%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET169^5 : 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 : n014.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 08:23:14 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 19 unt; 0 typ; 6 def)
% Number of atoms : 390 ( 93 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 412 ( 41 ~; 110 |; 57 &; 198 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 40 ( 0 sgn 12 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
vOR: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK0: a > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_10,type,
sK3: a ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( X2 @ X3 )
| ( X1 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ( X0 @ X4 )
& ( X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_70_pme) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ^ [X3: a] :
( ( X0 @ X3 )
& ( ( X2 @ X3 )
| ( X1 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X2 @ X4 )
& ( X0 @ X4 ) )
| ( ( X0 @ X4 )
& ( X1 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( X2 @ X3 )
& ( ( X0 @ X3 )
| ( X1 @ X3 ) ) ) )
= ( ^ [X4: a] :
( ( ( X0 @ X4 )
& ( X2 @ X4 ) )
| ( ( X2 @ X4 )
& ( X1 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X2 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > $o,X0: a > $o,X1: a > $o] :
( ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
& ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X1 @ Y0 )
| ( X0 @ Y0 ) )
& ( X2 @ Y0 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
& ( X0 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X2 @ Y0 )
| ( X1 @ Y0 ) )
& ( X0 @ Y0 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) ) )
!= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK3 ) )
| ( ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK3 )
= $true ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
| ( sK1 @ Y0 ) )
& ( sK0 @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( $false
= ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( $false
= ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( ( ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f21,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f20]) ).
thf(f23,plain,
( ( ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f24,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f24]) ).
thf(f28,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f25]) ).
thf(f29,plain,
( ( ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f30,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( ( ( ( sK2 @ sK3 )
| ( sK1 @ sK3 ) )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f41,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f42,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[],[f41]) ).
thf(f44,plain,
( ( ( ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
= $true )
| ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f30]) ).
thf(f45,plain,
( ( ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f44]) ).
thf(f51,plain,
( ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true )
| ( ( sK0 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f45]) ).
thf(f52,plain,
( ( sK0 @ sK3 )
= $true ),
inference(duplicate_literal_removal,[],[f51]) ).
thf(f55,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f56,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f58,definition,
( spl4_2
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f59,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f60,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f21,f58,f55]) ).
thf(f62,definition,
( spl4_3
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f63,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f66,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f28,f62,f55]) ).
thf(f68,definition,
( spl4_4
<=> ( ( sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f69,plain,
( ( ( sK0 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,definition,
( spl4_5
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f72,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f74,definition,
( spl4_6
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f75,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f78,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f42,f74,f71]) ).
thf(f82,plain,
spl4_4,
inference(avatar_split_clause,[],[f52,f68]) ).
thf(f84,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f72,f63]) ).
thf(f85,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f86,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f87,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_4 ),
inference(backward_demodulation,[],[f69,f56]) ).
thf(f88,plain,
( $false
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f89,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f88]) ).
thf(f90,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_6 ),
inference(forward_demodulation,[],[f75,f59]) ).
thf(f91,plain,
( $false
| ~ spl4_2
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f92,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f91]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s7,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f78]) ).
cnf(s11,plain,
spl4_4,
inference(sat_conversion,[],[f82]) ).
cnf(s13,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f86]) ).
cnf(s14,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f89]) ).
cnf(s15,plain,
( ~ spl4_2
| ~ spl4_6 ),
inference(sat_conversion,[],[f92]) ).
cnf(s16,plain,
~ spl4_1,
inference(rat,[],[s14,s11]) ).
cnf(s17,plain,
spl4_3,
inference(rat,[],[s4,s16]) ).
cnf(s18,plain,
~ spl4_5,
inference(rat,[],[s13,s17]) ).
cnf(s19,plain,
spl4_6,
inference(rat,[],[s7,s18]) ).
cnf(s20,plain,
~ spl4_2,
inference(rat,[],[s15,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s20,s16]) ).
thf(f93,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET169^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.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 13:37:00 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.22/0.29 % (2661601)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (2661625)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2282775898:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (2661625) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2661601-2661625"...
% 0.22/0.29 % (2661625)...printing done.
% 0.22/0.29 % (2661625)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (2661625)------------------------------
% 0.22/0.29 % (2661625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2661625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2661625)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2661625)Termination reason: Refutation
% 0.22/0.29 % (2661625)Time elapsed: 0.002 s
% 0.22/0.29 % (2661625)Peak memory usage: 13 MB
% 0.22/0.29 % (2661625)Instructions burned: 5 (million)
% 0.22/0.29 % (2661601)Success in time 0.037 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------