%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET183^5 : 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 : n001.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 08:23:15 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 141 ( 44 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 134 ( 23 ~; 21 |; 16 &; 64 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 31 ( 0 sgn 16 !; 4 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_42_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X3: a] :
( ( X1 @ X3 )
& ( X0 @ X3 ) ) )
= X0 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= X0 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
& ( X0 @ Y0 ) ) )
!= X1 ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X2: a] :
( ( $true
!= ( sK1 @ X2 ) )
| ( $true
= ( sK0 @ X2 ) ) )
& ( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
!= sK1 ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: a] :
( ( $true
!= ( sK1 @ X2 ) )
| ( $true
= ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( sK1 @ sK2 )
!= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f13,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f14,plain,
( ( ( sK1 @ sK2 )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f12]) ).
thf(f15,plain,
( ( ( sK1 @ sK2 )
= $false )
| ( ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(duplicate_literal_removal,[],[f16]) ).
thf(f18,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f20,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f20]) ).
thf(f23,definition,
( spl3_1
<=> ( $false
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,definition,
( spl3_2
<=> ( ( sK1 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f27,plain,
( ( ( sK1 @ sK2 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f17,f26,f23]) ).
thf(f29,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(backward_demodulation,[],[f21,f27]) ).
thf(f30,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f30]) ).
thf(f32,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f9,f21]) ).
thf(f33,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f33,f24]) ).
thf(f35,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f34]) ).
thf(f36,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f35]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
~ spl3_1,
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f37,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET183^5 : 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 : n001.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 13:43:21 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
% 0.07/0.23 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
% 0.19/0.28 % (1251316)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (1251339)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=501682330:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (1251339) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1251316-1251339"...
% 0.19/0.28 % (1251339)...printing done.
% 0.19/0.28 % (1251339)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (1251339)------------------------------
% 0.19/0.28 % (1251339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1251339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1251339)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1251339)Termination reason: Refutation
% 0.19/0.28 % (1251339)Time elapsed: 0.002 s
% 0.19/0.28 % (1251339)Peak memory usage: 13 MB
% 0.19/0.28 % (1251339)Instructions burned: 2 (million)
% 0.19/0.28 % (1251316)Success in time 0.037 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------