%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO134^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:46:41 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 21 unt; 0 typ; 9 def)
% Number of atoms : 246 ( 55 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 148 ( 35 ~; 30 |; 6 &; 60 @)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% 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 : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_2,type,
cP: $i > $o ).
thf(func_def_6,type,
sF0: $i > $o ).
thf(func_def_7,type,
sF1: $i > $o ).
thf(func_def_8,type,
sF2: $o ).
thf(func_def_9,type,
sF3: $o ).
thf(f1,conjecture,
( ( ( cP @ a )
=> ! [X0: $i] : ( cQ @ X0 ) )
=> ( ! [X0: $i] : ( cP @ X0 )
=> ( cQ @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cADDHYP1) ).
thf(f2,negated_conjecture,
~ ( ( ( cP @ a )
=> ! [X0: $i] : ( cQ @ X0 ) )
=> ( ! [X0: $i] : ( cP @ X0 )
=> ( cQ @ a ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( cP @ a )
=> ! [X0: $i] : ( cQ @ X0 ) )
=> ( ! [X1: $i] : ( cP @ X1 )
=> ( cQ @ a ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ( cP @ a )
= $true )
=> ! [X0: $i] :
( ( cQ @ X0 )
= $true ) )
=> ( ! [X1: $i] :
( $true
= ( cP @ X1 ) )
=> ( ( cQ @ a )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cQ @ a )
!= $true )
& ! [X1: $i] :
( $true
= ( cP @ X1 ) )
& ( ! [X0: $i] :
( ( cQ @ X0 )
= $true )
| ( ( cP @ a )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X1: $i] :
( $true
= ( cP @ X1 ) )
& ( ! [X0: $i] :
( ( cQ @ X0 )
= $true )
| ( ( cP @ a )
!= $true ) )
& ( ( cQ @ a )
!= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
& ( ! [X1: $i] :
( $true
= ( cQ @ X1 ) )
| ( ( cP @ a )
!= $true ) )
& ( ( cQ @ a )
!= $true ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( cQ @ a )
!= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X1: $i] :
( ( $true
= ( cQ @ X1 ) )
| ( ( cP @ a )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X0: $i] :
( ( cP @ X0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
! [X0: $i] :
( ( sF0 @ X0 )
= ( cP @ X0 ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f14,plain,
! [X0: $i] :
( ( cP @ X0 )
= ( sF0 @ X0 ) ),
inference(reorient_equations,[],[f13]) ).
thf(f15,plain,
! [X0: $i] :
( $true
= ( sF0 @ X0 ) ),
inference(definition_folding,[],[f10,f14]) ).
thf(f16,definition,
! [X1: $i] :
( ( sF1 @ X1 )
= ( cQ @ X1 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f17,definition,
( sF2
= ( cP @ a ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f18,plain,
( ( cP @ a )
= sF2 ),
inference(reorient_equations,[],[f17]) ).
thf(f19,plain,
! [X1: $i] :
( ( $true
= ( sF1 @ X1 ) )
| ( sF2 != $true ) ),
inference(definition_folding,[],[f9,f18,f16]) ).
thf(f20,definition,
( sF3
= ( cQ @ a ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f21,plain,
( ( cQ @ a )
= sF3 ),
inference(reorient_equations,[],[f20]) ).
thf(f22,plain,
$true != sF3,
inference(definition_folding,[],[f8,f21]) ).
thf(f23,plain,
! [X0: $i] :
( ( $false
= ( sF0 @ X0 ) )
| ( ( cP @ X0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f14]) ).
thf(f26,plain,
! [X1: $i] :
( ( $true
= ( cQ @ X1 ) )
| ( $false
= ( sF1 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f16]) ).
thf(f28,plain,
( ( $true = sF3 )
| ( ( cQ @ a )
= $false ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f30,plain,
( ( ( cP @ a )
= $false )
| ( sF2 = $true ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f32,definition,
( spl4_1
<=> ! [X1: $i] :
( $true
= ( sF1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f33,plain,
( ! [X1: $i] :
( $true
= ( sF1 @ X1 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,definition,
( spl4_2
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f38,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f19,f35,f32]) ).
thf(f40,definition,
( spl4_3
<=> ( ( cQ @ a )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f42,plain,
( ( ( cQ @ a )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f44,definition,
( spl4_4
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f47,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f28,f44,f40]) ).
thf(f57,plain,
~ spl4_4,
inference(avatar_split_clause,[],[f22,f44]) ).
thf(f59,definition,
( spl4_7
<=> ( ( cP @ a )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f61,plain,
( ( ( cP @ a )
= $false )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,plain,
( spl4_2
| spl4_7 ),
inference(avatar_split_clause,[],[f30,f59,f35]) ).
thf(f93,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( cP @ X0 )
= $true ) ),
inference(forward_demodulation,[],[f23,f15]) ).
thf(f94,plain,
! [X0: $i] :
( ( cP @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f96,plain,
( ( $false = $true )
| ~ spl4_7 ),
inference(constrained_superposition,[],[f61,f94]) ).
thf(f99,plain,
( $false
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f100,plain,
~ spl4_7,
inference(avatar_contradiction_clause,[],[f99]) ).
thf(f106,plain,
( ! [X1: $i] :
( ( $false = $true )
| ( $true
= ( cQ @ X1 ) ) )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f26,f33]) ).
thf(f107,plain,
( ! [X1: $i] :
( $true
= ( cQ @ X1 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f109,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_3 ),
inference(constrained_superposition,[],[f42,f107]) ).
thf(f112,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f113,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f112]) ).
cnf(s1,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s4,plain,
~ spl4_4,
inference(sat_conversion,[],[f57]) ).
cnf(s5,plain,
( spl4_2
| spl4_7 ),
inference(sat_conversion,[],[f62]) ).
cnf(s8,plain,
~ spl4_7,
inference(sat_conversion,[],[f100]) ).
cnf(s11,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f113]) ).
cnf(s12,plain,
spl4_2,
inference(rat,[],[s5,s8]) ).
cnf(s15,plain,
spl4_3,
inference(rat,[],[s2,s4]) ).
cnf(s16,plain,
~ spl4_1,
inference(rat,[],[s11,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s12,s16]) ).
thf(f114,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO134^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.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 16:34:45 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (25647)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (25658)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (25658)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
% 0.21/0.28 % (25658)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=232586987:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (25658) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-25647-25658"...
% 0.21/0.28 % (25654)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=871583906:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (25657)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2722925818:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (25655)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=3749093891: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)
% 0.21/0.28 % (25652)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1704802867:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (25653)lrs+10_16_si=on:nwc=1.5:random_seed=548570600:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (25658)...printing done.
% 0.21/0.28 % (25656)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1094150004:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (25654) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-25647-25654"...
% 0.21/0.28 % (25657) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-25647-25657"...
% 0.21/0.28 % (25658)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 % (25658)------------------------------
% 0.21/0.28 % (25658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (25658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (25658)CaDiCaL version: 2.1.3
% 0.21/0.28 % (25658)Termination reason: Refutation
% 0.21/0.28 % (25658)Time elapsed: 0.002 s
% 0.21/0.28 % (25658)Peak memory usage: 13 MB
% 0.21/0.28 % (25658)Instructions burned: 3 (million)
% 0.21/0.28 % (25647)Success in time 0.04 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------