%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU636^2 : 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 : 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 08:30:27 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 382 ( 123 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 360 ( 51 ~; 43 |; 24 &; 219 @)
% ( 5 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 47 !; 10 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
setunion: $i > $i ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_4,type,
setextsub: $o ).
thf(func_def_6,type,
setunionsingleton1: $o ).
thf(func_def_7,type,
setunionsingleton2: $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(f1,axiom,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(f2,axiom,
! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= setunionsingleton1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(f3,axiom,
( setunionsingleton2
= ( ! [X0: $i] : ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(f4,conjecture,
( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(f5,negated_conjecture,
~ ( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( subset @ X1 @ X0 )
= $true )
=> ( X0 = X1 ) ) )
<=> ( setextsub = $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= setunionsingleton1 ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= $true )
<=> ( setunionsingleton1 = $true ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( setunionsingleton2
= ( ! [X0: $i] : ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( ( setunionsingleton2 = $true )
<=> ! [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
~ ( ( setextsub = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setextsub = $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ( setextsub = $true )
& ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( setextsub = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f17,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 ) )
<=> ( setextsub = $true ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
( ( ! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= $true )
| ( setunionsingleton1 != $true ) )
& ( ( setunionsingleton1 = $true )
| ? [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f19,plain,
( ( ! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= $true )
| ( setunionsingleton1 != $true ) )
& ( ( setunionsingleton1 = $true )
| ? [X1: $i] :
( $true
!= ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( ! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= $true )
| ( setunionsingleton1 != $true ) )
& ( ( setunionsingleton1 = $true )
| ( $true
!= ( subset @ ( setunion @ ( setadjoin @ sK0 @ emptyset ) ) @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f19]) ).
thf(f21,plain,
( ( ( setunionsingleton2 = $true )
| ? [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
!= $true ) )
& ( ! [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
| ( setunionsingleton2 != $true ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f22,plain,
( ( ( setunionsingleton2 = $true )
| ? [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
!= $true ) )
& ( ! [X1: $i] :
( ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( setunionsingleton2 != $true ) ) ),
inference(rectify,[],[f21]) ).
thf(f23,plain,
( ( ( setunionsingleton2 = $true )
| ( ( subset @ sK1 @ ( setunion @ ( setadjoin @ sK1 @ emptyset ) ) )
!= $true ) )
& ( ! [X1: $i] :
( ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( setunionsingleton2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f22]) ).
thf(f24,plain,
( ( setextsub = $true )
& ( ( setunion @ ( setadjoin @ sK2 @ emptyset ) )
!= sK2 )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f15]) ).
thf(f25,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( subset @ X0 @ X1 )
= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[],[f17]) ).
thf(f26,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
= $true )
& ( ( subset @ X3 @ X2 )
= $true )
& ( X2 != X3 ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f27,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ( ( ( subset @ sK3 @ sK4 )
= $true )
& ( ( subset @ sK4 @ sK3 )
= $true )
& ( sK3 != sK4 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X2,sK3),skolemize(X3,sK4)],[f26]) ).
thf(f29,plain,
! [X0: $i] :
( ( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= $true )
| ( setunionsingleton1 != $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f30,plain,
! [X1: $i] :
( ( ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( setunionsingleton2 != $true ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
setunionsingleton1 = $true,
inference(cnf_transformation,[],[f24]) ).
thf(f33,plain,
setunionsingleton2 = $true,
inference(cnf_transformation,[],[f24]) ).
thf(f34,plain,
( ( setunion @ ( setadjoin @ sK2 @ emptyset ) )
!= sK2 ),
inference(cnf_transformation,[],[f24]) ).
thf(f35,plain,
setextsub = $true,
inference(cnf_transformation,[],[f24]) ).
thf(f39,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( setextsub != $true ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f42,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= $true ) ),
inference(definition_unfolding,[],[f29,f32]) ).
thf(f45,plain,
! [X1: $i] :
( ( ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f30,f33]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) ),
inference(definition_unfolding,[],[f39,f35]) ).
thf(f50,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f51,plain,
! [X1: $i] :
( ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f52,plain,
! [X0: $i] :
( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f53,plain,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
!= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f50,f51]) ).
thf(f55,plain,
! [X0: $i] :
( ( ( subset @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) @ X0 )
!= $true )
| ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ),
inference(trivial_inequality_removal,[],[f53]) ).
thf(f57,plain,
! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ),
inference(forward_subsumption_resolution,[],[f55,f52]) ).
thf(f59,plain,
sK2 != sK2,
inference(constrained_superposition,[],[f34,f57]) ).
thf(f62,plain,
$false,
inference(trivial_inequality_removal,[],[f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU636^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:00:53 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.28 % (1332077)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1332082)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1295935799:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1332082) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1332077-1332082"...
% 0.20/0.28 % (1332082)...printing done.
% 0.20/0.28 % (1332082)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1332082)------------------------------
% 0.20/0.28 % (1332082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1332082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1332082)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1332082)Termination reason: Refutation
% 0.20/0.28 % (1332082)Time elapsed: 0.002 s
% 0.20/0.28 % (1332082)Peak memory usage: 12 MB
% 0.20/0.28 % (1332082)Instructions burned: 4 (million)
% 0.20/0.28 % (1332077)Success in time 0.032 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------