%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU541^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:29:59 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 178 ( 52 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 130 ( 23 ~; 15 |; 10 &; 69 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 20 ( 4 ^; 13 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
prop2set: $o > $i ).
thf(func_def_3,type,
prop2setI: $o ).
thf(func_def_5,type,
set2prop: $i > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $o ).
thf(func_def_11,type,
sK1: $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(f1,axiom,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(f2,axiom,
( set2prop
= ( ^ [X0: $i] : ( in @ emptyset @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set2prop) ).
thf(f3,conjecture,
( prop2setI
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(f4,negated_conjecture,
~ ( prop2setI
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( prop2setI
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( prop2setI = $true )
=> ! [X0: $o] :
( ( $true = X0 )
=> ( ( set2prop @ ( prop2set @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( set2prop
= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f8,plain,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ( prop2setI = $true )
<=> ! [X0: $o] :
( ( $true = X0 )
=> ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ( prop2setI = $true )
<=> ! [X0: $o] :
( ( $true != X0 )
| ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ( prop2setI = $true )
& ? [X0: $o] :
( ( $true = X0 )
& ( ( set2prop @ ( prop2set @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ( ( prop2setI = $true )
| ? [X0: $o] :
( ( $true = X0 )
& ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true ) ) )
& ( ! [X0: $o] :
( ( $true != X0 )
| ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true ) )
| ( prop2setI != $true ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f13,plain,
( ( ( prop2setI = $true )
| ? [X0: $o] :
( ( $true = X0 )
& ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true ) ) )
& ( ! [X1: $o] :
( ( $true != X1 )
| ( ( in @ emptyset @ ( prop2set @ X1 ) )
= $true ) )
| ( prop2setI != $true ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ( prop2setI = $true )
| ( ( sK0 = $true )
& ( ( in @ emptyset @ ( prop2set @ sK0 ) )
!= $true ) ) )
& ( ! [X1: $o] :
( ( $true != X1 )
| ( ( in @ emptyset @ ( prop2set @ X1 ) )
= $true ) )
| ( prop2setI != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f13]) ).
thf(f15,plain,
( ( prop2setI = $true )
& ( sK1 = $true )
& ( $true
!= ( set2prop @ ( prop2set @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11]) ).
thf(f16,plain,
! [X1: $o] :
( ( $true != X1 )
| ( ( in @ emptyset @ ( prop2set @ X1 ) )
= $true )
| ( prop2setI != $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( set2prop
= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f20,plain,
( $true
!= ( set2prop @ ( prop2set @ sK1 ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
sK1 = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f22,plain,
prop2setI = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
! [X1: $o] :
( ( $true != X1 )
| ( ( in @ emptyset @ ( prop2set @ X1 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f16,f22]) ).
thf(f28,plain,
( ( ^ [Y0: $i] : ( in @ emptyset @ Y0 )
@ ( prop2set @ $true ) )
!= $true ),
inference(definition_unfolding,[],[f20,f19,f21]) ).
thf(f29,plain,
( ( $true != $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(equality_resolution,[],[f27]) ).
thf(f30,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
( ( in @ emptyset @ ( prop2set @ $true ) )
!= $true ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f32,plain,
$false,
inference(forward_subsumption_resolution,[],[f31,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU541^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:49:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.28 % (2885577)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (2885587)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3545874393:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.28 % (2885587) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2885577-2885587"...
% 0.22/0.28 % (2885587)...printing done.
% 0.22/0.28 % (2885587)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (2885587)------------------------------
% 0.22/0.28 % (2885587)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2885587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2885587)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2885587)Termination reason: Refutation
% 0.22/0.28 % (2885587)Time elapsed: 0.001 s
% 0.22/0.28 % (2885587)Peak memory usage: 12 MB
% 0.22/0.28 % (2885587)Instructions burned: 1 (million)
% 0.22/0.28 % (2885577)Success in time 0.032 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------