%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO238^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:47:15 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 116 ( 37 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 106 ( 20 ~; 12 |; 6 &; 42 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 8 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cB: $o ).
thf(func_def_2,type,
cP: $i > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [X0: $i] : X0 )
= ( ^ [X0: $i] : ( f @ ( f @ X0 ) ) ) )
=> cB )
=> ( ( cP @ x )
=> cB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cADDHYP5) ).
thf(f2,negated_conjecture,
~ ( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [X0: $i] : X0 )
= ( ^ [X0: $i] : ( f @ ( f @ X0 ) ) ) )
=> cB )
=> ( ( cP @ x )
=> cB ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [X1: $i] : X1 )
= ( ^ [X2: $i] : ( f @ ( f @ X2 ) ) ) )
=> cB )
=> ( ( cP @ x )
=> cB ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( $true
=> ! [X0: $i] :
( ( f @ X0 )
= X0 ) )
=> ( ( ( ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : Y0 ) )
=> ( cB = $true ) )
=> ( ( ( cP @ x )
= $true )
=> ( cB = $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= X0 )
=> ( ( ( ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : Y0 ) )
=> ( cB = $true ) )
=> ( ( ( cP @ x )
= $true )
=> ( cB = $true ) ) ) ),
inference(true_and_false_elimination,[],[f4]) ).
thf(f6,plain,
( ( cB != $true )
& ( ( cP @ x )
= $true )
& ( ( ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) )
!= ( ^ [Y0: $i] : Y0 ) )
| ( cB = $true ) )
& ! [X0: $i] :
( ( f @ X0 )
= X0 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( f @ X0 )
= X0 )
& ( cB != $true )
& ( ( ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) )
!= ( ^ [Y0: $i] : Y0 ) )
| ( cB = $true ) )
& ( ( cP @ x )
= $true ) ),
inference(flattening,[],[f6]) ).
thf(f9,plain,
( ( ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) )
!= ( ^ [Y0: $i] : Y0 ) )
| ( cB = $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
cB != $true,
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: $i] :
( ( f @ X0 )
= X0 ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,definition,
( spl0_1
<=> ( cB = $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( ( cB = $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f18,definition,
( spl0_2
<=> ( ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : Y0 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f19,plain,
( ( ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) ) )
!= ( ^ [Y0: $i] : Y0 ) )
| spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f20,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f9,f18,f15]) ).
thf(f21,plain,
( ( ( ^ [Y0: $i] : Y0
@ sK1 )
!= ( ^ [Y0: $i] : ( f @ ( f @ Y0 ) )
@ sK1 ) )
| spl0_2 ),
inference(negative_extensionality,[],[f19]) ).
thf(f22,plain,
( ( ( f @ ( f @ sK1 ) )
!= sK1 )
| spl0_2 ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( ( sK1
!= ( f @ sK1 ) )
| spl0_2 ),
inference(forward_demodulation,[],[f22,f11]) ).
thf(f24,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f23,f11]) ).
thf(f25,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f24]) ).
thf(f26,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f16,f10]) ).
thf(f27,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f26]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f28,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO238^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:44:03 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.19/0.27 % (3772734)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (3772750)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3981746279:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.27 % (3772750) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3772734-3772750"...
% 0.19/0.27 % (3772750)...printing done.
% 0.19/0.27 % (3772750)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (3772750)------------------------------
% 0.19/0.27 % (3772750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3772750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3772750)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3772750)Termination reason: Refutation
% 0.19/0.27 % (3772750)Time elapsed: 0.001 s
% 0.19/0.27 % (3772750)Peak memory usage: 13 MB
% 0.19/0.27 % (3772750)Instructions burned: 1 (million)
% 0.19/0.27 % (3772734)Success in time 0.038 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------