%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU814^2 : 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 : n014.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 08:31:39 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 378 ( 100 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 335 ( 35 ~; 31 |; 24 &; 204 @)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 11 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 74 ( 10 ^; 52 !; 12 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
subsetE: $o ).
thf(func_def_4,type,
transitiveset: $i > $o ).
thf(func_def_5,type,
transitivesetOp1: $o ).
thf(func_def_8,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vIMP: $o > $o > $o ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
sK8: $i > $i ).
thf(f1,axiom,
( subsetE
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(f2,axiom,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitiveset) ).
thf(f4,conjecture,
( subsetE
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X2: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivesetOp2) ).
thf(f5,negated_conjecture,
~ ( subsetE
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X2: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( subsetE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X2 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ X1 ) ) ) )
<=> ( subsetE = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
~ ( subsetE
=> ( transitivesetOp1
=> ! [X0: $i] :
( ( transitiveset @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( subsetE = $true )
=> ( ( transitivesetOp1 = $true )
=> ! [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
=> ! [X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( $true
= ( in @ X1 @ X2 ) )
=> ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f14,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) )
<=> ( subsetE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f15,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) ) ),
inference(flattening,[],[f14]) ).
thf(f17,plain,
( ? [X0: $i] :
( ? [X2: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
& ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( ( transitiveset @ X0 )
= $true ) )
& ( transitivesetOp1 = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f18,plain,
( ( subsetE = $true )
& ( transitivesetOp1 = $true )
& ? [X0: $i] :
( ( ( transitiveset @ X0 )
= $true )
& ? [X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X2 ) )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) ) ) ),
inference(flattening,[],[f17]) ).
thf(f19,plain,
( ( ( subsetE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
= ( subset @ X2 @ X1 ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X2 @ X1 ) ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[],[f15]) ).
thf(f20,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( subsetE = $true )
| ( ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
!= ( in @ sK2 @ sK0 ) )
& ( $true
= ( subset @ sK1 @ sK0 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f20]) ).
thf(f22,plain,
( ( subsetE = $true )
& ( transitivesetOp1 = $true )
& ( $true
= ( transitiveset @ sK3 ) )
& ( $true
= ( in @ sK4 @ sK5 ) )
& ( $true
= ( in @ sK5 @ sK3 ) )
& ( $true
!= ( in @ sK4 @ sK3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f18]) ).
thf(f26,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( subsetE != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f30,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f31,plain,
( $true
!= ( in @ sK4 @ sK3 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
( $true
= ( in @ sK5 @ sK3 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f33,plain,
( $true
= ( in @ sK4 @ sK5 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f34,plain,
( $true
= ( transitiveset @ sK3 ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f36,plain,
subsetE = $true,
inference(cnf_transformation,[],[f22]) ).
thf(f46,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) )
| ( $true != $true )
| ( $true
!= ( in @ X5 @ X4 ) ) ),
inference(definition_unfolding,[],[f26,f36]) ).
thf(f47,plain,
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) )
@ sK3 ) ),
inference(definition_unfolding,[],[f34,f30]) ).
thf(f52,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( subset @ Y0 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f53,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
=> ( subset @ Y0 @ sK3 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK3 )
=> ( subset @ X1 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK3 ) )
| ( $false
= ( in @ X1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f62,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ X4 ) )
| ( $true
= ( in @ X5 @ X3 ) )
| ( ( subset @ X4 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f64,plain,
! [X0: $i] :
( ( $true
= ( in @ sK4 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( subset @ sK5 @ X0 ) ) ),
inference(constrained_superposition,[],[f62,f33]) ).
thf(f65,plain,
! [X0: $i] :
( ( $true
!= ( subset @ sK5 @ X0 ) )
| ( $true
= ( in @ sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f67,plain,
( ( $false
= ( in @ sK5 @ sK3 ) )
| ( $true != $true )
| ( $true
= ( in @ sK4 @ sK3 ) ) ),
inference(constrained_superposition,[],[f65,f55]) ).
thf(f68,plain,
( ( $false
= ( in @ sK5 @ sK3 ) )
| ( $true
= ( in @ sK4 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f69,plain,
( $false
= ( in @ sK5 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f68,f31]) ).
thf(f70,plain,
$true = $false,
inference(backward_demodulation,[],[f32,f69]) ).
thf(f71,plain,
$false,
inference(trivial_inequality_removal,[],[f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU814^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n014.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:34:00 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.23/0.27 % (2749743)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.27 % (2749753)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1826758479:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.27 % (2749753) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2749743-2749753"...
% 0.23/0.27 % (2749753)...printing done.
% 0.23/0.27 % (2749753)Refutation found. Thanks to Tanya!
% 0.23/0.27 % SZS status Theorem for theBenchmark
% 0.23/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.27 % (2749753)------------------------------
% 0.23/0.27 % (2749753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.27 % (2749753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.27 % (2749753)CaDiCaL version: 2.1.3
% 0.23/0.27 % (2749753)Termination reason: Refutation
% 0.23/0.27 % (2749753)Time elapsed: 0.002 s
% 0.23/0.27 % (2749753)Peak memory usage: 12 MB
% 0.23/0.27 % (2749753)Instructions burned: 5 (million)
% 0.23/0.27 % (2749743)Success in time 0.025 s
% 0.23/0.27 % Vampire exiting
%------------------------------------------------------------------------------