%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL732^5 : 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 : n003.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 08:14:35 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 164 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 116 ( 30 ~; 15 |; 8 &; 45 @)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 8 sgn 11 !; 17 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
p: $i > $o ).
thf(f1,conjecture,
( ! [X0: b > $o] :
? [X1: b] :
( ? [X2: $i] : ( p @ X2 )
=> ( p @ y ) )
=> ? [X3: ( b > $o ) > b] :
! [X0: b > $o] :
( ? [X2: $i] : ( p @ X2 )
=> ( p @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5310_SUB3) ).
thf(f2,negated_conjecture,
~ ( ! [X0: b > $o] :
? [X1: b] :
( ? [X2: $i] : ( p @ X2 )
=> ( p @ y ) )
=> ? [X3: ( b > $o ) > b] :
! [X0: b > $o] :
( ? [X2: $i] : ( p @ X2 )
=> ( p @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ? [X2: $i] : ( p @ X2 )
=> ( p @ y ) )
=> ( ? [X5: $i] : ( p @ X5 )
=> ( p @ y ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ? [X2: $i] :
( ( p @ X2 )
= $true )
=> ( ( p @ y )
= $true ) )
=> ( ? [X5: $i] :
( $true
= ( p @ X5 ) )
=> ( ( p @ y )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ? [X0: $i] :
( $true
= ( p @ X0 ) )
=> ( ( p @ y )
= $true ) )
=> ( ? [X1: $i] :
( ( p @ X1 )
= $true )
=> ( ( p @ y )
= $true ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ( ( p @ y )
!= $true )
& ? [X1: $i] :
( ( p @ X1 )
= $true )
& ( ! [X0: $i] :
( $true
!= ( p @ X0 ) )
| ( ( p @ y )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( p @ y )
!= $true )
& ? [X1: $i] :
( ( p @ X1 )
= $true )
& ( ! [X0: $i] :
( $true
!= ( p @ X0 ) )
| ( ( p @ y )
= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ( p @ y )
!= $true )
& ? [X0: $i] :
( $true
= ( p @ X0 ) )
& ( ! [X1: $i] :
( ( p @ X1 )
!= $true )
| ( ( p @ y )
= $true ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( p @ y )
!= $true )
& ( $true
= ( p @ sK0 ) )
& ( ! [X1: $i] :
( ( p @ X1 )
!= $true )
| ( ( p @ y )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
! [X1: $i] :
( ( ( p @ y )
= $true )
| ( ( p @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( $true
= ( p @ sK0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( p @ y )
!= $true ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,definition,
( spl1_1
<=> ( ( p @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f19,definition,
( spl1_2
<=> ! [X1: $i] :
( ( p @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f20,plain,
( ! [X1: $i] :
( ( p @ X1 )
!= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f21,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f10,f19,f15]) ).
thf(f23,definition,
( spl1_3
<=> ( $true
= ( p @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
= ( p @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,plain,
spl1_3,
inference(avatar_split_clause,[],[f11,f23]) ).
thf(f27,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f12,f15]) ).
thf(f28,plain,
( ( $true != $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(superposition,[],[f20,f25]) ).
thf(f29,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f30,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f29]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
spl1_3,
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f30]) ).
cnf(s5,plain,
~ spl1_2,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
thf(f31,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL732^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 10:04:58 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.28 % (2316692)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (2316700)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=509991226: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)
% 0.22/0.28 % (2316700) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2316692-2316700"...
% 0.22/0.28 % (2316700)...printing done.
% 0.22/0.28 % (2316700)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (2316700)------------------------------
% 0.22/0.28 % (2316700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2316700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2316700)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2316700)Termination reason: Refutation
% 0.22/0.28 % (2316700)Time elapsed: 0.002 s
% 0.22/0.28 % (2316700)Peak memory usage: 12 MB
% 0.22/0.28 % (2316700)Instructions burned: 1 (million)
% 0.22/0.28 % (2316692)Success in time 0.03 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------