%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU511^2 : 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 : n005.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 08:29:52 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 219 ( 71 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 126 ( 29 ~; 19 |; 10 &; 55 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 44 ( 5 ^; 29 !; 10 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
emptysetE: $o ).
thf(func_def_4,type,
nonempty: $i > $o ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK3: $o ).
thf(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(f2,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f3,conjecture,
( emptysetE
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(f4,negated_conjecture,
~ ( emptysetE
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f6,plain,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) )
<=> ( emptysetE = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( emptysetE
=> ! [X0: $i] :
( ? [X1: $i] : ( in @ X1 @ X0 )
=> ( nonempty @ X0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
~ ( ( emptysetE = $true )
=> ! [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
=> ( ( nonempty @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true )
& ( ( nonempty @ X0 )
!= $true ) )
& ( emptysetE = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
<=> ( emptysetE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f12,plain,
( ( ( in @ sK1 @ sK0 )
= $true )
& ( ( nonempty @ sK0 )
!= $true )
& ( emptysetE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f10]) ).
thf(f13,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f14,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X2: $i] :
( ( ( in @ X2 @ emptyset )
= $true )
& ? [X3: $o] : ( $true != X3 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f15,plain,
( ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ( ( ( in @ sK2 @ emptyset )
= $true )
& ( sK3 != $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2),skolemize(X3,sK3)],[f14]) ).
thf(f16,plain,
emptysetE = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( ( nonempty @ sK0 )
!= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f21,plain,
! [X0: $i,X1: $o] :
( ( emptysetE != $true )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( $true = X1 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f22,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f25,plain,
! [X0: $i,X1: $o] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( $true = X1 ) ),
inference(forward_subsumption_resolution,[],[f21,f16]) ).
thf(f26,plain,
! [X1: $i] :
( ( nonempty @ X1 )
= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X1 ) ),
inference(argument_congruence,[],[f22]) ).
thf(f27,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ X1 ) )
| ( ( nonempty @ X1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f32,plain,
! [X1: $i] :
( ( $false
= ( emptyset != X1 ) )
| ( ( nonempty @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f33,plain,
! [X1: $i] :
( ( ( emptyset = X1 )
= $true )
| ( ( nonempty @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X1: $i] :
( ( ( nonempty @ X1 )
= $true )
| ( emptyset = X1 ) ),
inference(equality_proxy_clausification,[],[f33]) ).
thf(f37,plain,
( ( $true != $true )
| ( emptyset = sK0 ) ),
inference(superposition,[],[f17,f34]) ).
thf(f39,plain,
emptyset = sK0,
inference(trivial_inequality_removal,[],[f37]) ).
thf(f40,plain,
( ( in @ sK1 @ emptyset )
= $true ),
inference(superposition,[],[f18,f39]) ).
thf(f41,plain,
( ( nonempty @ emptyset )
!= $true ),
inference(superposition,[],[f17,f39]) ).
thf(f44,plain,
! [X0: $o] :
( ( $true != $true )
| ( $true = X0 ) ),
inference(superposition,[],[f25,f40]) ).
thf(f45,plain,
! [X0: $o] : ( $true = X0 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f50,plain,
$true != $true,
inference(superposition,[],[f41,f45]) ).
thf(f52,plain,
$false,
inference(trivial_inequality_removal,[],[f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU511^2 : 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 : n005.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 13:47:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 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
% 0.09/0.28 % (1690553)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.28 % (1690577)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3352158029:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.28 % (1690577) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1690553-1690577"...
% 0.09/0.28 % (1690577)...printing done.
% 0.09/0.28 % (1690579)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.28 % (1690579)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
% 0.09/0.28 % (1690577)Refutation found. Thanks to Tanya!
% 0.09/0.28 % SZS status Theorem for theBenchmark
% 0.09/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.28 % (1690577)------------------------------
% 0.09/0.28 % (1690577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1690577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1690577)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1690577)Termination reason: Refutation
% 0.09/0.28 % (1690577)Time elapsed: 0.001 s
% 0.09/0.28 % (1690577)Peak memory usage: 12 MB
% 0.09/0.28 % (1690577)Instructions burned: 3 (million)
% 0.09/0.28 % (1690553)Success in time 0.032 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------