%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU541^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 108 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 91 ( 9 ~; 2 |; 4 &; 58 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 6 con; 0-4 aty)
% ( 3 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 18 ( 8 ^; 9 !; 1 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
prop2set: $o > $i ).
thf(func_def_3,type,
prop2setI: $o ).
thf(func_def_5,type,
set2prop: $i > $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
vIMP: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
sK0: $o ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(f1,axiom,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(f2,axiom,
( set2prop
= ( ^ [X0: $i] : ( in @ emptyset @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set2prop) ).
thf(f3,conjecture,
( prop2setI
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(f4,negated_conjecture,
~ ( prop2setI
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( set2prop
= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f8,plain,
~ ( prop2setI
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
~ ( ( prop2setI = $true )
=> ! [X0: $o] :
( ( $true = X0 )
=> ( ( set2prop @ ( prop2set @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ? [X0: $o] :
( ( ( set2prop @ ( prop2set @ X0 ) )
!= $true )
& ( $true = X0 ) )
& ( prop2setI = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ( $true
!= ( set2prop @ ( prop2set @ sK0 ) ) )
& ( $true = sK0 )
& ( prop2setI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10]) ).
thf(f12,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
( set2prop
= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
prop2setI = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
$true = sK0,
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
( $true
!= ( set2prop @ ( prop2set @ sK0 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f12,f14]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 )
@ ( prop2set @ $true ) ) ),
inference(definition_unfolding,[],[f16,f13,f15]) ).
thf(f21,plain,
( $true
!= ( in @ emptyset @ ( prop2set @ $true ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
! [X1: $o] :
( $true
= ( ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f23,plain,
! [X1: $o] :
( $true
= ( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X1: $o] :
( ( $true
= ( in @ emptyset @ ( prop2set @ X1 ) ) )
| ( $false = X1 ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $true != $true )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f21,f24]) ).
thf(f26,plain,
$false,
inference(trivial_inequality_removal,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU541^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n009.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 13:49:15 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (4022356)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (4022373)dis+10_1_sil=32000:sp=arity:random_seed=3492395946:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (4022373) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4022356-4022373"...
% 0.21/0.28 % (4022373)...printing done.
% 0.21/0.28 % (4022373)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (4022373)------------------------------
% 0.21/0.28 % (4022373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (4022373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (4022373)CaDiCaL version: 2.1.3
% 0.21/0.28 % (4022373)Termination reason: Refutation
% 0.21/0.28 % (4022373)Time elapsed: 0.001 s
% 0.21/0.28 % (4022373)Peak memory usage: 12 MB
% 0.21/0.28 % (4022373)Instructions burned: 1 (million)
% 0.21/0.28 % (4022356)Success in time 0.036 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------