%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU531^2 : 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 : n017.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 08:29:57 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 487 ( 174 equ; 0 cnn)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 457 ( 82 ~; 80 |; 44 &; 214 @)
% ( 7 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 16 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 89 !; 21 ?; 110 :)
% 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,
setadjoinE: $o ).
thf(func_def_5,type,
uniqinunit: $o ).
thf(func_def_13,type,
sK5: $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(f2,axiom,
( uniqinunit
= ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f3,conjecture,
( setadjoinE
=> ( uniqinunit
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X0 )
| ( X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(f4,negated_conjecture,
~ ( setadjoinE
=> ( uniqinunit
=> ! [X1: $i,X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X0 )
| ( X2 = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( setadjoinE
=> ( uniqinunit
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( ( X1 = X2 )
| ( X0 = X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( setadjoinE = $true )
=> ( ( uniqinunit = $true )
=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
=> ( ( X0 = X1 )
| ( X1 = X2 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( ( uniqinunit = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> X3 )
=> ( ( ( in @ X1 @ X2 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( setadjoinE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> ( $true = X3 ) )
=> ( ( ( ( in @ X1 @ X2 )
= $true )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
<=> ( uniqinunit = $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( setadjoinE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( ( in @ X1 @ X2 )
= $true )
& ( $true != X3 ) )
| ( ( $true != X3 )
& ( X0 = X1 ) ) )
| ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
( ( setadjoinE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( X0 = X1 ) )
| ( ( ( in @ X1 @ X2 )
= $true )
& ( $true != X3 ) ) )
| ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
!= $true ) ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( X0 != X1 )
& ( X1 != X2 )
& ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true ) )
& ( uniqinunit = $true )
& ( setadjoinE = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f15,plain,
( ( uniqinunit = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ( X1 != X2 )
& ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
& ( X0 != X1 ) )
& ( setadjoinE = $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ? [X2: $i,X3: $i] :
( ( X2 != X3 )
& ( ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
= $true ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true ) )
| ( uniqinunit != $true ) )
& ( ( uniqinunit = $true )
| ( ( sK0 != sK1 )
& ( ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f17]) ).
thf(f19,plain,
( ( ( setadjoinE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( X0 != X1 ) )
& ( ( ( in @ X1 @ X2 )
!= $true )
| ( $true = X3 ) ) )
& ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( X0 = X1 ) )
| ( ( ( in @ X1 @ X2 )
= $true )
& ( $true != X3 ) ) )
| ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
!= $true ) )
| ( setadjoinE != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f20,plain,
( ( ( setadjoinE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( X0 != X2 ) )
& ( ( ( in @ X0 @ X1 )
!= $true )
| ( $true = X3 ) ) )
& ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( X4 = X6 ) )
| ( ( ( in @ X4 @ X5 )
= $true )
& ( $true != X7 ) ) )
| ( ( in @ X4 @ ( setadjoin @ X6 @ X5 ) )
!= $true ) )
| ( setadjoinE != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( setadjoinE = $true )
| ( ( sK5 != $true )
& ( ( sK5 = $true )
| ( sK2 != sK4 ) )
& ( ( ( in @ sK2 @ sK3 )
!= $true )
| ( sK5 = $true ) )
& ( ( in @ sK2 @ ( setadjoin @ sK4 @ sK3 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( X4 = X6 ) )
| ( ( ( in @ X4 @ X5 )
= $true )
& ( $true != X7 ) ) )
| ( ( in @ X4 @ ( setadjoin @ X6 @ X5 ) )
!= $true ) )
| ( setadjoinE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f20]) ).
thf(f22,plain,
( ( uniqinunit = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= $true )
& ( X0 != X2 ) )
& ( setadjoinE = $true ) ),
inference(rectify,[],[f15]) ).
thf(f23,plain,
( ( uniqinunit = $true )
& ( sK7 != sK8 )
& ( ( in @ sK8 @ ( setadjoin @ sK7 @ ( setadjoin @ sK6 @ emptyset ) ) )
= $true )
& ( sK8 != sK6 )
& ( setadjoinE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f22]) ).
