%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV175^5 : 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 : 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 08:37:58 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 20 unt; 0 typ; 4 def)
% Number of atoms : 174 ( 64 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 358 ( 67 ~; 24 |; 34 &; 205 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 7 con; 0-4 aty)
% ( 0 !!; 24 ??; 0 @@+; 0 @@-)
% Number of variables : 68 ( 0 sgn 8 !; 9 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_11,type,
sK1: $i > $o ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ~ ( X1 @ ( X0 @ X1 ) )
& ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM144A_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ~ ( X1 @ ( X0 @ X1 ) )
& ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ~ ( X1 @ ( X0 @ X1 ) )
& ( ( X0 @ X1 )
= ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( sK0 @ X1 )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
! [X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( ( X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true ),
inference(equality_resolution,[],[f8]) ).
thf(f11,plain,
( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f12,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( ~ ( sK1 @ ( sK0 @ sK1 ) )
& ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f14,plain,
( ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( ~ ( sK1 @ ( sK0 @ sK1 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f13]) ).
thf(f16,plain,
( ( sK1 @ ( sK0 @ sK1 ) )
= $false ),
inference(not_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f14]) ).
thf(f19,definition,
( spl2_1
<=> ( ( sK1 @ ( sK0 @ sK1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f21,plain,
( ( ( sK1 @ ( sK0 @ sK1 ) )
= $false )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
spl2_1,
inference(avatar_split_clause,[],[f16,f19]) ).
thf(f24,definition,
( spl2_2
<=> ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f26,plain,
( ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
spl2_2,
inference(avatar_split_clause,[],[f17,f24]) ).
thf(f28,plain,
( ( ( sK1
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $false )
| ~ spl2_1
| ~ spl2_2 ),
inference(superposition,[],[f21,f26]) ).
thf(f29,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( ( sK1
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ~ spl2_2 ),
inference(superposition,[],[f8,f26]) ).
thf(f30,plain,
( ( ( sK1
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f32,definition,
( spl2_3
<=> ( ( sK1
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f34,plain,
( ( ( sK1
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,plain,
( spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f30,f24,f32]) ).
thf(f37,definition,
( spl2_4
<=> ( ( sK1
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f39,plain,
( ( ( sK1
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
= $false )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl2_4
| ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f28,f24,f19,f37]) ).
thf(f42,plain,
( ( $true = $false )
| ~ spl2_3
| ~ spl2_4 ),
inference(superposition,[],[f34,f39]) ).
thf(f45,plain,
( $false
| ~ spl2_3
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f46,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f45]) ).
cnf(s1,plain,
spl2_1,
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
spl2_2,
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s4,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s6,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f46]) ).
cnf(s7,plain,
spl2_3,
inference(rat,[],[s3,s2]) ).
cnf(s8,plain,
~ spl2_4,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl2_1,
inference(rat,[],[s4,s2,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s9]) ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV175^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:17:51 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.29 % (2239898)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.29 % (2239906)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=358829085: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)
% 0.23/0.29 % (2239903)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1426200181:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.29 % (2239904)lrs+10_16_si=on:nwc=1.5:random_seed=1672320879:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.29 % (2239905)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=157847583:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.29 % (2239905)Refutation not found, incomplete strategy
% 0.23/0.29 % (2239905)------------------------------
% 0.23/0.29 % (2239905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2239905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2239905)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2239905)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.29 % (2239905)Time elapsed: 0.001 s
% 0.23/0.29 % (2239905)Peak memory usage: 12 MB
% 0.23/0.29 % (2239905)Instructions burned: 1 (million)
% 0.23/0.29 % (2239903) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2239898-2239903"...
% 0.23/0.29 % (2239906) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2239898-2239906"...
% 0.23/0.29 % (2239904) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2239898-2239904"...
% 0.23/0.29 % (2239905)------------------------------
% 0.23/0.29 % (2239905)------------------------------
% 0.23/0.29 % (2239908)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=36725986:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.29 % (2239906)...printing done.
% 0.23/0.29 % (2239903)...printing done.
% 0.23/0.29 % (2239904)...printing done.
% 0.23/0.29 % (2239906)Refutation found. Thanks to Tanya!
% 0.23/0.29 % SZS status Theorem for theBenchmark
% 0.23/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.29 % (2239906)------------------------------
% 0.23/0.29 % (2239906)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.29 % (2239906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.29 % (2239906)CaDiCaL version: 2.1.3
% 0.23/0.29 % (2239906)Termination reason: Refutation
% 0.23/0.29 % (2239906)Time elapsed: 0.004 s
% 0.23/0.29 % (2239906)Peak memory usage: 13 MB
% 0.23/0.29 % (2239906)Instructions burned: 5 (million)
% 0.23/0.29 % (2239898)Success in time 0.038 s
% 0.23/0.29 % Vampire exiting
%------------------------------------------------------------------------------