%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO161^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:46:45 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 5 unt; 0 typ; 5 def)
% Number of atoms : 245 ( 51 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 209 ( 50 ~; 41 |; 20 &; 73 @)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 10 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 29 !; 18 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $o ).
thf(f1,conjecture,
( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X1 )
=> ( cP @ X0 ) )
& ( ( cP @ X0 )
=> ( cP @ X1 ) ) )
=> ( ( ? [X0: $i] : ( cP @ X0 )
=> ! [X1: $i] : ( cP @ X1 ) )
& ( ! [X1: $i] : ( cP @ X1 )
=> ? [X0: $i] : ( cP @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2125_HALF) ).
thf(f2,negated_conjecture,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X1 )
=> ( cP @ X0 ) )
& ( ( cP @ X0 )
=> ( cP @ X1 ) ) )
=> ( ( ? [X0: $i] : ( cP @ X0 )
=> ! [X1: $i] : ( cP @ X1 ) )
& ( ! [X1: $i] : ( cP @ X1 )
=> ? [X0: $i] : ( cP @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X1 )
=> ( cP @ X0 ) )
& ( ( cP @ X0 )
=> ( cP @ X1 ) ) )
=> ( ( ? [X2: $i] : ( cP @ X2 )
=> ! [X3: $i] : ( cP @ X3 ) )
& ( ! [X4: $i] : ( cP @ X4 )
=> ? [X5: $i] : ( cP @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP @ X0 )
= $true )
=> ( ( cP @ X1 )
= $true ) )
& ( ( ( cP @ X1 )
= $true )
=> ( ( cP @ X0 )
= $true ) ) )
=> ( ( ! [X4: $i] :
( ( cP @ X4 )
= $true )
=> ? [X5: $i] :
( ( cP @ X5 )
= $true ) )
& ( ? [X2: $i] :
( $true
= ( cP @ X2 ) )
=> ! [X3: $i] :
( $true
= ( cP @ X3 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( ! [X4: $i] :
( ( cP @ X4 )
= $true )
& ! [X5: $i] :
( ( cP @ X5 )
!= $true ) )
| ( ? [X3: $i] :
( $true
!= ( cP @ X3 ) )
& ? [X2: $i] :
( $true
= ( cP @ X2 ) ) ) )
& ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ( ( cP @ X1 )
!= $true )
| ( ( cP @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
& ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
| ( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
& ? [X3: $i] :
( $true
= ( cP @ X3 ) ) ) )
& ? [X4: $i] :
! [X5: $i] :
( ( ( ( cP @ X5 )
= $true )
| ( ( cP @ X4 )
!= $true ) )
& ( ( ( cP @ X5 )
!= $true )
| ( ( cP @ X4 )
= $true ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ( ! [X0: $i] :
( ( cP @ X0 )
= $true )
& ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
| ( ( ( cP @ sK0 )
!= $true )
& ( $true
= ( cP @ sK1 ) ) ) )
& ! [X5: $i] :
( ( ( ( cP @ X5 )
= $true )
| ( $true
!= ( cP @ sK2 ) ) )
& ( ( ( cP @ X5 )
!= $true )
| ( $true
= ( cP @ sK2 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0),skolemize(X3,sK1),skolemize(X4,sK2)],[f6]) ).
thf(f8,plain,
! [X5: $i] :
( ( $true
= ( cP @ sK2 ) )
| ( ( cP @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X5: $i] :
( ( ( cP @ X5 )
= $true )
| ( $true
!= ( cP @ sK2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X1: $i] :
( ( ( cP @ X1 )
!= $true )
| ( ( cP @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X0: $i] :
( ( ( cP @ X0 )
= $true )
| ( $true
= ( cP @ sK1 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,definition,
( spl3_1
<=> ! [X0: $i] :
( ( cP @ X0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,definition,
( spl3_2
<=> ( ( cP @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( cP @ sK0 )
!= $true )
| spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f24,definition,
( spl3_3
<=> ( $true
= ( cP @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f28,definition,
( spl3_4
<=> ! [X5: $i] :
( ( cP @ X5 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f29,plain,
( ! [X5: $i] :
( ( cP @ X5 )
!= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f30,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f8,f28,f24]) ).
thf(f32,definition,
( spl3_5
<=> ( $true
= ( cP @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
= ( cP @ sK1 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f36,plain,
( ~ spl3_2
| spl3_4 ),
inference(avatar_split_clause,[],[f11,f28,f19]) ).
thf(f37,plain,
( spl3_5
| spl3_1 ),
inference(avatar_split_clause,[],[f12,f16,f32]) ).
thf(f38,plain,
( spl3_1
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f9,f24,f16]) ).
thf(f39,plain,
( ( $true != $true )
| ~ spl3_4
| ~ spl3_5 ),
inference(superposition,[],[f29,f34]) ).
thf(f40,plain,
( $false
| ~ spl3_4
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f39]) ).
thf(f41,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f40]) ).
thf(f42,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f17,f29]) ).
thf(f43,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f42]) ).
thf(f44,plain,
( ( $true != $true )
| ~ spl3_1
| spl3_2 ),
inference(superposition,[],[f21,f17]) ).
thf(f45,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f46,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f45]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f36]) ).
cnf(s5,plain,
( spl3_1
| spl3_5 ),
inference(sat_conversion,[],[f37]) ).
cnf(s6,plain,
( spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s7,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f41]) ).
cnf(s8,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s9,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f46]) ).
cnf(s10,plain,
spl3_1,
inference(rat,[],[s7,s2,s5,s6]) ).
cnf(s11,plain,
spl3_2,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
~ spl3_4,
inference(rat,[],[s8,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s4,s12,s11]) ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO161^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:36:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.27 % (313440)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (313448)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=2240641115: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)
% 0.20/0.27 % (313448) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-313440-313448"...
% 0.20/0.27 % (313448)...printing done.
% 0.20/0.27 % (313448)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (313448)------------------------------
% 0.20/0.27 % (313448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (313448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (313448)CaDiCaL version: 2.1.3
% 0.20/0.27 % (313448)Termination reason: Refutation
% 0.20/0.27 % (313448)Time elapsed: 0.002 s
% 0.20/0.27 % (313448)Peak memory usage: 13 MB
% 0.20/0.27 % (313448)Instructions burned: 2 (million)
% 0.20/0.27 % (313440)Success in time 0.026 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------