thf(f26,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( uniqinunit != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f28,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true = X7 )
| ( X4 = X6 )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X6 @ X5 ) )
!= $true )
| ( setadjoinE != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f35,plain,
setadjoinE = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f36,plain,
sK8 != sK6,
inference(cnf_transformation,[],[f23]) ).
thf(f37,plain,
( ( in @ sK8 @ ( setadjoin @ sK7 @ ( setadjoin @ sK6 @ emptyset ) ) )
= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f38,plain,
sK7 != sK8,
inference(cnf_transformation,[],[f23]) ).
thf(f39,plain,
uniqinunit = $true,
inference(cnf_transformation,[],[f23]) ).
thf(f42,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( $true != $true )
| ( X0 = X1 ) ),
inference(definition_unfolding,[],[f26,f39]) ).
thf(f51,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X4 @ ( setadjoin @ X6 @ X5 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( $true = X7 )
| ( X4 = X6 ) ),
inference(definition_unfolding,[],[f28,f35]) ).
thf(f56,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X6 @ X5 ) )
!= $true )
| ( $true = X7 )
| ( X4 = X6 )
| ( ( in @ X4 @ X5 )
= $true ) ),
inference(trivial_inequality_removal,[],[f51]) ).
thf(f58,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f60,definition,
( spl9_1
<=> ! [X7: $o] : ( $true = X7 ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f61,plain,
( ! [X7: $o] : ( $true = X7 )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f63,definition,
( spl9_2
<=> ! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X6 @ X5 ) )
!= $true )
| ( ( in @ X4 @ X5 )
= $true )
| ( X4 = X6 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f64,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X6 @ X5 ) )
!= $true )
| ( X4 = X6 )
| ( ( in @ X4 @ X5 )
= $true ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f65,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f56,f63,f60]) ).
thf(f66,plain,
( ( sK7 = sK8 )
| ( ( in @ sK8 @ ( setadjoin @ sK6 @ emptyset ) )
= $true )
| ( $true != $true )
| ~ spl9_2 ),
inference(constrained_superposition,[],[f64,f37]) ).
thf(f67,plain,
( ( ( in @ sK8 @ ( setadjoin @ sK6 @ emptyset ) )
= $true )
| ( sK7 = sK8 )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f68,plain,
( ( ( in @ sK8 @ ( setadjoin @ sK6 @ emptyset ) )
= $true )
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f67,f38]) ).
thf(f69,plain,
( ( sK8 = sK6 )
| ( $true != $true )
| ~ spl9_2 ),
inference(constrained_superposition,[],[f58,f68]) ).
thf(f72,plain,
( ( sK8 = sK6 )
| ~ spl9_2 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f74,plain,
( $false
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f72,f36]) ).
thf(f75,plain,
~ spl9_2,
inference(avatar_contradiction_clause,[],[f74]) ).
thf(f77,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true != $true ) )
| ~ spl9_1 ),
inference(constrained_superposition,[],[f58,f61]) ).
thf(f80,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f87,plain,
( ! [X0: $i] : ( sK8 != X0 )
| ~ spl9_1 ),
inference(constrained_superposition,[],[f36,f80]) ).
thf(f107,plain,
( $false
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f87,f80]) ).
thf(f108,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[],[f107]) ).
cnf(s1,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s2,plain,
~ spl9_2,
inference(sat_conversion,[],[f75]) ).
cnf(s6,plain,
~ spl9_1,
inference(sat_conversion,[],[f108]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s2,s6]) ).
thf(f109,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU531^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n017.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 13:43:53 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.27 % (360176)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (360181)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2454115489:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.27 % (360181) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-360176-360181"...
% 0.22/0.27 % (360181)...printing done.
% 0.22/0.27 % (360181)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (360181)------------------------------
% 0.22/0.27 % (360181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (360181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (360181)CaDiCaL version: 2.1.3
% 0.22/0.27 % (360181)Termination reason: Refutation
% 0.22/0.27 % (360181)Time elapsed: 0.003 s
% 0.22/0.27 % (360181)Peak memory usage: 13 MB
% 0.22/0.27 % (360181)Instructions burned: 6 (million)
% 0.22/0.27 % (360176)Success in time 0.019 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------