%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO520^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:48:10 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.28s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 90 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 92 ( 25 ~; 13 |; 0 &; 49 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 9 !; 3 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
p: $i > $o ).
thf(func_def_5,type,
vNOT: $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_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epschoice) ).
thf(f2,axiom,
( p
@ ( eps
@ ^ [X0: $i] :
~ ( p @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f3,axiom,
~ ( p @ ( eps @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(f4,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( p @ ( eps @ p ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( p
@ ( eps
@ ^ [X0: $i] :
~ ( p @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( $true
= ( p
@ ( eps
@ ^ [Y0: $i] :
~ ( p @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(flattening,[],[f7]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f12,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f13,plain,
( $true
= ( p
@ ( eps
@ ^ [Y0: $i] :
~ ( p @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( p @ ( eps @ p ) )
!= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f17,definition,
( spl0_1
<=> ( ( p @ ( eps @ p ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f19,plain,
( ( ( p @ ( eps @ p ) )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f20,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f14,f17]) ).
thf(f22,definition,
( spl0_2
<=> ( $true
= ( p
@ ( eps
@ ^ [Y0: $i] :
~ ( p @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f24,plain,
( ( $true
= ( p
@ ( eps
@ ^ [Y0: $i] :
~ ( p @ Y0 ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f25,plain,
spl0_2,
inference(avatar_split_clause,[],[f13,f22]) ).
thf(f30,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( p @ X0 )
!= $true ) )
| spl0_1 ),
inference(superposition,[],[f19,f12]) ).
thf(f33,plain,
( ! [X0: $i] :
( ( p @ X0 )
!= $true )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f71,plain,
( ( $true != $true )
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f33,f24]) ).
thf(f75,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f76,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f75]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f76]) ).
cnf(s4,plain,
spl0_1,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
thf(f77,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO520^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n019.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 17:12:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.10/0.28 % (1097133)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.28 % (1097141)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=189477197:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.10/0.28 % (1097141) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1097133-1097141"...
% 0.10/0.28 % (1097141)...printing done.
% 0.10/0.28 % (1097141)Refutation found. Thanks to Tanya!
% 0.10/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.28 % (1097141)------------------------------
% 0.10/0.28 % (1097141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.28 % (1097141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.28 % (1097141)CaDiCaL version: 2.1.3
% 0.10/0.28 % (1097141)Termination reason: Refutation
% 0.10/0.28 % (1097141)Time elapsed: 0.002 s
% 0.10/0.28 % (1097141)Peak memory usage: 13 MB
% 0.10/0.28 % (1097141)Instructions burned: 3 (million)
% 0.10/0.28 % (1097133)Success in time 0.031 s
% 0.10/0.28 % Vampire exiting
%------------------------------------------------------------------------------