%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU575^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Wed Sep 30 08:30:08 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 314 ( 101 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 220 ( 42 ~; 35 |; 21 &; 100 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 35 !; 8 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
emptysetsubset: $o ).
thf(func_def_4,type,
setextsub: $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(f1,axiom,
( emptysetsubset
= ( ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(f2,axiom,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(f3,conjecture,
( emptysetsubset
=> ( setextsub
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f4,negated_conjecture,
~ ( emptysetsubset
=> ( setextsub
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ( setextsub = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( subset @ X1 @ X0 )
= $true )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( emptysetsubset
=> ( setextsub
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( emptysetsubset = $true )
=> ( ( setextsub = $true )
=> ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
=> ( emptyset = X0 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( emptysetsubset
= ( ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( emptysetsubset = $true )
<=> ! [X0: $i] :
( ( subset @ emptyset @ X0 )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( setextsub = $true )
<=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( setextsub = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ( ( subset @ X0 @ emptyset )
= $true ) )
& ( setextsub = $true )
& ( emptysetsubset = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
( ( setextsub = $true )
& ? [X0: $i] :
( ( emptyset != X0 )
& ( ( subset @ X0 @ emptyset )
= $true ) )
& ( emptysetsubset = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ( setextsub = $true )
& ( emptyset != sK0 )
& ( ( subset @ sK0 @ emptyset )
= $true )
& ( emptysetsubset = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
= $true )
& ( X2 != X3 )
& ( ( subset @ X2 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ( ( ( subset @ sK2 @ sK1 )
= $true )
& ( sK2 != sK1 )
& ( ( subset @ sK1 @ sK2 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1),skolemize(X3,sK2)],[f17]) ).
thf(f19,plain,
( ( ( emptysetsubset = $true )
| ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( subset @ emptyset @ X0 )
= $true )
| ( emptysetsubset != $true ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f20,plain,
( ( ( emptysetsubset = $true )
| ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( ( subset @ emptyset @ X1 )
= $true )
| ( emptysetsubset != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( emptysetsubset = $true )
| ( $true
!= ( subset @ emptyset @ sK3 ) ) )
& ( ! [X1: $i] :
( ( subset @ emptyset @ X1 )
= $true )
| ( emptysetsubset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f20]) ).
thf(f22,plain,
emptysetsubset = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
( ( subset @ sK0 @ emptyset )
= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
emptyset != sK0,
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
setextsub = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( setextsub != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f30,plain,
! [X1: $i] :
( ( ( subset @ emptyset @ X1 )
= $true )
| ( emptysetsubset != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f34,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( $true != $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(definition_unfolding,[],[f29,f25]) ).
thf(f39,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( subset @ emptyset @ X1 )
= $true ) ),
inference(definition_unfolding,[],[f30,f22]) ).
thf(f40,plain,
! [X1: $i] :
( ( subset @ emptyset @ X1 )
= $true ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f42,plain,
( ( emptyset = sK0 )
| ( $true != $true )
| ( ( subset @ emptyset @ sK0 )
!= $true ) ),
inference(constrained_superposition,[],[f41,f23]) ).
thf(f45,plain,
( ( ( subset @ emptyset @ sK0 )
!= $true )
| ( emptyset = sK0 ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f46,plain,
emptyset = sK0,
inference(forward_subsumption_resolution,[],[f45,f40]) ).
thf(f47,plain,
$false,
inference(forward_subsumption_resolution,[],[f46,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU575^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:51:04 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.12 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.16 % (138370)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.16 % (138381)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.16 % (138381)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.08/0.16 % (138377)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2241568301:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.16 % (138375)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1240399465:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.16 % (138378)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3115483941:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.08/0.16 % (138376)lrs+10_16_si=on:nwc=1.5:random_seed=1315972480:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.16 % (138379)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3113462865:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.16 % (138380)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2911371387:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.16 % (138381)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=405643567:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.16 % (138377)Refutation not found, incomplete strategy
% 0.08/0.16 % (138377)------------------------------
% 0.08/0.16 % (138377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (138377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (138377)CaDiCaL version: 2.1.3
% 0.08/0.16 % (138377)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.16 % (138377)Time elapsed: 0.001 s
% 0.08/0.16 % (138377)Peak memory usage: 12 MB
% 0.08/0.16 % (138377)Instructions burned: 1 (million)
% 0.08/0.16 % (138375) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-138370-138375"...
% 0.08/0.16 % (138376) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-138370-138376"...
% 0.08/0.16 % (138379) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-138370-138379"...
% 0.08/0.16 % (138377)------------------------------
% 0.08/0.16 % (138377)------------------------------
% 0.08/0.16 % (138380) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-138370-138380"...
% 0.08/0.16 % (138378) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-138370-138378"...
% 0.08/0.16 % (138375)...printing done.
% 0.08/0.16 % (138379)...printing done.
% 0.08/0.16 % (138376)...printing done.
% 0.08/0.16 % (138380)...printing done.
% 0.08/0.16 % (138375)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.16 % (138375)------------------------------
% 0.08/0.16 % (138375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (138375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (138375)CaDiCaL version: 2.1.3
% 0.08/0.16 % (138375)Termination reason: Refutation
% 0.08/0.16 % (138375)Time elapsed: 0.001 s
% 0.08/0.16 % (138375)Peak memory usage: 12 MB
% 0.08/0.16 % (138375)Instructions burned: 2 (million)
% 0.08/0.16 % (138370)Success in time 0.031 s
% 0.08/0.16 % Vampire exiting
%------------------------------------------------------------------------------