%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO233^5 : 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 08:47:15 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 40 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 62 ( 13 ~; 6 |; 2 &; 32 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cN: $i > $i ).
thf(func_def_1,type,
cM: $i > $i ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
=> ( X1 @ ( cN @ X0 ) ) )
=> ( cM = cN ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cLEIBNIZ) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
=> ( X1 @ ( cN @ X0 ) ) )
=> ( cM = cN ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i,X1: $i > $o] :
( ( X1 @ ( cM @ X0 ) )
=> ( X1 @ ( cN @ X0 ) ) )
=> ( cM = cN ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X1: $i > $o,X0: $i] :
( ( ( X1 @ ( cM @ X0 ) )
= $true )
=> ( ( X1 @ ( cN @ X0 ) )
= $true ) )
=> ( cM = cN ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cM != cN )
& ! [X1: $i > $o,X0: $i] :
( ( ( X1 @ ( cM @ X0 ) )
!= $true )
| ( ( X1 @ ( cN @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( cM != cN )
& ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( cM @ X1 ) )
!= $true )
| ( ( X0 @ ( cN @ X1 ) )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ ( cN @ X1 ) )
= $true )
| ( ( X0 @ ( cM @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
cM != cN,
inference(cnf_transformation,[],[f6]) ).
thf(f11,definition,
( spl0_1
<=> ( cM = cN ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f13,plain,
( ( cM != cN )
| spl0_1 ),
inference(avatar_component_clause,[],[f11]) ).
thf(f14,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f8,f11]) ).
thf(f15,plain,
! [X0: $i] :
( ( cM @ X0 )
= ( cN @ X0 ) ),
inference(leibniz_equality_elimination,[],[f7]) ).
thf(f25,plain,
( ( ( cN @ sK1 )
!= ( cM @ sK1 ) )
| spl0_1 ),
inference(negative_extensionality,[],[f13]) ).
thf(f26,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f25,f15]) ).
thf(f27,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f26]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f14]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
thf(f28,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO233^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:43:48 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.07/0.26 % (3771964)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.26 % (3771972)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=1586669880: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)
% 0.07/0.26 % (3771972) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3771964-3771972"...
% 0.07/0.26 % (3771972)...printing done.
% 0.07/0.26 % (3771972)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (3771972)------------------------------
% 0.07/0.26 % (3771972)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3771972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3771972)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3771972)Termination reason: Refutation
% 0.07/0.26 % (3771972)Time elapsed: 0.001 s
% 0.07/0.26 % (3771972)Peak memory usage: 13 MB
% 0.07/0.26 % (3771972)Instructions burned: 1 (million)
% 0.07/0.26 % (3771964)Success in time 0.016 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------