%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU786^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 08:33:25 AM UTC 2026
% Result : Theorem 0.06s 0.24s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 21 unt; 0 typ; 2 def)
% Number of atoms : 323 ( 63 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 463 ( 23 ~; 30 |; 21 &; 337 @)
% ( 2 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 11 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 72 ( 0 sgn 44 !; 10 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_2,type,
binunionE: $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
breln1: $i > $i > $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vOR: $o > $o > $o ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(f1,axiom,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f2,conjecture,
( binunionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionE) ).
thf(f3,negated_conjecture,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( binunionE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( binunionE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( breln1 @ X0 @ X2 )
= $true ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( binunionE = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK4 @ sK0 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( breln1 @ sK0 @ sK2 ) )
& ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( binunionE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f9]) ).
thf(f11,plain,
( binunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
binunionE = $true,
inference(cnf_transformation,[],[f10]) ).
thf(f17,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f11,f12]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( binunion @ Y2 @ Y1 ) )
=> ( ( in @ Y0 @ Y2 )
| ( in @ Y0 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( binunion @ Y1 @ Y0 ) )
=> ( ( in @ X1 @ Y1 )
| ( in @ X1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( binunion @ Y0 @ X2 ) )
=> ( ( in @ X1 @ Y0 )
| ( in @ X1 @ X2 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( binunion @ X3 @ X2 ) )
=> ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( $true
= ( ( in @ X1 @ X3 )
| ( in @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( binunion @ X3 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( $true = $false )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
inference(constrained_superposition,[],[f30,f17]) ).
thf(f34,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f36,definition,
( spl5_1
<=> ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl5_2
<=> ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f42,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f44,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f34,f40,f36]) ).
thf(f45,plain,
( ( $true != $true )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f19,f42]) ).
thf(f46,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f47,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f46]) ).
thf(f48,plain,
( ( $true != $true )
| ~ spl5_1 ),
inference(constrained_superposition,[],[f18,f38]) ).
thf(f49,plain,
( $false
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f50,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f49]) ).
cnf(s2,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f47]) ).
cnf(s4,plain,
~ spl5_1,
inference(sat_conversion,[],[f50]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s3,s4]) ).
thf(f51,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU786^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n004.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 14:28:37 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.24 % (1364378)Will run a generic schedule for satisfiability detection.
% 0.06/0.24 % (1364389)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=225335348:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.24 % (1364389) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1364378-1364389"...
% 0.06/0.24 % (1364389)...printing done.
% 0.06/0.24 % (1364389)Refutation found. Thanks to Tanya!
% 0.06/0.24 % SZS status Theorem for theBenchmark
% 0.06/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.24 % (1364389)------------------------------
% 0.06/0.24 % (1364389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.24 % (1364389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.24 % (1364389)CaDiCaL version: 2.1.3
% 0.06/0.24 % (1364389)Termination reason: Refutation
% 0.06/0.24 % (1364389)Time elapsed: 0.003 s
% 0.06/0.24 % (1364389)Peak memory usage: 12 MB
% 0.06/0.24 % (1364389)Instructions burned: 6 (million)
% 0.06/0.24 % (1364378)Success in time 0.027 s
% 0.06/0.24 % Vampire exiting
%------------------------------------------------------------------------------