%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET595^5 : 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 : n005.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 08:23:19 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 193 ( 53 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 201 ( 41 ~; 46 |; 16 &; 87 @)
% ( 3 <=>; 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 : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn 15 !; 2 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( X0 @ X3 ) ) )
= X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_54_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( X0 @ X3 ) ) )
= X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ( ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( X0 @ X3 ) ) )
= X1 ) ),
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 @ Y0 ) ) ) )
= X1 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) )
!= X1 )
& ! [X2: a] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
& ! [X2: a] :
( ( $true
!= ( sK0 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
! [X2: a] :
( ( $true
!= ( sK0 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( ( sK1 @ sK2 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f13,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
@ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(xor_proxy_clausification,[],[f11]) ).
thf(f14,plain,
( ( ( ( sK0 @ sK2 )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
= $false )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
( ( ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) )
= $false )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f16,plain,
( ( ( sK1 @ sK2 )
= $false )
| ( ( sK0 @ sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f14]) ).
thf(f17,plain,
( ( ( ~ ( sK0 @ sK2 ) )
= $false )
| ( ( sK1 @ sK2 )
= $false )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f15]) ).
thf(f18,plain,
( ( ( sK1 @ sK2 )
= $false )
| ( $true
= ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( ( sK1 @ sK2 )
= $false ) ),
inference(duplicate_literal_removal,[],[f18]) ).
thf(f20,plain,
( ( $true
= ( ( sK0 @ sK2 )
| ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f12]) ).
thf(f21,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f24,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f23]) ).
thf(f27,definition,
( spl3_1
<=> ( ( sK1 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f29,plain,
( ( ( sK1 @ sK2 )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl3_2
<=> ( ( sK0 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f33,plain,
( ( ( sK0 @ sK2 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f16,f31,f27]) ).
thf(f36,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f19,f36,f27]) ).
thf(f40,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(forward_subsumption_resolution,[],[f24,f7]) ).
thf(f41,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f33,f38]) ).
thf(f42,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f43,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f42]) ).
thf(f45,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f29,f40]) ).
thf(f46,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f47,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f46]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
spl3_3,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
~ spl3_2,
inference(rat,[],[s3,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s4]) ).
thf(f48,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET595^5 : 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 : n005.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 13:38:16 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 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
% 0.21/0.28 % (1673469)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1673474)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2986278532:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (1673474) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1673469-1673474"...
% 0.21/0.28 % (1673474)...printing done.
% 0.21/0.28 % (1673474)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1673474)------------------------------
% 0.21/0.28 % (1673474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1673474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1673474)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1673474)Termination reason: Refutation
% 0.21/0.28 % (1673474)Time elapsed: 0.002 s
% 0.21/0.28 % (1673474)Peak memory usage: 13 MB
% 0.21/0.28 % (1673474)Instructions burned: 2 (million)
% 0.21/0.28 % (1673469)Success in time 0.029 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------