%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV411^5 : 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 : 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 08:38:36 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 132 ( 31 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 112 ( 21 ~; 22 |; 4 &; 48 @)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 20 !; 1 ?; 21 :)
% 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(f1,conjecture,
( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDUAL_EG1_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) )
=> ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( cA @ X0 )
=> ( cB @ X0 ) )
| ! [X1: $i] :
( ( cA @ X1 )
=> ( cB @ X1 ) ) )
=> ! [X2: $i] :
( ( cA @ X2 )
=> ( cB @ X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( ( cA @ X0 )
= $true )
=> ( ( cB @ X0 )
= $true ) )
| ! [X1: $i] :
( ( $true
= ( cA @ X1 ) )
=> ( $true
= ( cB @ X1 ) ) ) )
=> ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
=> ( $true
= ( cB @ X2 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) )
| ! [X1: $i] :
( ( $true
= ( cB @ X1 ) )
| ( $true
!= ( cA @ X1 ) ) ) )
& ? [X2: $i] :
( ( $true
!= ( cB @ X2 ) )
& ( ( cA @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ! [X0: $i] :
( ( ( cB @ X0 )
= $true )
| ( ( cA @ X0 )
!= $true ) )
| ! [X1: $i] :
( ( $true
= ( cB @ X1 ) )
| ( $true
!= ( cA @ X1 ) ) ) )
& ( $true
!= ( cB @ sK0 ) )
& ( ( cA @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f5]) ).
thf(f7,plain,
( ( cA @ sK0 )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( $true
!= ( cB @ sK0 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cB @ X1 ) )
| ( ( cA @ X0 )
!= $true )
| ( $true
!= ( cA @ X1 ) )
| ( ( cB @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,definition,
( spl1_1
<=> ! [X1: $i] :
( ( $true
= ( cB @ X1 ) )
| ( $true
!= ( cA @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f14,plain,
( ! [X1: $i] :
( ( $true
!= ( cA @ X1 ) )
| ( $true
= ( cB @ X1 ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f15,plain,
( spl1_1
| spl1_1 ),
inference(avatar_split_clause,[],[f9,f13,f13]) ).
thf(f16,plain,
( ( $true
= ( cB @ sK0 ) )
| ( $true != $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f14,f7]) ).
thf(f17,plain,
( ( $true
= ( cB @ sK0 ) )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f18,plain,
( $false
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f17,f8]) ).
thf(f19,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f18]) ).
cnf(s1,plain,
( spl1_1
| spl1_1 ),
inference(sat_conversion,[],[f15]) ).
cnf(s2,plain,
spl1_1,
inference(rat,[],[s1]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f19]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
thf(f20,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV411^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:48:33 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.19/0.27 % (3694666)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (3694677)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1540273561:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (3694677) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3694666-3694677"...
% 0.19/0.27 % (3694677)...printing done.
% 0.19/0.27 % (3694677)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (3694677)------------------------------
% 0.19/0.27 % (3694677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3694677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3694677)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3694677)Termination reason: Refutation
% 0.19/0.27 % (3694677)Time elapsed: 0.001 s
% 0.19/0.27 % (3694677)Peak memory usage: 13 MB
% 0.19/0.27 % (3694677)Instructions burned: 1 (million)
% 0.19/0.27 % (3694666)Success in time 0.033 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------