%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU533^2 : 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 08:29:57 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 266 ( 77 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 280 ( 33 ~; 24 |; 17 &; 192 @)
% ( 3 <=>; 11 =>; 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 : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 62 !; 16 ?; 78 :)
% 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,
setadjoinIL: $o ).
thf(func_def_5,type,
setadjoinIR: $o ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
= setadjoinIR ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(f3,conjecture,
( setadjoinIL
=> ( setadjoinIR
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(f4,negated_conjecture,
~ ( setadjoinIL
=> ( setadjoinIR
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
= setadjoinIR ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( ( setadjoinIR = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
=> ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( ( setadjoinIL = $true )
<=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( setadjoinIL
=> ( setadjoinIR
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setadjoinIR = $true )
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
& ( setadjoinIR = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ? [X1: $i,X0: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ( setadjoinIR = $true )
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f14,plain,
( ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ? [X0: $i,X1: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f15,plain,
( ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ( ( in @ sK0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
thf(f16,plain,
( ( ( setadjoinIR = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
& ( $true
= ( in @ X2 @ X0 ) ) ) )
& ( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X2 @ X0 ) ) )
| ( setadjoinIR != $true ) ) ),
inference(nnf_transformation,[],[f13]) ).
thf(f17,plain,
( ( ( setadjoinIR = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setadjoinIR != $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( setadjoinIR = $true )
| ( ( ( in @ sK2 @ ( setadjoin @ sK4 @ sK3 ) )
!= $true )
& ( ( in @ sK2 @ sK3 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( setadjoinIR != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f17]) ).
thf(f19,plain,
( ( ( setadjoinIL = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
& ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f20,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( setadjoinIL = $true )
| ( ( in @ sK6 @ ( setadjoin @ sK6 @ sK5 ) )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f20]) ).
thf(f22,plain,
( ( in @ sK0 @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
!= $true ),
inference(cnf_transformation,[],[f15]) ).
thf(f23,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
setadjoinIR = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X4 )
!= $true )
| ( setadjoinIR != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f28,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f34,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true != $true )
| ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(definition_unfolding,[],[f25,f24]) ).
thf(f36,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f28,f23]) ).
thf(f37,plain,
! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f38,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
!= $true )
| ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f39,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f38,f37]) ).
thf(f40,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f42,plain,
$true != $true,
inference(constrained_superposition,[],[f22,f40]) ).
thf(f43,plain,
$false,
inference(trivial_inequality_removal,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU533^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n004.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 13:48:37 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 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
% 0.20/0.27 % (1314437)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1314444)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=702509625:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (1314444) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1314437-1314444"...
% 0.20/0.27 % (1314444)...printing done.
% 0.20/0.27 % (1314444)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1314444)------------------------------
% 0.20/0.27 % (1314444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1314444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1314444)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1314444)Termination reason: Refutation
% 0.20/0.27 % (1314444)Time elapsed: 0.002 s
% 0.20/0.27 % (1314444)Peak memory usage: 12 MB
% 0.20/0.27 % (1314444)Instructions burned: 3 (million)
% 0.20/0.27 % (1314437)Success in time 0.028 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------