%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU848^5 : 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 08:31:48 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 9 unt; 0 typ; 8 def)
% Number of atoms : 338 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 337 ( 74 ~; 116 |; 6 &; 122 @)
% ( 13 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 12 con; 0-4 aty)
% Number of variables : 57 ( 0 sgn 26 !; 8 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,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(func_def_10,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 )
<=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM38_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 )
<=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= X0 )
<=> ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
<=> ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
<=> ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X1: a > $o,X0: a > $o] :
( ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 )
<~> ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X1: a > $o,X0: a > $o] :
( ( ? [X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X1 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
!= X0 ) )
& ( ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X0 @ Y0 ) ) )
= X0 ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) )
!= X1 ) )
& ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
| ( X1 @ Y0 ) ) )
= X1 ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( ( $true
!= ( sK1 @ sK2 ) )
& ( ( sK0 @ sK2 )
= $true ) )
| ( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) )
& ( ! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) )
| ( sK1
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( sK1
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
| ( ( sK0 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
| ( $true
!= ( sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,definition,
( spl3_1
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
( ( $true
!= ( sK1 @ sK2 ) )
| spl3_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f19,definition,
( spl3_2
<=> ( sK1
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f20,plain,
( ( sK1
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f21,plain,
( ( sK1
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) ) ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f12,f19,f15]) ).
thf(f24,definition,
( spl3_3
<=> ! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f25,plain,
( ! [X3: a] :
( ( ( sK1 @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f26,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f10,f24,f19]) ).
thf(f28,definition,
( spl3_4
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f30,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f31,plain,
( ~ spl3_2
| spl3_4 ),
inference(avatar_split_clause,[],[f11,f28,f19]) ).
thf(f32,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK4 )
!= ( sK1 @ sK4 ) )
| spl3_2 ),
inference(negative_extensionality,[],[f21]) ).
thf(f33,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK4 )
= $true )
| spl3_2 ),
inference(xor_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ sK4 )
= $false )
| ( ( sK1 @ sK4 )
= $false )
| spl3_2 ),
inference(xor_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ( ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) )
= $false )
| ( ( sK1 @ sK4 )
= $false )
| spl3_2 ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
( ( ( sK1 @ sK4 )
= $false )
| ( ( sK1 @ sK4 )
= $false )
| spl3_2 ),
inference(or_proxy_clausification,[],[f35]) ).
thf(f38,plain,
( ( ( sK1 @ sK4 )
= $false )
| spl3_2 ),
inference(duplicate_literal_removal,[],[f36]) ).
thf(f39,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| spl3_2 ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f40,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| spl3_2 ),
inference(or_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| spl3_2 ),
inference(duplicate_literal_removal,[],[f40]) ).
thf(f43,definition,
( spl3_5
<=> ( ( sK1 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f45,plain,
( ( ( sK1 @ sK4 )
= $false )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f51,plain,
( spl3_5
| spl3_2 ),
inference(avatar_split_clause,[],[f38,f19,f43]) ).
thf(f53,definition,
( spl3_7
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
thf(f55,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f57,definition,
( spl3_8
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
thf(f60,plain,
( spl3_7
| spl3_8
| spl3_2 ),
inference(avatar_split_clause,[],[f41,f19,f57,f53]) ).
thf(f61,plain,
( ! [X1: a] :
( ( sK1 @ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl3_2 ),
inference(argument_congruence,[],[f20]) ).
thf(f62,plain,
( ! [X1: a] :
( ( ( ^ [Y0: a] :
( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
@ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl3_2 ),
inference(iff_proxy_clausification,[],[f61]) ).
thf(f66,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( ( sK0 @ X1 )
| ( sK1 @ X1 ) )
= $false ) )
| ~ spl3_2 ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f68,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( sK0 @ X1 )
= $false ) )
| ~ spl3_2 ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f69,plain,
( ( ( sK0 @ sK2 )
= $false )
| ( $true != $true )
| spl3_1
| ~ spl3_2 ),
inference(superposition,[],[f17,f68]) ).
thf(f71,plain,
( ( ( sK0 @ sK2 )
= $false )
| spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f74,definition,
( spl3_9
<=> ( ( sK0 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
thf(f76,plain,
( ( ( sK0 @ sK2 )
= $false )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f77,plain,
( spl3_9
| spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f71,f19,f15,f74]) ).
thf(f81,plain,
( ( $true = $false )
| ~ spl3_4
| ~ spl3_9 ),
inference(superposition,[],[f30,f76]) ).
thf(f82,plain,
( $false
| ~ spl3_4
| ~ spl3_9 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f83,plain,
( ~ spl3_4
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[],[f82]) ).
thf(f91,plain,
( ( $true = $false )
| ( $true
!= ( sK0 @ sK4 ) )
| ~ spl3_3
| ~ spl3_5 ),
inference(superposition,[],[f25,f45]) ).
thf(f93,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f91]) ).
thf(f99,plain,
( ~ spl3_8
| ~ spl3_3
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f93,f43,f24,f57]) ).
thf(f100,plain,
( ( $true = $false )
| ~ spl3_5
| ~ spl3_7 ),
inference(forward_demodulation,[],[f55,f45]) ).
thf(f101,plain,
( $false
| ~ spl3_5
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f102,plain,
( ~ spl3_5
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f101]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s5,plain,
( spl3_2
| spl3_5 ),
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
( spl3_2
| spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f60]) ).
cnf(s7,plain,
( spl3_1
| ~ spl3_2
| spl3_9 ),
inference(sat_conversion,[],[f77]) ).
cnf(s9,plain,
( ~ spl3_4
| ~ spl3_9 ),
inference(sat_conversion,[],[f83]) ).
cnf(s14,plain,
( ~ spl3_3
| ~ spl3_5
| ~ spl3_8 ),
inference(sat_conversion,[],[f99]) ).
cnf(s15,plain,
( ~ spl3_5
| ~ spl3_7 ),
inference(sat_conversion,[],[f102]) ).
cnf(s18,plain,
spl3_2,
inference(rat,[],[s6,s14,s15,s2,s5]) ).
cnf(s19,plain,
spl3_4,
inference(rat,[],[s3,s18]) ).
cnf(s20,plain,
~ spl3_9,
inference(rat,[],[s9,s19]) ).
cnf(s21,plain,
~ spl3_1,
inference(rat,[],[s1,s18]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s7,s21,s18,s20]) ).
thf(f104,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU848^5 : 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 : n001.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 14:45:51 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
% 0.22/0.27 % (1340031)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (1340039)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=1591862007: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)
% 0.22/0.27 % (1340039) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1340031-1340039"...
% 0.22/0.27 % (1340039)...printing done.
% 0.22/0.27 % (1340042)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.27 % (1340042)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.27 % (1340039)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (1340039)------------------------------
% 0.22/0.27 % (1340039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (1340039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (1340039)CaDiCaL version: 2.1.3
% 0.22/0.27 % (1340039)Termination reason: Refutation
% 0.22/0.27 % (1340039)Time elapsed: 0.003 s
% 0.22/0.27 % (1340039)Peak memory usage: 13 MB
% 0.22/0.27 % (1340039)Instructions burned: 5 (million)
% 0.22/0.27 % (1340031)Success in time 0.019 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------