%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU539^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:32:22 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 27 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 105 ( 23 ~; 5 |; 11 &; 56 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 19 !; 11 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_5,type,
sK1: $i > $o ).
thf(f1,conjecture,
! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ~ ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ~ ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ~ ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( X1 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ~ ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ~ ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( X1 @ X3 )
= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: $i,X1: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ? [X3: $i] :
( ( ( X1 @ X3 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X2: $i] :
( ( $true
= ( sK1 @ X2 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) )
& ( $true
!= ( sK1 @ sK2 ) )
& ( $true
= ( in @ sK2 @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f7]) ).
thf(f9,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
!= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK0 ) )
| ( $true
= ( sK1 @ X2 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(constrained_superposition,[],[f11,f9]) ).
thf(f15,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
$false,
inference(forward_subsumption_resolution,[],[f15,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU539^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n011.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
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:49:02 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26 % (125858)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (125873)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1292251652:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.10/0.26 % (125873) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-125858-125873"...
% 0.10/0.26 % (125873)...printing done.
% 0.10/0.26 % (125873)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (125873)------------------------------
% 0.10/0.26 % (125873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (125873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (125873)CaDiCaL version: 2.1.3
% 0.10/0.26 % (125873)Termination reason: Refutation
% 0.10/0.26 % (125873)Time elapsed: 0.001 s
% 0.10/0.26 % (125873)Peak memory usage: 12 MB
% 0.10/0.26 % (125873)Instructions burned: 1 (million)
% 0.10/0.26 % (125858)Success in time 0.016 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------