%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV396^5 : 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 : n018.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 08:38:34 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 6 unt; 0 typ; 8 def)
% Number of atoms : 422 ( 85 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 332 ( 74 ~; 91 |; 31 &; 119 @)
% ( 12 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 12 con; 0-4 aty)
% Number of variables : 39 ( 0 sgn 15 !; 2 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) )
<=> ( cR
= ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM31_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) )
<=> ( cR
= ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) )
<=> ( cR
= ( ^ [X1: $i] :
( ( cR @ X1 )
& ( cS @ X1 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) )
<=> ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
<~> ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
| ( ( cR @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) )
| ( cR
!= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) )
& ( ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
| ( ( cR @ X0 )
!= $true ) )
| ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) )
| ( cR
!= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) )
& ( ! [X1: $i] :
( ( $true
= ( cS @ X1 ) )
| ( $true
!= ( cR @ X1 ) ) )
| ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( ( $true
!= ( cS @ sK0 ) )
& ( $true
= ( cR @ sK0 ) ) )
| ( cR
!= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) )
& ( ! [X1: $i] :
( ( $true
= ( cS @ X1 ) )
| ( $true
!= ( cR @ X1 ) ) )
| ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
! [X1: $i] :
( ( $true
!= ( cR @ X1 ) )
| ( $true
= ( cS @ X1 ) )
| ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( cR
!= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
| ( $true
= ( cR @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( $true
!= ( cS @ sK0 ) )
| ( cR
!= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,definition,
( spl1_1
<=> ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f15,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f16,plain,
( ( cR
!= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
| spl1_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f18,definition,
( spl1_2
<=> ( $true
= ( cS @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f20,plain,
( ( $true
!= ( cS @ sK0 ) )
| spl1_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f11,f18,f14]) ).
thf(f23,definition,
( spl1_3
<=> ( $true
= ( cR @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
= ( cR @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,plain,
( spl1_3
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f10,f14,f23]) ).
thf(f28,definition,
( spl1_4
<=> ! [X1: $i] :
( ( $true
!= ( cR @ X1 ) )
| ( $true
= ( cS @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f29,plain,
( ! [X1: $i] :
( ( $true
= ( cS @ X1 ) )
| ( $true
!= ( cR @ X1 ) ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f30,plain,
( spl1_1
| spl1_4 ),
inference(avatar_split_clause,[],[f9,f28,f14]) ).
thf(f31,plain,
( ( ( cR @ sK2 )
!= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ sK2 ) )
| spl1_1 ),
inference(negative_extensionality,[],[f16]) ).
thf(f32,plain,
( ( ( cR @ sK2 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ sK2 ) )
| spl1_1 ),
inference(xor_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( ( cR @ sK2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ sK2 )
= $false )
| spl1_1 ),
inference(xor_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( ( ( cS @ sK2 )
& ( cR @ sK2 ) )
= $false )
| ( ( cR @ sK2 )
= $false )
| spl1_1 ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
( ( $false
= ( cS @ sK2 ) )
| ( ( cR @ sK2 )
= $false )
| ( ( cR @ sK2 )
= $false )
| spl1_1 ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
( ( $false
= ( cS @ sK2 ) )
| ( ( cR @ sK2 )
= $false )
| spl1_1 ),
inference(duplicate_literal_removal,[],[f35]) ).
thf(f37,plain,
( ( ( cR @ sK2 )
= $true )
| ( $true
= ( ( cS @ sK2 )
& ( cR @ sK2 ) ) )
| spl1_1 ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f38,plain,
( ( ( cR @ sK2 )
= $true )
| ( ( cR @ sK2 )
= $true )
| spl1_1 ),
inference(and_proxy_clausification,[],[f37]) ).
thf(f40,plain,
( ( ( cR @ sK2 )
= $true )
| spl1_1 ),
inference(duplicate_literal_removal,[],[f38]) ).
thf(f42,definition,
( spl1_5
<=> ( ( cR @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f44,plain,
( ( ( cR @ sK2 )
= $false )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f46,definition,
( spl1_6
<=> ( $false
= ( cS @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f48,plain,
( ( $false
= ( cS @ sK2 ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl1_5
| spl1_6
| spl1_1 ),
inference(avatar_split_clause,[],[f36,f14,f46,f42]) ).
thf(f51,definition,
( spl1_7
<=> ( ( cR @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
thf(f53,plain,
( ( ( cR @ sK2 )
= $true )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f59,plain,
( spl1_7
| spl1_1 ),
inference(avatar_split_clause,[],[f40,f14,f51]) ).
