rectify,[],[f16]) ).
fof(f23,plain,
xu != xv,
inference(flattening,[],[f18]) ).
fof(f24,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f28]) ).
fof(f37,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [X0] :
( sdtlseqdt0(X0,xu)
| ~ aElementOf0(X0,xS) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X1] :
( sdtlseqdt0(xu,X1)
| ( ( ~ aElementOf0(X1,xT)
| ? [X2] :
( ~ sdtlseqdt0(X2,X1)
& aElementOf0(X2,xS) ) )
& ~ aUpperBoundOfIn0(X1,xS,xT) ) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X3] :
( sdtlseqdt0(X3,xv)
| ~ aElementOf0(X3,xS) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X4] :
( sdtlseqdt0(xv,X4)
| ( ( ~ aElementOf0(X4,xT)
| ? [X5] :
( ~ sdtlseqdt0(X5,X4)
& aElementOf0(X5,xS) ) )
& ~ aUpperBoundOfIn0(X4,xS,xT) ) )
& aSupremumOfIn0(xv,xS,xT) ),
inference(ennf_transformation,[],[f22]) ).
fof(f61,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [X0] :
( sdtlseqdt0(X0,xu)
| ~ aElementOf0(X0,xS) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [X1] :
( sdtlseqdt0(xu,X1)
| ( ( ~ aElementOf0(X1,xT)
| ( ~ sdtlseqdt0(sK6(X1),X1)
& aElementOf0(sK6(X1),xS) ) )
& ~ aUpperBoundOfIn0(X1,xS,xT) ) )
& aSupremumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [X3] :
( sdtlseqdt0(X3,xv)
| ~ aElementOf0(X3,xS) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [X4] :
( sdtlseqdt0(xv,X4)
| ( ( ~ aElementOf0(X4,xT)
| ( ~ sdtlseqdt0(sK7(X4),X4)
& aElementOf0(sK7(X4),xS) ) )
& ~ aUpperBoundOfIn0(X4,xS,xT) ) )
& aSupremumOfIn0(xv,xS,xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,sK6(X1)),skolemize(X5,sK7(X4))],[f37]) ).
fof(f62,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f70,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f90,plain,
aSet0(xT),
inference(cnf_transformation,[],[f14]) ).
fof(f95,plain,
! [X4] :
( ~ aUpperBoundOfIn0(X4,xS,xT)
| sdtlseqdt0(xv,X4) ),
inference(cnf_transformation,[],[f61]) ).
fof(f98,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(cnf_transformation,[],[f61]) ).
fof(f100,plain,
aElementOf0(xv,xT),
inference(cnf_transformation,[],[f61]) ).
fof(f103,plain,
! [X1] :
( ~ aUpperBoundOfIn0(X1,xS,xT)
| sdtlseqdt0(xu,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f106,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(cnf_transformation,[],[f61]) ).
fof(f108,plain,
aElementOf0(xu,xT),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
xu != xv,
inference(cnf_transformation,[],[f23]) ).
fof(f111,definition,
! [X0,X1] :
( sQ8_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ8_eqProxy])],[equality_proxy_definition]) ).
fof(f112,plain,
! [X0,X1] :
( sQ8_eqProxy(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(equality_proxy_replacement,[],[f70,f111]) ).
fof(f113,plain,
~ sQ8_eqProxy(xu,xv),
inference(equality_proxy_replacement,[],[f110,f111]) ).
fof(f119,plain,
sdtlseqdt0(xv,xu),
inference(resolution,[],[f95,f106]) ).
fof(f120,plain,
sdtlseqdt0(xu,xv),
inference(resolution,[],[f103,f98]) ).
fof(f166,plain,
( ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(resolution,[],[f112,f113]) ).
fof(f169,definition,
( spl9_5
<=> aElement0(xu) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f170,plain,
( ~ aElement0(xu)
| spl9_5 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,definition,
( spl9_6
<=> aElement0(xv) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f173,plain,
( ~ aElement0(xv)
| spl9_6 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f175,definition,
( spl9_7
<=> sdtlseqdt0(xu,xv) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
fof(f176,plain,
( ~ sdtlseqdt0(xu,xv)
| spl9_7 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,definition,
( spl9_8
<=> sdtlseqdt0(xv,xu) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
fof(f179,plain,
( ~ sdtlseqdt0(xv,xu)
| spl9_8 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( ~ spl9_6
| ~ spl9_5
| ~ spl9_8
| ~ spl9_7 ),
inference(avatar_split_clause,[],[f166,f175,f178,f169,f172]) ).
