%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO558^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:48:25 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 182 ( 48 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 247 ( 66 ~; 38 |; 0 &; 126 @)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 8 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 71 ( 0 sgn 22 !; 3 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
sK0: $i > $o ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).
thf(f2,conjecture,
( ( ^ [X0: $i > $o] :
( X0
@ ( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) )
= ( ^ [X0: $i > $o] : ( !! @ $i @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
( ( ^ [X0: $i > $o] :
( X0
@ ( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) )
!= ( ^ [X0: $i > $o] : ( !! @ $i @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
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,
( ( ^ [X0: $i > $o] :
( X0
@ ( eps
@ ^ [X1: $i] :
~ ( X0 @ X1 ) ) ) )
!= ( ^ [X2: $i > $o] : ( !! @ $i @ X2 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] : ( !! @ $i @ Y0 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] : ( !! @ $i @ Y0 ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $o] : ( !! @ $i @ Y0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( !!
@ ( $i
!= ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f15,plain,
( ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) )
@ sK0 )
!= ( !! @ $i @ sK0 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f16,plain,
( ( $true
= ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) )
@ sK0 ) )
| ( $true
= ( !! @ $i @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) )
@ sK0 ) )
| ( $false
= ( !! @ $i @ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f18,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) )
@ sK0 ) )
| ( $false
= ( sK0 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( sK0 @ sK1 ) )
| ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i > $o] :
( Y0
@ ( eps
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 ) ) )
@ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f21,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ X1 ) )
| ( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f23,definition,
( spl2_1
<=> ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $false
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,definition,
( spl2_2
<=> ( $false
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f27,plain,
( ( $false
= ( sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f19,f26,f23]) ).
thf(f30,definition,
( spl2_3
<=> ( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
= ( sK0
@ ( eps
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 ) ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f33,definition,
( spl2_4
<=> ! [X1: $i] :
( $true
= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f34,plain,
( ! [X1: $i] :
( $true
= ( sK0 @ X1 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f35,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f21,f33,f30]) ).
thf(f39,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( $true
!= ( ^ [Y0: $i] :
~ ( X2 @ Y0 )
@ X1 ) ) ),
inference(primitive_instantiation,[],[f10]) ).
thf(f45,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( ~ ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) ) )
| ( $true
!= ( ~ ( X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f46,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( $true
!= ( ~ ( X2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( X2
@ ( eps
@ ^ [Y0: $i] :
~ ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f46]) ).
thf(f81,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 )
= $true )
| ( $true = $false ) )
| ~ spl2_3 ),
inference(constrained_superposition,[],[f47,f31]) ).
thf(f110,plain,
( ! [X0: $i] :
( ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X0 )
= $true )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f111,plain,
( ! [X0: $i] :
( $true
= ( sK0 @ X0 ) )
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f174,plain,
( spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f111,f30,f33]) ).
thf(f189,plain,
( ( $true = $false )
| ~ spl2_2
| ~ spl2_4 ),
inference(backward_demodulation,[],[f27,f34]) ).
thf(f190,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f191,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f190]) ).
thf(f195,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_demodulation,[],[f24,f34]) ).
thf(f196,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f197,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f196]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f35]) ).
cnf(s5,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f174]) ).
cnf(s12,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f191]) ).
cnf(s14,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f197]) ).
cnf(s15,plain,
spl2_4,
inference(rat,[],[s2,s5]) ).
cnf(s16,plain,
~ spl2_1,
inference(rat,[],[s14,s15]) ).
cnf(s17,plain,
~ spl2_2,
inference(rat,[],[s12,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s17,s16]) ).
thf(f198,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO558^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n008.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 17:15:39 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.28 % (3454267)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (3454277)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1287736962:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.28 % (3454278)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (3454278)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (3454277) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3454267-3454277"...
% 0.22/0.28 % (3454277)...printing done.
% 0.22/0.28 % (3454277)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (3454277)------------------------------
% 0.22/0.28 % (3454277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (3454277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (3454277)CaDiCaL version: 2.1.3
% 0.22/0.28 % (3454277)Termination reason: Refutation
% 0.22/0.28 % (3454277)Time elapsed: 0.004 s
% 0.22/0.28 % (3454277)Peak memory usage: 13 MB
% 0.22/0.28 % (3454277)Instructions burned: 12 (million)
% 0.22/0.28 % (3454267)Success in time 0.034 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------