%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU528^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:29:56 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 158 ( 33 ~; 16 |; 10 &; 84 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 30 !; 6 ?; 36 :)
% 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,
uniqinunit: $o ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f2,conjecture,
( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(f3,negated_conjecture,
~ ( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ( uniqinunit
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) )
= uniqinunit ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( ( uniqinunit = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
~ ( ( uniqinunit = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f10,plain,
( ( uniqinunit = $true )
& ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f11,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
& ( X2 != X3 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f13,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( ( in @ sK0 @ ( setadjoin @ sK1 @ emptyset ) )
= $true )
& ( sK0 != sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f12]) ).
thf(f14,plain,
( ( uniqinunit = $true )
& ( sK3 != sK2 )
& ( $true
= ( in @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f10]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
= ( in @ sK3 @ ( setadjoin @ sK2 @ emptyset ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
sK3 != sK2,
inference(cnf_transformation,[],[f14]) ).
thf(f20,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f26,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f27,plain,
( ( sK3 = sK2 )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f26,f18]) ).
thf(f28,plain,
sK3 = sK2,
inference(trivial_inequality_removal,[],[f27]) ).
thf(f29,plain,
$false,
inference(forward_subsumption_resolution,[],[f28,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU528^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.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 13:48:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (4019863)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (4019882)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1576676:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (4019882) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4019863-4019882"...
% 0.21/0.28 % (4019882)...printing done.
% 0.21/0.28 % (4019882)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 % (4019882)------------------------------
% 0.21/0.28 % (4019882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (4019882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (4019882)CaDiCaL version: 2.1.3
% 0.21/0.28 % (4019882)Termination reason: Refutation
% 0.21/0.28 % (4019882)Time elapsed: 0.001 s
% 0.21/0.28 % (4019882)Peak memory usage: 12 MB
% 0.21/0.28 % (4019882)Instructions burned: 1 (million)
% 0.21/0.28 % (4019863)Success in time 0.033 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------