%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO154^5 : 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 08:46:44 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 144 ( 35 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 132 ( 23 ~; 11 |; 17 &; 68 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 22 !; 4 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
cQ: $i > $o ).
thf(func_def_3,type,
f: $i > $i ).
thf(func_def_4,type,
cP: $i > $o ).
thf(f1,conjecture,
( ( ( cP @ a )
& ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ ( g @ X1 ) ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDEMO_TRIV1) ).
thf(f2,negated_conjecture,
~ ( ( ( cP @ a )
& ! [X1: $i] :
( ( cQ @ X1 )
=> ( cR @ ( g @ X1 ) ) )
& ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ ( f @ X0 ) ) ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( cP @ a )
& ! [X0: $i] :
( ( cQ @ X0 )
=> ( cR @ ( g @ X0 ) ) )
& ! [X1: $i] :
( ( cP @ X1 )
=> ( cQ @ ( f @ X1 ) ) ) )
=> ? [X2: $i] : ( cR @ X2 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X1: $i] :
( ( $true
= ( cP @ X1 ) )
=> ( ( cQ @ ( f @ X1 ) )
= $true ) )
& ! [X0: $i] :
( ( ( cQ @ X0 )
= $true )
=> ( $true
= ( cR @ ( g @ X0 ) ) ) )
& ( ( cP @ a )
= $true ) )
=> ? [X2: $i] :
( ( cR @ X2 )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X2: $i] :
( ( cR @ X2 )
!= $true )
& ! [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
| ( ( cQ @ ( f @ X1 ) )
= $true ) )
& ! [X0: $i] :
( ( $true
= ( cR @ ( g @ X0 ) ) )
| ( ( cQ @ X0 )
!= $true ) )
& ( ( cP @ a )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X1: $i] :
( ( $true
!= ( cP @ X1 ) )
| ( ( cQ @ ( f @ X1 ) )
= $true ) )
& ! [X2: $i] :
( ( cR @ X2 )
!= $true )
& ! [X0: $i] :
( ( $true
= ( cR @ ( g @ X0 ) ) )
| ( ( cQ @ X0 )
!= $true ) )
& ( ( cP @ a )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cQ @ ( f @ X0 ) )
= $true ) )
& ! [X1: $i] :
( ( cR @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( cR @ ( g @ X2 ) )
= $true )
| ( $true
!= ( cQ @ X2 ) ) )
& ( ( cP @ a )
= $true ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( cP @ a )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: $i] :
( ( $true
!= ( cQ @ X2 ) )
| ( ( cR @ ( g @ X2 ) )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X1: $i] :
( ( cR @ X1 )
!= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X0: $i] :
( ( ( cQ @ ( f @ X0 ) )
= $true )
| ( ( cP @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,definition,
( spl0_1
<=> ( ( cP @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( ( ( cP @ a )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f17,plain,
spl0_1,
inference(avatar_split_clause,[],[f8,f14]) ).
thf(f18,plain,
! [X2: $i] :
( $true
!= ( cQ @ X2 ) ),
inference(forward_subsumption_resolution,[],[f9,f10]) ).
thf(f19,plain,
! [X0: $i] :
( ( cP @ X0 )
!= $true ),
inference(forward_subsumption_resolution,[],[f11,f18]) ).
thf(f20,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(superposition,[],[f19,f16]) ).
thf(f21,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f21]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
~ spl0_1,
inference(sat_conversion,[],[f22]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
thf(f23,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO154^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n015.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Tue Sep 29 16:39:04 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.33 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
% 0.25/0.36 % (3760818)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.36 % (3760826)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=3961783478: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)
% 0.25/0.36 % (3760826) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3760818-3760826"...
% 0.25/0.36 % (3760826)...printing done.
% 0.25/0.36 % (3760826)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.36 % (3760826)------------------------------
% 0.25/0.36 % (3760826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (3760826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (3760826)CaDiCaL version: 2.1.3
% 0.25/0.36 % (3760826)Termination reason: Refutation
% 0.25/0.36 % (3760826)Time elapsed: 0.002 s
% 0.25/0.36 % (3760826)Peak memory usage: 13 MB
% 0.25/0.36 % (3760826)Instructions burned: 2 (million)
% 0.25/0.36 % (3760818)Success in time 0.026 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------