%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU893^5 : 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 : n013.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 08:31:53 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 149 ( 60 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 164 ( 35 ~; 29 |; 24 &; 70 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 14 !; 18 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cF: b > a ).
thf(func_def_1,type,
cS: b > $o ).
thf(func_def_2,type,
cR: b > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: b ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( X0
= ( cF @ X1 ) )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
=> ( ? [X1: b] :
( ( X0
= ( cF @ X1 ) )
& ( cS @ X1 ) )
| ? [X1: b] :
( ( cR @ X1 )
& ( X0
= ( cF @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM34A_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( cF @ X1 ) )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
=> ( ? [X1: b] :
( ( X0
= ( cF @ X1 ) )
& ( cS @ X1 ) )
| ? [X1: b] :
( ( cR @ X1 )
& ( X0
= ( cF @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( cF @ X1 ) )
& ( ( cR @ X1 )
| ( cS @ X1 ) ) )
=> ( ? [X2: b] :
( ( ( cF @ X2 )
= X0 )
& ( cS @ X2 ) )
| ? [X3: b] :
( ( cR @ X3 )
& ( ( cF @ X3 )
= X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) )
& ( ( cF @ X1 )
= X0 ) )
=> ( ? [X2: b] :
( ( ( cS @ X2 )
= $true )
& ( ( cF @ X2 )
= X0 ) )
| ? [X3: b] :
( ( $true
= ( cR @ X3 ) )
& ( ( cF @ X3 )
= X0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ! [X2: b] :
( ( ( cS @ X2 )
!= $true )
| ( ( cF @ X2 )
!= X0 ) )
& ! [X3: b] :
( ( ( cF @ X3 )
!= X0 )
| ( $true
!= ( cR @ X3 ) ) )
& ? [X1: b] :
( ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) )
& ( ( cF @ X1 )
= X0 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a] :
( ! [X2: b] :
( ( ( cS @ X2 )
!= $true )
| ( ( cF @ X2 )
!= X0 ) )
& ? [X1: b] :
( ( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $true ) )
& ( ( cF @ X1 )
= X0 ) )
& ! [X3: b] :
( ( ( cF @ X3 )
!= X0 )
| ( $true
!= ( cR @ X3 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a] :
( ! [X1: b] :
( ( ( cS @ X1 )
!= $true )
| ( ( cF @ X1 )
!= X0 ) )
& ? [X2: b] :
( ( ( ( cS @ X2 )
= $true )
| ( $true
= ( cR @ X2 ) ) )
& ( ( cF @ X2 )
= X0 ) )
& ! [X3: b] :
( ( ( cF @ X3 )
!= X0 )
| ( $true
!= ( cR @ X3 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X1: b] :
( ( ( cS @ X1 )
!= $true )
| ( ( cF @ X1 )
!= sK0 ) )
& ( ( $true
= ( cS @ sK1 ) )
| ( $true
= ( cR @ sK1 ) ) )
& ( sK0
= ( cF @ sK1 ) )
& ! [X3: b] :
( ( sK0
!= ( cF @ X3 ) )
| ( $true
!= ( cR @ X3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f7]) ).
thf(f9,plain,
! [X3: b] :
( ( sK0
!= ( cF @ X3 ) )
| ( $true
!= ( cR @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( sK0
= ( cF @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( $true
= ( cS @ sK1 ) )
| ( $true
= ( cR @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X1: b] :
( ( ( cF @ X1 )
!= sK0 )
| ( ( cS @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,definition,
( spl2_1
<=> ( $true
= ( cR @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f20,definition,
( spl2_2
<=> ( $true
= ( cS @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f22,plain,
( ( $true
= ( cS @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f23,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f11,f20,f16]) ).
thf(f24,plain,
( ( $true
!= ( cR @ sK1 ) )
| ( sK0 != sK0 ) ),
inference(constrained_superposition,[],[f9,f10]) ).
thf(f25,plain,
( $true
!= ( cR @ sK1 ) ),
inference(trivial_inequality_removal,[],[f24]) ).
thf(f26,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f25,f16]) ).
thf(f27,plain,
( ( $true
!= ( cS @ sK1 ) )
| ( sK0 != sK0 ) ),
inference(constrained_superposition,[],[f12,f10]) ).
thf(f28,plain,
( $true
!= ( cS @ sK1 ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f29,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f28,f22]) ).
thf(f30,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f29]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
~ spl2_1,
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
thf(f31,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU893^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n013.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 14:43:51 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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
% 0.10/0.25 % (2212401)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.25 % (2212408)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1974860769:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.10/0.25 % (2212408) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2212401-2212408"...
% 0.10/0.25 % (2212408)...printing done.
% 0.10/0.25 % (2212408)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (2212408)------------------------------
% 0.10/0.26 % (2212408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (2212408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (2212408)CaDiCaL version: 2.1.3
% 0.10/0.26 % (2212408)Termination reason: Refutation
% 0.10/0.26 % (2212408)Time elapsed: 0.001 s
% 0.10/0.26 % (2212408)Peak memory usage: 13 MB
% 0.10/0.26 % (2212408)Instructions burned: 2 (million)
% 0.10/0.26 % (2212401)Success in time 0.026 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------