%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU618^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 08:32:42 AM UTC 2026
% Result : Theorem 0.26s 0.35s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 254 ( 49 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 405 ( 8 ~; 7 |; 6 &; 330 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 8 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 80 ( 28 ^; 48 !; 4 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
setunionI: $o ).
thf(func_def_6,type,
secondinupair: $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIMP: $o > $o > $o ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(f2,axiom,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(f3,conjecture,
( setunionI
=> ( secondinupair
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(f4,negated_conjecture,
~ ( setunionI
=> ( secondinupair
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( secondinupair
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( setunionI
=> ( secondinupair
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( setunionI = $true )
=> ( ( secondinupair = $true )
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( secondinupair = $true )
& ( setunionI = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( secondinupair = $true )
& ( setunionI = $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( $true
!= ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( secondinupair = $true )
& ( setunionI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
setunionI = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
secondinupair = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
!= ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f14,f16]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f15,f17]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X2 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X2 @ ( setunion @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X2 @ ( setunion @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ X1 ) )
| ( $true
= ( ( in @ X1 @ X3 )
=> ( in @ X2 @ ( setunion @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ X1 ) )
| ( $false
= ( in @ X1 @ X3 ) )
| ( $true
= ( in @ X2 @ ( setunion @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f42,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( in @ X2 @ X0 )
= $false )
| ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ),
inference(constrained_superposition,[],[f26,f34]) ).
thf(f44,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) )
| ( ( in @ X2 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f72,plain,
( ( $true != $true )
| ( $false
= ( in @ sK1 @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) ) ),
inference(constrained_superposition,[],[f18,f44]) ).
thf(f75,plain,
( $false
= ( in @ sK1 @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f77,plain,
$true = $false,
inference(forward_demodulation,[],[f75,f26]) ).
thf(f78,plain,
$false,
inference(trivial_inequality_removal,[],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU618^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.26 % Computer : n026.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 14:00:57 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.26/0.35 % (643428)Will run a generic schedule for satisfiability detection.
% 0.26/0.35 % (643437)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1573117815:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.26/0.35 % (643437)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.26/0.35 % (643437) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-643428-643437"...
% 0.26/0.35 % (643435)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3321847500:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.26/0.35 % (643437)...printing done.
% 0.26/0.35 % (643437)Refutation found. Thanks to Tanya!
% 0.26/0.35 % SZS status Theorem for theBenchmark
% 0.26/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.35 % (643437)------------------------------
% 0.26/0.35 % (643437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.35 % (643437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.35 % (643437)CaDiCaL version: 2.1.3
% 0.26/0.35 % (643437)Termination reason: Refutation
% 0.26/0.35 % (643437)Time elapsed: 0.005 s
% 0.26/0.35 % (643437)Peak memory usage: 12 MB
% 0.26/0.35 % (643437)Instructions burned: 8 (million)
% 0.26/0.35 % (643428)Success in time 0.027 s
% 0.26/0.35 % Vampire exiting
%------------------------------------------------------------------------------