%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU514^2 : 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 : n001.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 08:29:53 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 328 ( 94 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 351 ( 57 ~; 56 |; 26 &; 196 @)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 17 ( 14 usr; 13 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 42 !; 15 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
setadjoinAx: $o ).
thf(f1,axiom,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
<=> ( ( X2 = X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f2,conjecture,
( setadjoinAx
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
<=> ( ( X2 = X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ( setadjoinAx = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 ) )
<=> ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setadjoinAx
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setadjoinAx = $true )
=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( setadjoinAx = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( setadjoinAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( setadjoinAx = $true )
& ( ( in @ sK1 @ ( setadjoin @ sK2 @ sK0 ) )
!= $true )
& ( ( in @ sK1 @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f9]) ).
thf(f11,plain,
( ( ( setadjoinAx = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
| ( ( ( in @ X2 @ X1 )
!= $true )
& ( X0 != X2 ) ) )
& ( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( ( ( in @ X2 @ X1 )
!= $true )
& ( X0 != X2 ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f12,plain,
( ( ( setadjoinAx = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
| ( ( ( in @ X2 @ X1 )
!= $true )
& ( X0 != X2 ) ) )
& ( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( ( ( in @ X2 @ X1 )
!= $true )
& ( X0 != X2 ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( ( in @ X4 @ X3 )
= $true )
| ( X4 = X5 )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true ) )
& ( ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true )
| ( ( ( in @ X4 @ X3 )
!= $true )
& ( X4 != X5 ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ( setadjoinAx = $true )
| ( ( ( $true
!= ( in @ sK4 @ ( setadjoin @ sK5 @ sK3 ) ) )
| ( ( $true
!= ( in @ sK4 @ sK3 ) )
& ( sK4 != sK5 ) ) )
& ( ( $true
= ( in @ sK4 @ ( setadjoin @ sK5 @ sK3 ) ) )
| ( $true
= ( in @ sK4 @ sK3 ) )
| ( sK4 = sK5 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( ( in @ X4 @ X3 )
= $true )
| ( X4 = X5 )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
!= $true ) )
& ( ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true )
| ( ( ( in @ X4 @ X3 )
!= $true )
& ( X4 != X5 ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f13]) ).
thf(f15,plain,
( ( in @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f16,plain,
( ( in @ sK1 @ ( setadjoin @ sK2 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f17,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f10]) ).
thf(f19,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setadjoinAx != $true )
| ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f27,definition,
( spl6_1
<=> ( ( in @ sK1 @ ( setadjoin @ sK2 @ sK0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f29,plain,
( ( ( in @ sK1 @ ( setadjoin @ sK2 @ sK0 ) )
!= $true )
| spl6_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f16,f27]) ).
thf(f40,definition,
( spl6_4
<=> ( setadjoinAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f48,plain,
spl6_4,
inference(avatar_split_clause,[],[f17,f40]) ).
thf(f55,definition,
( spl6_7
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f56,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X3 )
!= $true ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f57,plain,
( ~ spl6_4
| spl6_7 ),
inference(avatar_split_clause,[],[f19,f55,f40]) ).
thf(f60,definition,
( spl6_8
<=> ( ( in @ sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f62,plain,
( ( ( in @ sK1 @ sK0 )
= $true )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f63,plain,
spl6_8,
inference(avatar_split_clause,[],[f15,f60]) ).
thf(f69,plain,
( ( ( in @ sK1 @ sK0 )
!= $true )
| ( $true != $true )
| spl6_1
| ~ spl6_7 ),
inference(superposition,[],[f29,f56]) ).
thf(f70,plain,
( ( ( in @ sK1 @ sK0 )
!= $true )
| spl6_1
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f71,plain,
( $false
| spl6_1
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_subsumption_resolution,[],[f70,f62]) ).
thf(f72,plain,
( spl6_1
| ~ spl6_7
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f71]) ).
cnf(s1,plain,
~ spl6_1,
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
spl6_4,
inference(sat_conversion,[],[f48]) ).
cnf(s6,plain,
( ~ spl6_4
| spl6_7 ),
inference(sat_conversion,[],[f57]) ).
cnf(s8,plain,
spl6_8,
inference(sat_conversion,[],[f63]) ).
cnf(s10,plain,
( spl6_1
| ~ spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f72]) ).
cnf(s12,plain,
spl6_7,
inference(rat,[],[s6,s4]) ).
cnf(s13,plain,
spl6_1,
inference(rat,[],[s10,s8,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s13]) ).
thf(f73,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU514^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n001.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:53:21 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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
% 0.19/0.27 % (1270386)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (1270403)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1743233121:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.27 % (1270403) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1270386-1270403"...
% 0.19/0.27 % (1270403)...printing done.
% 0.19/0.27 % (1270403)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (1270403)------------------------------
% 0.19/0.27 % (1270403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1270403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1270403)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1270403)Termination reason: Refutation
% 0.19/0.27 % (1270403)Time elapsed: 0.002 s
% 0.19/0.27 % (1270403)Peak memory usage: 13 MB
% 0.19/0.27 % (1270403)Instructions burned: 4 (million)
% 0.19/0.27 % (1270386)Success in time 0.042 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------