%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU595^2 : 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 : n011.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 08:30:14 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 197 ( 58 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 226 ( 23 ~; 17 |; 10 &; 163 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 85 ( 31 ^; 45 !; 9 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
dsetconstrER: $o ).
thf(func_def_4,type,
binintersect: $i > $i > $i ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK5: $i > $o ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(f2,axiom,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersect) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( binintersect @ X0 @ X1 ) )
=> ( in @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( ! [X1: $i,X0: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( ( X2 @ X1 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( binintersect @ X0 @ X2 ) )
=> ( in @ X1 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f8,plain,
~ ( ( dsetconstrER = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
=> ( ( in @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( dsetconstrER = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( binintersect @ X0 @ X2 ) ) )
& ( ( in @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
( ( dsetconstrER = $true )
& ( ( in @ sK1 @ ( binintersect @ sK0 @ sK2 ) )
= $true )
& ( ( in @ sK1 @ sK2 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
thf(f14,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( ( X2 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
thf(f15,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
!= ( X5 @ X4 ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( ( in @ sK4
@ ( dsetconstr @ sK3
@ ^ [Y0: $i] : ( sK5 @ Y0 ) ) )
= $true )
& ( ( sK5 @ sK4 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f15]) ).
thf(f17,plain,
( ( in @ sK1 @ sK2 )
!= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( ( in @ sK1 @ ( binintersect @ sK0 @ sK2 ) )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f19,plain,
dsetconstrER = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f26,plain,
( ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK0
@ sK2 ) )
= $true ),
inference(definition_unfolding,[],[f18,f20]) ).
thf(f27,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(definition_unfolding,[],[f23,f19]) ).
thf(f30,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f31,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) ) )
| ( ( X2 @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
( ( in @ sK1
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f26]) ).
thf(f33,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] : ( in @ Y0 @ sK2 )
@ sK1 )
= $true ) ),
inference(constrained_superposition,[],[f31,f32]) ).
thf(f34,plain,
( ( ^ [Y0: $i] : ( in @ Y0 @ sK2 )
@ sK1 )
= $true ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( ( in @ sK1 @ sK2 )
= $true ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f35,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU595^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.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 13:56:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.29 % (132523)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (132528)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2598729821:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (132528) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-132523-132528"...
% 0.23/0.29 % (132528)...printing done.
% 0.23/0.29 % (132528)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (132528)------------------------------
% 0.23/0.29 % (132528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (132528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (132528)CaDiCaL version: 2.1.3
% 0.23/0.29 % (132528)Termination reason: Refutation
% 0.23/0.29 % (132528)Time elapsed: 0.001 s
% 0.23/0.29 % (132528)Peak memory usage: 12 MB
% 0.23/0.29 % (132528)Instructions burned: 3 (million)
% 0.23/0.29 % (132523)Success in time 0.032 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------