%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT382+1 : 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 : n007.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 11:47:33 AM UTC 2026
% Result : Theorem 2.72s 1.35s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 18 unt; 0 def)
% Number of atoms : 183 ( 9 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 228 ( 101 ~; 95 |; 23 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 60 !; 3 ?)
% 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(f12,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> ! [X2] :
( aInfimumOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( aLowerBoundOfIn0(X3,X1,X0)
=> sdtlseqdt0(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInf) ).
fof(f15,axiom,
aSet0(xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).
fof(f16,axiom,
aSubsetOf0(xS,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773_01) ).
fof(f17,axiom,
( aInfimumOfIn0(xu,xS,xT)
& aInfimumOfIn0(xv,xS,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__792) ).
fof(f18,conjecture,
xu = xv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
xu != xv,
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
xu != xv,
inference(flattening,[],[f19]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( aInfimumOfIn0(X2,X1,X0)
<=> ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0) ) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f26]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aLowerBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aLowerBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ? [X3] :
( ~ sdtlseqdt0(X3,X2)
& aLowerBoundOfIn0(X3,X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aLowerBoundOfIn0(X4,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( aInfimumOfIn0(X2,X1,X0)
| ~ aElementOf0(X2,X0)
| ~ aLowerBoundOfIn0(X2,X1,X0)
| ( ~ sdtlseqdt0(sK1(X0,X1,X2),X2)
& aLowerBoundOfIn0(sK1(X0,X1,X2),X1,X0) ) )
& ( ( aElementOf0(X2,X0)
& aLowerBoundOfIn0(X2,X1,X0)
& ! [X4] :
( sdtlseqdt0(X4,X2)
| ~ aLowerBoundOfIn0(X4,X1,X0) ) )
| ~ aInfimumOfIn0(X2,X1,X0) ) )
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f39]) ).
fof(f45,plain,
aSet0(xT),
inference(cnf_transformation,[],[f15]) ).
fof(f46,plain,
aSubsetOf0(xS,xT),
inference(cnf_transformation,[],[f16]) ).
fof(f47,plain,
aInfimumOfIn0(xv,xS,xT),
inference(cnf_transformation,[],[f17]) ).
fof(f48,plain,
aInfimumOfIn0(xu,xS,xT),
inference(cnf_transformation,[],[f17]) ).
fof(f49,plain,
xu != xv,
inference(cnf_transformation,[],[f20]) ).
fof(f54,plain,
! [X2,X0,X1,X4] :
( ~ aInfimumOfIn0(X2,X1,X0)
| ~ aLowerBoundOfIn0(X4,X1,X0)
| sdtlseqdt0(X4,X2)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f55,plain,
! [X2,X0,X1] :
( aLowerBoundOfIn0(X2,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ aInfimumOfIn0(X2,X1,X0)
| aElementOf0(X2,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f59,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f86,plain,
( aElementOf0(xv,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f56,f47]) ).
fof(f87,plain,
( aElementOf0(xu,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f56,f48]) ).
fof(f88,plain,
( aElementOf0(xu,xT)
| ~ aSet0(xT) ),
inference(forward_subsumption_resolution,[],[f87,f46]) ).
fof(f89,plain,
( aElementOf0(xv,xT)
| ~ aSet0(xT) ),
inference(forward_subsumption_resolution,[],[f86,f46]) ).
fof(f90,plain,
aElementOf0(xu,xT),
inference(forward_subsumption_resolution,[],[f88,f45]) ).
fof(f91,plain,
aElementOf0(xv,xT),
inference(forward_subsumption_resolution,[],[f89,f45]) ).
fof(f92,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(resolution,[],[f90,f66]) ).
fof(f93,plain,
aElement0(xu),
inference(forward_subsumption_resolution,[],[f92,f45]) ).
fof(f94,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(resolution,[],[f91,f66]) ).
fof(f95,plain,
aElement0(xv),
inference(forward_subsumption_resolution,[],[f94,f45]) ).
fof(f110,plain,
! [X0] :
( ~ aLowerBoundOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xv)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f54,f47]) ).
fof(f111,plain,
! [X0] :
( ~ aLowerBoundOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xu)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f54,f48]) ).
fof(f112,plain,
! [X0] :
( ~ aLowerBoundOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xu)
| ~ aSet0(xT) ),
inference(forward_subsumption_resolution,[],[f111,f46]) ).
fof(f113,plain,
! [X0] :
( ~ aLowerBoundOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xv)
| ~ aSet0(xT) ),
inference(forward_subsumption_resolution,[],[f110,f46]) ).
