%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU522^2 : 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 : n013.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 08:32:17 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 223 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 273 ( 8 ~; 9 |; 22 &; 203 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 8 con; 0-4 aty)
% ( 8 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 65 ( 20 ^; 37 !; 8 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setunion: $i > $i ).
thf(func_def_2,type,
setunionAx: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIFF: $o > $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_9,type,
vAND: $o > $o > $o ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
sK3: $i > $i > $i ).
thf(f1,axiom,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
<=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(f2,conjecture,
( setunionAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(f3,negated_conjecture,
~ ( setunionAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
<=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( setunionAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setunionAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setunionAx = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X1 @ ( setunion @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
= $true ) )
& ( setunionAx = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
= $true ) )
& ( setunionAx = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ( $true
!= ( in @ sK1 @ ( setunion @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK1 @ sK2 ) )
& ( setunionAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f9]) ).
thf(f11,plain,
( setunionAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f12,plain,
setunionAx = $true,
inference(cnf_transformation,[],[f10]) ).
thf(f13,plain,
( $true
= ( in @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f14,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f15,plain,
( $true
!= ( in @ sK1 @ ( setunion @ sK0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f11,f12]) ).
thf(f19,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
& ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
& ( in @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setunion @ X2 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X2 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) ) ) ),
inference(iff_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f23]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ( in @ X1 @ X3 )
& ( in @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( in @ X3 @ X2 ) )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f31]) ).
thf(f55,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ sK1 @ X0 ) ) ),
inference(constrained_superposition,[],[f15,f32]) ).
thf(f61,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f77,plain,
( ( $true = $false )
| ( ( in @ sK1 @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f14,f61]) ).
thf(f78,plain,
( ( in @ sK1 @ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f86,plain,
$true = $false,
inference(constrained_superposition,[],[f13,f78]) ).
thf(f87,plain,
$false,
inference(trivial_inequality_removal,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU522^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:47:21 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.21/0.28 % (2140080)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (2140086)% WARNING: option uhcvi not known.
% 0.21/0.28 % (2140087)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1157902705:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (2140085)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1336874293_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (2140086)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2183729617:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (2140086)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % Exception at run slice level
% 0.21/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (2140086)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.28
% 0.21/0.28 % (2140091)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3616197059:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.28 % (2140090)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2486997566:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.28 % (2140086) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2140080-2140086"...
% 0.21/0.28 % (2140091) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2140080-2140091"...
% 0.21/0.28 % (2140086)...printing done.
% 0.21/0.28 % (2140091)...printing done.
% 0.21/0.28 % (2140086)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (2140086)------------------------------
% 0.21/0.28 % (2140086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2140086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2140086)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2140086)Termination reason: Refutation
% 0.21/0.28 % (2140086)Time elapsed: 0.005 s
% 0.21/0.28 % (2140086)Peak memory usage: 12 MB
% 0.21/0.28 % (2140086)Instructions burned: 7 (million)
% 0.21/0.28 % (2140080)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------