%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET628^5 : 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 : n011.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 08:23:24 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 184 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 150 ( 46 ~; 43 |; 11 &; 42 @)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 46 ( 21 sgn 15 !; 10 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_7,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( ( ^ [X1: a] : $false )
!= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_110_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( ( ^ [X1: a] : $false )
!= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( ( ^ [X2: a] : $false )
!= X0 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ( ( ^ [Y0: a] : $false )
!= X0 )
<=> ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o] :
( ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
<~> ( ( ^ [Y0: a] : $false )
!= X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
= X0 )
| ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X1 )
!= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
!= X0 )
| ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
= X0 )
| ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X1 )
!= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
!= X0 )
| ? [X2: a] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( sK0
= ( ^ [Y0: a] : $false ) )
| ! [X1: a] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X1 ) ) ) )
& ( ( sK0
!= ( ^ [Y0: a] : $false ) )
| ( ( $true
= ( sK0 @ sK1 ) )
& ( $true
= ( sK0 @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f7]) ).
thf(f9,plain,
( ( sK0
!= ( ^ [Y0: a] : $false ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X1: a] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X1 ) )
| ( sK0
= ( ^ [Y0: a] : $false ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X1: a] :
( ( sK0
= ( ^ [Y0: a] : $false ) )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f11]) ).
thf(f16,definition,
( spl2_1
<=> ( sK0
= ( ^ [Y0: a] : $false ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f17,plain,
( ( sK0
!= ( ^ [Y0: a] : $false ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f18,plain,
( ( sK0
= ( ^ [Y0: a] : $false ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f20,definition,
( spl2_2
<=> ! [X1: a] :
( $true
!= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f21,plain,
( ! [X1: a] :
( $true
!= ( sK0 @ X1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f14,f20,f16]) ).
thf(f24,definition,
( spl2_3
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f9,f24,f16]) ).
thf(f29,plain,
( ( ( sK0 @ sK3 )
!= ( ^ [Y0: a] : $false
@ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f17]) ).
thf(f30,plain,
( ( ( ^ [Y0: a] : $false
@ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f29]) ).
thf(f33,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( $false = $true )
| spl2_1 ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f34,plain,
( ( ( sK0 @ sK3 )
= $true )
| spl2_1 ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f34,f21]) ).
thf(f36,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f35]) ).
thf(f37,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( sK0 @ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[],[f18]) ).
thf(f38,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: a] : $false
@ X1 ) ) )
| ~ spl2_1 ),
inference(iff_proxy_clausification,[],[f37]) ).
thf(f41,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false = $true ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f42,plain,
( ! [X1: a] :
( $false
= ( sK0 @ X1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f44,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3 ),
inference(constrained_superposition,[],[f26,f42]) ).
thf(f47,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f44]) ).
thf(f48,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f47]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( ~ spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s4,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f36]) ).
cnf(s6,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s7,plain,
spl2_1,
inference(rat,[],[s1,s4]) ).
cnf(s8,plain,
~ spl2_3,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s8,s7]) ).
thf(f49,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:40:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.27 % (106390)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (106397)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4067288009:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (106397)Refutation not found, incomplete strategy
% 0.20/0.27 % (106397)------------------------------
% 0.20/0.27 % (106397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (106397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (106397)CaDiCaL version: 2.1.3
% 0.20/0.27 % (106397)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.27 % (106397)Time elapsed: 0.0000 s
% 0.20/0.27 % (106397)Peak memory usage: 12 MB
% 0.20/0.27 % (106397)------------------------------
% 0.20/0.27 % (106397)------------------------------
% 0.20/0.27 % (106396)lrs+10_16_si=on:nwc=1.5:random_seed=3068908169:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (106395)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1089095573:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (106396) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-106390-106396"...
% 0.20/0.27 % (106395) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-106390-106395"...
% 0.20/0.27 % (106403)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2757322214:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.27 % (106399)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=264601438:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (106396)...printing done.
% 0.20/0.27 % (106395)...printing done.
% 0.20/0.27 % (106400)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1250511397:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (106403) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-106390-106403"...
% 0.20/0.27 % (106396)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (106396)------------------------------
% 0.20/0.27 % (106396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (106396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (106396)CaDiCaL version: 2.1.3
% 0.20/0.27 % (106396)Termination reason: Refutation
% 0.20/0.27 % (106396)Time elapsed: 0.003 s
% 0.20/0.27 % (106396)Peak memory usage: 13 MB
% 0.20/0.27 % (106396)Instructions burned: 2 (million)
% 0.20/0.27 % (106390)Success in time 0.041 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------