%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO095^5 : 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 08:46:36 AM UTC 2026
% Result : Theorem 0.08s 0.24s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 202 ( 43 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 226 ( 29 ~; 23 |; 16 &; 140 @)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 52 !; 10 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cR: $i > $i > $o ).
thf(f1,conjecture,
( ( ! [X3: $i,X2: $i] :
( ( cR @ X2 @ X2 )
<=> ( cR @ X3 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
<=> ( cR @ X0 @ X0 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM81) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: $i,X2: $i] :
( ( cR @ X2 @ X2 )
<=> ( cR @ X3 @ X2 ) )
& ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
<=> ( cR @ X0 @ X0 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cR @ X1 @ X1 )
<=> ( cR @ X0 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X3 @ X2 )
<=> ( cR @ X3 @ X3 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
= ( cR @ X1 @ X1 ) )
& ! [X3: $i,X2: $i] :
( ( cR @ X3 @ X2 )
= ( cR @ X3 @ X3 ) ) )
=> ( ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
=> ! [X5: $i] :
( ( cR @ X5 @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X5: $i] :
( ( cR @ X5 @ X5 )
!= $true )
& ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
& ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
= ( cR @ X1 @ X1 ) )
& ! [X3: $i,X2: $i] :
( ( cR @ X3 @ X2 )
= ( cR @ X3 @ X3 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X5: $i] :
( ( cR @ X5 @ X5 )
!= $true )
& ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
& ! [X1: $i,X0: $i] :
( ( cR @ X0 @ X1 )
= ( cR @ X1 @ X1 ) )
& ! [X3: $i,X2: $i] :
( ( cR @ X3 @ X2 )
= ( cR @ X3 @ X3 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
& ? [X1: $i] :
( ( cR @ X1 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X3 @ X2 ) )
& ! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( cR @ sK0 @ sK0 ) )
& ( ( cR @ sK1 @ sK1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X3 @ X2 ) )
& ! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f9,plain,
! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X3 @ X2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( cR @ sK1 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
!= ( cR @ sK0 @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X4: $i,X5: $i] :
( ( $false
= ( cR @ X4 @ X5 ) )
| ( ( cR @ X4 @ X4 )
= $true ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f17,plain,
! [X2: $i,X3: $i] :
( ( ( cR @ X3 @ X2 )
= $true )
| ( ( cR @ X2 @ X2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f19,definition,
( spl2_1
<=> ( ( cR @ sK1 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f21,plain,
( ( ( cR @ sK1 @ sK1 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
spl2_1,
inference(avatar_split_clause,[],[f11,f19]) ).
thf(f24,definition,
( spl2_2
<=> ( $true
= ( cR @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
!= ( cR @ sK0 @ sK0 ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f12,f24]) ).
thf(f51,definition,
( spl2_4
<=> ! [X1: $i] :
( ( cR @ X1 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f52,plain,
( ! [X1: $i] :
( ( cR @ X1 @ X1 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f54,definition,
( spl2_5
<=> ! [X0: $i] :
( ( cR @ X0 @ X0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f55,plain,
( ! [X0: $i] :
( ( cR @ X0 @ X0 )
= $false )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f59,plain,
! [X0: $i,X1: $i] :
( ( ( cR @ X1 @ X1 )
= $false )
| ( ( cR @ X0 @ X0 )
= $true )
| ( $true = $false ) ),
inference(superposition,[],[f17,f14]) ).
thf(f66,plain,
! [X0: $i,X1: $i] :
( ( ( cR @ X0 @ X0 )
= $true )
| ( ( cR @ X1 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f68,plain,
( spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f66,f54,f51]) ).
thf(f74,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_5 ),
inference(superposition,[],[f55,f21]) ).
thf(f82,plain,
( $false
| ~ spl2_1
| ~ spl2_5 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f83,plain,
( ~ spl2_1
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f82]) ).
thf(f89,plain,
( ( $true != $true )
| spl2_2
| ~ spl2_4 ),
inference(superposition,[],[f26,f52]) ).
thf(f94,plain,
( $false
| spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f95,plain,
( spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f94]) ).
cnf(s1,plain,
spl2_1,
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f27]) ).
cnf(s8,plain,
( spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f68]) ).
cnf(s10,plain,
( ~ spl2_1
| ~ spl2_5 ),
inference(sat_conversion,[],[f83]) ).
cnf(s12,plain,
( spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f95]) ).
cnf(s14,plain,
~ spl2_4,
inference(rat,[],[s12,s2]) ).
cnf(s16,plain,
spl2_5,
inference(rat,[],[s8,s14]) ).
cnf(s17,plain,
~ spl2_1,
inference(rat,[],[s10,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s17]) ).
thf(f98,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO095^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:33:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.08/0.24 % (305709)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.24 % (305718)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=3134030048: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)
% 0.08/0.24 % (305718) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-305709-305718"...
% 0.08/0.24 % (305718)...printing done.
% 0.08/0.24 % (305718)Refutation found. Thanks to Tanya!
% 0.08/0.24 % SZS status Theorem for theBenchmark
% 0.08/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.24 % (305718)------------------------------
% 0.08/0.24 % (305718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.24 % (305718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.24 % (305718)CaDiCaL version: 2.1.3
% 0.08/0.24 % (305718)Termination reason: Refutation
% 0.08/0.24 % (305718)Time elapsed: 0.002 s
% 0.08/0.24 % (305718)Peak memory usage: 13 MB
% 0.08/0.24 % (305718)Instructions burned: 5 (million)
% 0.08/0.24 % (305709)Success in time 0.017 s
% 0.08/0.24 % Vampire exiting
%------------------------------------------------------------------------------