%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU535^2 : 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 : n010.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 08:32:21 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 144 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 123 ( 17 ~; 11 |; 4 &; 65 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 8 con; 0-4 aty)
% ( 9 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 36 ( 0 sgn 23 !; 2 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
emptysetE: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: $i > $o ).
thf(func_def_12,type,
vNOT: $o > $o ).
thf(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(f2,conjecture,
( emptysetE
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(f3,negated_conjecture,
~ ( emptysetE
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( emptysetE
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( emptysetE = $true )
=> ! [X0: $i > $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $true )
=> ( ( X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
& ( ( in @ X1 @ emptyset )
= $true ) )
& ( emptysetE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( sK0 @ sK1 ) )
& ( $true
= ( in @ sK1 @ emptyset ) )
& ( emptysetE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
emptysetE = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
= ( in @ sK1 @ emptyset ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( $true
!= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) )
= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ emptyset )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( ( !! @ $o
@ ^ [Y0: $o] : Y0 )
= $true ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true
= ( ^ [Y0: $o] : Y0
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( $true = X2 ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f23,definition,
( spl2_1
<=> ! [X2: $o] : ( $true = X2 ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f24,plain,
( ! [X2: $o] : ( $true = X2 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,definition,
( spl2_2
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f27,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f21,f26,f23]) ).
thf(f29,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f27,f12]) ).
thf(f33,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f34,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f33]) ).
thf(f36,plain,
( ( $true != $true )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f13,f24]) ).
thf(f37,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f38,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f37]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f34]) ).
cnf(s4,plain,
~ spl2_1,
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
thf(f41,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU535^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:49:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.08/0.26 % (2884588)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (2884596)dis+10_1_sil=32000:sp=arity:random_seed=3551443879:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (2884596) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2884588-2884596"...
% 0.08/0.26 % (2884596)...printing done.
% 0.08/0.26 % (2884594)% WARNING: option uhcvi not known.
% 0.08/0.26 % (2884596)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (2884596)------------------------------
% 0.08/0.26 % (2884596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2884596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2884596)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2884596)Termination reason: Refutation
% 0.08/0.26 % (2884596)Time elapsed: 0.002 s
% 0.08/0.26 % (2884596)Peak memory usage: 12 MB
% 0.08/0.26 % (2884596)Instructions burned: 2 (million)
% 0.08/0.26 % (2884588)Success in time 0.025 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------