%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO305^5 : 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 : n017.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 08:47:24 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 175 ( 42 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 146 ( 33 ~; 23 |; 9 &; 58 @)
% ( 3 <=>; 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 : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 24 !; 4 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cB: $i > $o ).
thf(func_def_1,type,
cA: $i > $o ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) )
=> ! [X1: $i] :
( ( X0 @ X1 )
=> ( cB @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSET79_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) )
=> ! [X1: $i] :
( ( X0 @ X1 )
=> ( cB @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ( cA @ X2 ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( cB @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) )
=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ( cA @ X2 )
= $true ) )
=> ! [X3: $i] :
( ( $true
= ( X1 @ X3 ) )
=> ( ( cB @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X1: $i > $o] :
( ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( $true
= ( X1 @ X3 ) ) ) )
& ! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
( ( ( cA @ X1 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
& ? [X2: $i] :
( ( ( cB @ X2 )
!= $true )
& ( $true
= ( X0 @ X2 ) ) ) )
& ! [X3: $i] :
( ( ( cB @ X3 )
= $true )
| ( ( cA @ X3 )
!= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X1: $i] :
( ( ( cA @ X1 )
= $true )
| ( ( sK0 @ X1 )
!= $true ) )
& ( ( cB @ sK1 )
!= $true )
& ( ( sK0 @ sK1 )
= $true )
& ! [X3: $i] :
( ( ( cB @ X3 )
= $true )
| ( ( cA @ X3 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f6]) ).
thf(f8,plain,
! [X3: $i] :
( ( ( cB @ X3 )
= $true )
| ( ( cA @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( cB @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X1: $i] :
( ( ( cA @ X1 )
= $true )
| ( ( sK0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,definition,
( spl2_1
<=> ( ( sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f16,plain,
( ( ( sK0 @ sK1 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f17,plain,
spl2_1,
inference(avatar_split_clause,[],[f9,f14]) ).
thf(f19,definition,
( spl2_2
<=> ( ( cB @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( cB @ sK1 )
!= $true )
| spl2_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f10,f19]) ).
thf(f23,plain,
( ( $true != $true )
| ( $true
!= ( cA @ sK1 ) )
| spl2_2 ),
inference(superposition,[],[f21,f8]) ).
thf(f24,plain,
( ( $true
!= ( cA @ sK1 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f26,definition,
( spl2_3
<=> ( $true
= ( cA @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
!= ( cA @ sK1 ) )
| spl2_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f29,plain,
( ~ spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f24,f19,f26]) ).
thf(f30,plain,
( ( $true != $true )
| ( ( sK0 @ sK1 )
!= $true )
| spl2_3 ),
inference(superposition,[],[f28,f11]) ).
thf(f31,plain,
( ( ( sK0 @ sK1 )
!= $true )
| spl2_3 ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( $false
| ~ spl2_1
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f31,f16]) ).
thf(f33,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f32]) ).
cnf(s1,plain,
spl2_1,
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
( spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f29]) ).
cnf(s4,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s5,plain,
~ spl2_3,
inference(rat,[],[s3,s2]) ).
cnf(s6,plain,
~ spl2_1,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6]) ).
thf(f34,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO305^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.20 % Computer : n017.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Sep 29 16:39:52 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.24 Running higher-order theorem proving
% 0.12/0.25 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
% 0.22/0.29 % (577777)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (577791)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=3721636355: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)
% 0.22/0.29 % (577791) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-577777-577791"...
% 0.22/0.29 % (577791)...printing done.
% 0.22/0.29 % (577791)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (577791)------------------------------
% 0.22/0.29 % (577791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (577791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (577791)CaDiCaL version: 2.1.3
% 0.22/0.29 % (577791)Termination reason: Refutation
% 0.22/0.29 % (577791)Time elapsed: 0.001 s
% 0.22/0.29 % (577791)Peak memory usage: 13 MB
% 0.22/0.29 % (577791)Instructions burned: 2 (million)
% 0.22/0.29 % (577777)Success in time 0.029 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------