%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU786^2 : 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 : n013.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 08:31:22 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 364 ( 95 equ; 0 cnn)
% Maximal formula atoms : 8 ( 14 avg)
% Number of connectives : 443 ( 31 ~; 31 |; 37 &; 314 @)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 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 : 71 ( 0 ^; 50 !; 21 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
binunion: $i > $i > $i ).
thf(func_def_2,type,
binunionE: $o ).
thf(func_def_4,type,
kpair: $i > $i > $i ).
thf(func_def_5,type,
breln1: $i > $i > $o ).
thf(f1,axiom,
( binunionE
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X0 @ X1 ) )
=> ( ( in @ X2 @ X1 )
| ( in @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(f2,conjecture,
( binunionE
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionE) ).
thf(f3,negated_conjecture,
~ ( binunionE
=> ! [X1: $i,X0: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( binunionE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binunion @ X1 @ X0 ) )
=> ( ( in @ X2 @ X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( ( binunionE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
=> ( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( binunionE
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
| ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( binunionE = $true )
=> ! [X1: $i,X0: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
& ( $true
= ( in @ X4 @ X1 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
& ( $true
= ( breln1 @ X1 @ X2 ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( binunionE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( $true
= ( breln1 @ X1 @ X2 ) )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X0 @ X2 ) ) )
& ( $true
= ( in @ X4 @ X1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( binunionE = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ( binunionE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f11,plain,
( ( binunionE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( binunion @ X1 @ X2 ) )
= $true )
& ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
!= $true ) )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( ( breln1 @ X0 @ X1 )
= $true ) )
& ( binunionE = $true ) ),
inference(rectify,[],[f9]) ).
thf(f13,plain,
( ( $true
= ( breln1 @ sK0 @ sK2 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) ) )
& ( $true
= ( in @ sK4 @ sK0 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( ( breln1 @ sK0 @ sK1 )
= $true )
& ( binunionE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f12]) ).
thf(f14,plain,
( ( ( binunionE = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
= $true ) )
| ( binunionE != $true ) ) ),
inference(nnf_transformation,[],[f11]) ).
thf(f15,plain,
( ( ( binunionE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binunion @ X1 @ X2 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ X1 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
| ( $true
= ( in @ X3 @ X5 ) )
| ( $true
= ( in @ X3 @ X4 ) ) )
| ( binunionE != $true ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ( binunionE = $true )
| ( ( $true
= ( in @ sK5 @ ( binunion @ sK6 @ sK7 ) ) )
& ( $true
!= ( in @ sK5 @ sK7 ) )
& ( $true
!= ( in @ sK5 @ sK6 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
| ( $true
= ( in @ X3 @ X5 ) )
| ( $true
= ( in @ X3 @ X4 ) ) )
| ( binunionE != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f15]) ).
thf(f17,plain,
binunionE = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f22,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ ( binunion @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f23,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f25,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( binunionE != $true )
| ( $true
= ( in @ X3 @ X4 ) )
| ( $true
!= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
| ( $true
= ( in @ X3 @ X5 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f31,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( binunion @ X4 @ X5 ) ) )
| ( $true
= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ X5 ) ) ),
inference(forward_subsumption_resolution,[],[f25,f17]) ).
thf(f32,plain,
( ( $true != $true )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) ) ),
inference(superposition,[],[f31,f22]) ).
thf(f33,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK2 ) )
| ( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 ) ),
inference(forward_subsumption_resolution,[],[f33,f23]) ).
thf(f35,plain,
$false,
inference(forward_subsumption_resolution,[],[f34,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU786^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:28:06 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.25 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
% 0.20/0.30 % (2196190)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (2196199)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=266663803:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (2196199) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2196190-2196199"...
% 0.20/0.30 % (2196199)...printing done.
% 0.20/0.30 % (2196199)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (2196199)------------------------------
% 0.20/0.30 % (2196199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (2196199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (2196199)CaDiCaL version: 2.1.3
% 0.20/0.30 % (2196199)Termination reason: Refutation
% 0.20/0.30 % (2196199)Time elapsed: 0.002 s
% 0.20/0.30 % (2196199)Peak memory usage: 12 MB
% 0.20/0.30 % (2196199)Instructions burned: 4 (million)
% 0.20/0.30 % (2196190)Success in time 0.048 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------