%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO220^5 : 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 08:47:13 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 102 ( 26 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 91 ( 20 ~; 12 |; 6 &; 42 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 20 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_5,type,
sK2: $i > $i > $o ).
thf(f1,conjecture,
! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47A) ).
thf(f2,negated_conjecture,
~ ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X1 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
=> ( ( X2 @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: $i,X0: $i] :
( ? [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
& ( ( X2 @ X1 @ X0 )
!= $true ) )
& ( X0 = X1 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: $i,X1: $i] :
( ? [X2: $i > $i > $o] :
( ! [X3: $i] :
( ( X2 @ X3 @ X3 )
= $true )
& ( ( X2 @ X0 @ X1 )
!= $true ) )
& ( X0 = X1 ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true )
& ( ( sK2 @ sK0 @ sK1 )
!= $true )
& ( sK1 = sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
sK1 = sK0,
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( sK2 @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X3: $i] :
( ( sK2 @ X3 @ X3 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
( spl3_1
<=> ( ( sK2 @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f15,plain,
( ( ( sK2 @ sK0 @ sK1 )
!= $true )
| spl3_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f16,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f9,f13]) ).
thf(f18,definition,
( spl3_2
<=> ( sK1 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f20,plain,
( ( sK1 = sK0 )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
spl3_2,
inference(avatar_split_clause,[],[f8,f18]) ).
thf(f22,plain,
( ( $true
!= ( sK2 @ sK0 @ sK0 ) )
| spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f15,f20]) ).
thf(f24,definition,
( spl3_3
<=> ( $true
= ( sK2 @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
!= ( sK2 @ sK0 @ sK0 ) )
| spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( ~ spl3_3
| spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f22,f18,f13,f24]) ).
thf(f28,plain,
( ( $true != $true )
| spl3_3 ),
inference(superposition,[],[f26,f10]) ).
thf(f29,plain,
( $false
| spl3_3 ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f30,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f29]) ).
cnf(s1,plain,
~ spl3_1,
inference(sat_conversion,[],[f16]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
( spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
spl3_3,
inference(sat_conversion,[],[f30]) ).
cnf(s5,plain,
( spl3_1
| ~ spl3_2 ),
inference(rat,[],[s3,s4]) ).
cnf(s6,plain,
spl3_1,
inference(rat,[],[s5,s2]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6]) ).
thf(f31,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO220^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n015.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:43:18 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.29 % (3770233)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3770241)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=2765587288: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)
% 0.21/0.29 % (3770241) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3770233-3770241"...
% 0.21/0.29 % (3770241)...printing done.
% 0.21/0.29 % (3770241)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (3770241)------------------------------
% 0.21/0.29 % (3770241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3770241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3770241)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3770241)Termination reason: Refutation
% 0.21/0.29 % (3770241)Time elapsed: 0.001 s
% 0.21/0.29 % (3770241)Peak memory usage: 12 MB
% 0.21/0.29 % (3770241)Instructions burned: 1 (million)
% 0.21/0.29 % (3770233)Success in time 0.04 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------