%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU582^2 : 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 : n003.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 08:30:10 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 102 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 371 ( 41 ~; 33 |; 21 &; 254 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 13 con; 0-4 aty)
% Number of variables : 96 ( 10 ^; 70 !; 16 ?; 96 :)
% 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,
setadjoinIL: $o ).
thf(func_def_6,type,
setunionI: $o ).
thf(func_def_7,type,
binunion: $i > $i > $i ).
thf(func_def_10,type,
db1:
!>[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(f1,axiom,
! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
( setunionI
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(f3,axiom,
( binunion
= ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunion) ).
thf(f4,conjecture,
( setadjoinIL
=> ( setunionI
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(f5,negated_conjecture,
~ ( setadjoinIL
=> ( setunionI
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ( setadjoinIL
=> ( setunionI
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setunionI = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( ( setunionI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f13,plain,
( ( setunionI = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f14,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X0 @ X2 )
!= $true ) )
<=> ( setunionI = $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) ) )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setunion @ X2 ) ) )
& ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f14]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setunion @ X0 ) )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setunion @ X3 ) )
!= $true )
& ( $true
= ( in @ X5 @ X4 ) )
& ( $true
= ( in @ X4 @ X3 ) ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setunion @ X0 ) )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) )
| ( setunionI != $true ) )
& ( ( setunionI = $true )
| ( ( $true
!= ( in @ sK2 @ ( setunion @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( ( in @ sK1 @ sK0 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f21,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f22,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK4 @ ( setadjoin @ sK4 @ sK3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3),skolemize(X3,sK4)],[f21]) ).
thf(f23,plain,
( ( $true
= ( in @ sK5 @ sK6 ) )
& ( $true
!= ( in @ sK5 @ ( binunion @ sK6 @ sK7 ) ) )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f16]) ).
thf(f27,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( setunionI != $true )
| ( $true
!= ( in @ X1 @ X0 ) )
| ( ( in @ X2 @ ( setunion @ X0 ) )
= $true )
| ( $true
!= ( in @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( setadjoinIL != $true )
| ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f31,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
setunionI = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f33,plain,
( $true
!= ( in @ sK5 @ ( binunion @ sK6 @ sK7 ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f34,plain,
( $true
= ( in @ sK5 @ sK6 ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ),
inference(forward_subsumption_resolution,[],[f29,f31]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ X1 )
= ( binunion @ X1 ) ),
inference(argument_congruence,[],[f30]) ).
thf(f40,plain,
! [X1: $i] :
( ( binunion @ X1 )
= ( ^ [Y0: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 )
= ( binunion @ X1 @ X2 ) ),
inference(argument_congruence,[],[f40]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
= ( binunion @ X1 @ X2 ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( ( in @ X2 @ ( setunion @ X0 ) )
= $true )
| ( $true
!= ( in @ X1 @ X0 ) ) ),
inference(forward_subsumption_resolution,[],[f27,f32]) ).
thf(f44,plain,
! [X0: $i] :
( ( $true
= ( in @ sK5 @ ( setunion @ X0 ) ) )
| ( $true != $true )
| ( ( in @ sK6 @ X0 )
!= $true ) ),
inference(superposition,[],[f43,f34]) ).
thf(f47,plain,
! [X0: $i] :
( ( $true
= ( in @ sK5 @ ( setunion @ X0 ) ) )
| ( ( in @ sK6 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f48,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ sK6 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
| ( $true
= ( in @ sK5 @ ( binunion @ X0 @ X1 ) ) ) ),
inference(superposition,[],[f47,f42]) ).
thf(f154,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK5 @ ( binunion @ sK6 @ X0 ) )
= $true ) ),
inference(superposition,[],[f48,f38]) ).
thf(f155,plain,
! [X0: $i] :
( ( in @ sK5 @ ( binunion @ sK6 @ X0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f156,plain,
$true != $true,
inference(superposition,[],[f33,f155]) ).
thf(f158,plain,
$false,
inference(trivial_inequality_removal,[],[f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU582^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n003.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:54:14 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.09/0.26 % (2539830)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (2539839)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3620553948:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.26 % (2539841)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.26 % (2539841)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.09/0.26 % (2539839) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2539830-2539839"...
% 0.09/0.26 % (2539839)...printing done.
% 0.09/0.26 % (2539839)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (2539839)------------------------------
% 0.21/0.26 % (2539839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (2539839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (2539839)CaDiCaL version: 2.1.3
% 0.21/0.26 % (2539839)Termination reason: Refutation
% 0.21/0.26 % (2539839)Time elapsed: 0.006 s
% 0.21/0.26 % (2539839)Peak memory usage: 12 MB
% 0.21/0.26 % (2539839)Instructions burned: 18 (million)
% 0.21/0.26 % (2539830)Success in time 0.031 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------