thf(f60,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ X1 )
= ( cR @ X1 ) )
| ~ spl1_1 ),
inference(argument_congruence,[],[f15]) ).
thf(f61,plain,
( ! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ X1 ) )
| ( $false
= ( cR @ X1 ) ) )
| ~ spl1_1 ),
inference(iff_proxy_clausification,[],[f60]) ).
thf(f65,plain,
( ! [X1: $i] :
( ( $true
= ( ( cS @ X1 )
& ( cR @ X1 ) ) )
| ( $false
= ( cR @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f67,plain,
( ! [X1: $i] :
( ( $true
= ( cS @ X1 ) )
| ( $false
= ( cR @ X1 ) ) )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( ( $true != $true )
| ( $false
= ( cR @ sK0 ) )
| ~ spl1_1
| spl1_2 ),
inference(superposition,[],[f20,f67]) ).
thf(f71,plain,
( ( $false
= ( cR @ sK0 ) )
| ~ spl1_1
| spl1_2 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f75,definition,
( spl1_9
<=> ( $false
= ( cR @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
thf(f77,plain,
( ( $false
= ( cR @ sK0 ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f78,plain,
( spl1_9
| ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f71,f18,f14,f75]) ).
thf(f80,plain,
( ( $true = $false )
| ~ spl1_5
| ~ spl1_7 ),
inference(forward_demodulation,[],[f53,f44]) ).
thf(f81,plain,
( $false
| ~ spl1_5
| ~ spl1_7 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f82,plain,
( ~ spl1_5
| ~ spl1_7 ),
inference(avatar_contradiction_clause,[],[f81]) ).
thf(f84,plain,
( ( $true = $false )
| ~ spl1_3
| ~ spl1_9 ),
inference(superposition,[],[f77,f25]) ).
thf(f88,plain,
( $false
| ~ spl1_3
| ~ spl1_9 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f89,plain,
( ~ spl1_3
| ~ spl1_9 ),
inference(avatar_contradiction_clause,[],[f88]) ).
thf(f94,plain,
( ( $true = $false )
| ( ( cR @ sK2 )
!= $true )
| ~ spl1_4
| ~ spl1_6 ),
inference(superposition,[],[f48,f29]) ).
thf(f96,plain,
( ( ( cR @ sK2 )
!= $true )
| ~ spl1_4
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f98,plain,
( ~ spl1_7
| ~ spl1_4
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f96,f46,f28,f51]) ).
cnf(s1,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( ~ spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
( spl1_1
| spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f49]) ).
cnf(s6,plain,
( spl1_1
| spl1_7 ),
inference(sat_conversion,[],[f59]) ).
cnf(s8,plain,
( ~ spl1_1
| spl1_2
| spl1_9 ),
inference(sat_conversion,[],[f78]) ).
cnf(s10,plain,
( ~ spl1_5
| ~ spl1_7 ),
inference(sat_conversion,[],[f82]) ).
cnf(s13,plain,
( ~ spl1_3
| ~ spl1_9 ),
inference(sat_conversion,[],[f89]) ).
cnf(s14,plain,
( ~ spl1_4
| ~ spl1_6
| ~ spl1_7 ),
inference(sat_conversion,[],[f98]) ).
cnf(s16,plain,
spl1_1,
inference(rat,[],[s4,s14,s10,s3,s6]) ).
cnf(s17,plain,
spl1_3,
inference(rat,[],[s2,s16]) ).
cnf(s18,plain,
~ spl1_2,
inference(rat,[],[s1,s16]) ).
cnf(s19,plain,
~ spl1_9,
inference(rat,[],[s13,s17]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s8,s16,s19,s18]) ).
thf(f99,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV396^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.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 15:46:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.28 % (249373)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (249381)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=912175156: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)
% 0.20/0.28 % (249381) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-249373-249381"...
% 0.20/0.28 % (249381)...printing done.
% 0.20/0.28 % (249384)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (249384)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
% 0.20/0.28 % (249381)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (249381)------------------------------
% 0.20/0.28 % (249381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (249381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (249381)CaDiCaL version: 2.1.3
% 0.20/0.28 % (249381)Termination reason: Refutation
% 0.20/0.28 % (249381)Time elapsed: 0.003 s
% 0.20/0.28 % (249381)Peak memory usage: 12 MB
% 0.20/0.28 % (249381)Instructions burned: 5 (million)
% 0.20/0.28 % (249373)Success in time 0.04 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------