fof(f114,plain,
! [X0] :
( ~ aLowerBoundOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xu) ),
inference(forward_subsumption_resolution,[],[f112,f45]) ).
fof(f115,plain,
! [X0] :
( ~ aLowerBoundOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xv) ),
inference(forward_subsumption_resolution,[],[f113,f45]) ).
fof(f116,plain,
! [X0] :
( sdtlseqdt0(X0,xu)
| ~ aInfimumOfIn0(X0,xS,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f114,f55]) ).
fof(f117,plain,
! [X0] :
( sdtlseqdt0(X0,xu)
| ~ aInfimumOfIn0(X0,xS,xT)
| ~ aSet0(xT) ),
inference(forward_subsumption_resolution,[],[f116,f46]) ).
fof(f118,plain,
! [X0] :
( ~ aInfimumOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xu) ),
inference(forward_subsumption_resolution,[],[f117,f45]) ).
fof(f119,plain,
! [X0] :
( sdtlseqdt0(X0,xv)
| ~ aInfimumOfIn0(X0,xS,xT)
| ~ aSubsetOf0(xS,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f115,f55]) ).
fof(f120,plain,
! [X0] :
( sdtlseqdt0(X0,xv)
| ~ aInfimumOfIn0(X0,xS,xT)
| ~ aSet0(xT) ),
inference(forward_subsumption_resolution,[],[f119,f46]) ).
fof(f121,plain,
! [X0] :
( ~ aInfimumOfIn0(X0,xS,xT)
| sdtlseqdt0(X0,xv) ),
inference(forward_subsumption_resolution,[],[f120,f45]) ).
fof(f125,plain,
sdtlseqdt0(xv,xu),
inference(resolution,[],[f118,f47]) ).
fof(f129,plain,
( ~ sdtlseqdt0(xu,xv)
| xu = xv
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(resolution,[],[f125,f59]) ).
fof(f130,plain,
( ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(forward_subsumption_resolution,[],[f129,f49]) ).
fof(f131,plain,
( ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ),
inference(forward_subsumption_resolution,[],[f130,f93]) ).
fof(f132,plain,
~ sdtlseqdt0(xu,xv),
inference(forward_subsumption_resolution,[],[f131,f95]) ).
fof(f463,plain,
sdtlseqdt0(xu,xv),
inference(resolution,[],[f121,f48]) ).
fof(f464,plain,
$false,
inference(forward_subsumption_resolution,[],[f463,f132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT382+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:10:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.72/1.35 % (1566829)Detected formulas, will run a generic FOF schedule.
% 2.72/1.35 % (1566838)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=571988559:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.35 % (1566838)First to succeed.
% 2.72/1.35 % (1566838)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1566829"
% 2.72/1.35 % (1566837)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2918582608:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.35 % (1566839)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2364116403:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.35 % (1566840)dis-21_1_sil=8000:lcm=predicate:random_seed=3090409439: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)
% 2.72/1.35 % (1566836)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=3006303491:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.35 % (1566834)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=1479814313:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.35 % (1566835)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=1722113516:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.35 % (1566837)Refutation not found, incomplete strategy
% 2.72/1.35 % (1566837)------------------------------
% 2.72/1.35 % (1566837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.35 % (1566837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.35 % (1566837)CaDiCaL version: 2.1.3
% 2.72/1.35 % (1566837)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.35 % (1566837)Time elapsed: 0.002 s
% 2.72/1.35 % (1566837)Peak memory usage: 88 MB
% 2.72/1.35 % (1566837)Instructions burned: 1 (million)
% 2.72/1.35 % (1566840)Also succeeded, but the first one will report.
% 2.72/1.35 % (1566839)Also succeeded, but the first one will report.
% 2.72/1.35 % (1566838)Refutation found. Thanks to Tanya!
% 2.72/1.35 % SZS status Theorem for theBenchmark
% 2.72/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.36 % (1566838)------------------------------
% 2.72/1.36 % (1566838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.36 % (1566838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.36 % (1566838)CaDiCaL version: 2.1.3
% 2.72/1.36 % (1566838)Termination reason: Refutation
% 2.72/1.36 % (1566838)Time elapsed: 0.012 s
% 2.72/1.36 % (1566838)Peak memory usage: 88 MB
% 2.72/1.36 % (1566838)Instructions burned: 46 (million)
% 2.72/1.36 % (1566838)------------------------------
% 2.72/1.36 % (1566838)------------------------------
% 2.72/1.36 % (1566829)Success in time 0.302 s
% 2.72/1.36 % Vampire exiting
%------------------------------------------------------------------------------