fof(f182,plain,
( ! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(xu,X0) )
| spl9_5 ),
inference(resolution,[],[f170,f62]) ).
fof(f183,plain,
( ~ aElementOf0(xu,xT)
| spl9_5 ),
inference(resolution,[],[f182,f90]) ).
fof(f187,plain,
( $false
| spl9_5 ),
inference(resolution,[],[f183,f108]) ).
fof(f188,plain,
spl9_5,
inference(avatar_contradiction_clause,[],[f187]) ).
fof(f189,plain,
( ! [X0] :
( ~ aSet0(X0)
| ~ aElementOf0(xv,X0) )
| spl9_6 ),
inference(resolution,[],[f173,f62]) ).
fof(f190,plain,
( ~ aElementOf0(xv,xT)
| spl9_6 ),
inference(resolution,[],[f189,f90]) ).
fof(f192,plain,
( $false
| spl9_6 ),
inference(resolution,[],[f190,f100]) ).
fof(f193,plain,
spl9_6,
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f194,plain,
( $false
| spl9_7 ),
inference(resolution,[],[f176,f120]) ).
fof(f198,plain,
spl9_7,
inference(avatar_contradiction_clause,[],[f194]) ).
fof(f210,plain,
( $false
| spl9_8 ),
inference(resolution,[],[f179,f119]) ).
fof(f214,plain,
spl9_8,
inference(avatar_contradiction_clause,[],[f210]) ).
cnf(s6,plain,
( ~ spl9_5
| ~ spl9_6
| ~ spl9_7
| ~ spl9_8 ),
inference(sat_conversion,[],[f181]) ).
cnf(s7,plain,
spl9_5,
inference(sat_conversion,[],[f188]) ).
cnf(s8,plain,
spl9_6,
inference(sat_conversion,[],[f193]) ).
cnf(s9,plain,
spl9_7,
inference(sat_conversion,[],[f198]) ).
cnf(s12,plain,
spl9_8,
inference(sat_conversion,[],[f214]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s6,s12,s9,s8,s7]) ).
fof(f226,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT381+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 15:07:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.56/1.33 % (2706321)Detected formulas, will run a generic FOF schedule.
% 2.56/1.33 % (2706332)dis-21_1_sil=8000:lcm=predicate:random_seed=797408629:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.56/1.33 % (2706332)First to succeed.
% 2.56/1.33 % (2706332)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2706321"
% 2.56/1.33 % (2706327)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3175075621:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.33 % (2706331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2161774888:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.33 % (2706329)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1918647286:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.33 % (2706328)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2048173672:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.33 % (2706326)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3604787138:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.33 % (2706329)Refutation not found, incomplete strategy
% 2.56/1.33 % (2706329)------------------------------
% 2.56/1.33 % (2706329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.33 % (2706329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.33 % (2706329)CaDiCaL version: 2.1.3
% 2.56/1.33 % (2706329)Termination reason: Refutation not found, incomplete strategy
% 2.56/1.33 % (2706329)Time elapsed: 0.004 s
% 2.56/1.33 % (2706329)Peak memory usage: 88 MB
% 2.56/1.33 % (2706329)Instructions burned: 4 (million)
% 2.56/1.33 % (2706331)Also succeeded, but the first one will report.
% 2.56/1.33 % (2706330)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3641641994:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.33 % (2706330)Also succeeded, but the first one will report.
% 2.56/1.33 % (2706332)Refutation found. Thanks to Tanya!
% 2.56/1.33 % SZS status Theorem for theBenchmark
% 2.56/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.33 % (2706332)------------------------------
% 2.56/1.33 % (2706332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.33 % (2706332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.33 % (2706332)CaDiCaL version: 2.1.3
% 2.56/1.33 % (2706332)Termination reason: Refutation
% 2.56/1.33 % (2706332)Time elapsed: 0.003 s
% 2.56/1.33 % (2706332)Peak memory usage: 89 MB
% 2.56/1.33 % (2706332)Instructions burned: 4 (million)
% 2.56/1.33 % (2706332)------------------------------
% 2.56/1.33 % (2706332)------------------------------
% 2.56/1.33 % (2706321)Success in time 0.271 s
% 2.56/1.33 % Vampire exiting
%------------------------------------------------------------------------------