%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:48:25 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 162 ( 34 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 133 ( 28 ~; 18 |; 1 &; 74 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 18 !; 6 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
epso: ( $o > $o ) > $o ).
thf(func_def_2,type,
epsoo: ( ( $o > $o ) > $o ) > $o > $o ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
! [X0: $o > $o] :
( ? [X1: $o] : ( X0 @ X1 )
=> ( X0 @ ( epso @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceaxo) ).
thf(f2,axiom,
! [X0: ( $o > $o ) > $o] :
( ? [X1: $o > $o] : ( X0 @ X1 )
=> ( X0 @ ( epsoo @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceaxoo) ).
thf(f3,conjecture,
( ( epsoo @ epso @ $false )
=> ( epsoo @ epso @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
thf(f4,negated_conjecture,
~ ( ( epsoo @ epso @ $false )
=> ( epsoo @ epso @ $true ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: ( $o > $o ) > $o] :
( ? [X1: $o > $o] : ( X0 @ X1 )
=> ( X0 @ ( epsoo @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
! [X0: ( $o > $o ) > $o] :
( ? [X1: $o > $o] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( epsoo @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: $o > $o] :
( ? [X1: $o] : ( X0 @ X1 )
=> ( X0 @ ( epso @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
! [X0: $o > $o] :
( ? [X1: $o] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( epso @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( ( epsoo @ epso @ $false )
=> ( epsoo @ epso @ $true ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( $true
= ( epsoo @ epso @ $false ) )
=> ( $true
= ( epsoo @ epso @ $true ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $o > $o] :
( ! [X1: $o] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epso @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
( ( $true
= ( epsoo @ epso @ $false ) )
& ( $true
!= ( epsoo @ epso @ $true ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f13,plain,
! [X0: ( $o > $o ) > $o] :
( ! [X1: $o > $o] :
( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsoo @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f14,plain,
! [X0: $o > $o,X1: $o] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epso @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( $true
!= ( epsoo @ epso @ $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
( $true
= ( epsoo @ epso @ $false ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
! [X0: ( $o > $o ) > $o,X1: $o > $o] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( epsoo @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
! [X1: $o] :
( ( ( ^ [Y0: $o] : Y0
@ X1 )
!= $true )
| ( $true
= ( ^ [Y0: $o] : Y0
@ ( epso
@ ^ [Y0: $o] : Y0 ) ) ) ),
inference(primitive_instantiation,[],[f14]) ).
thf(f27,plain,
( ( $true
= ( epsoo @ epso @ ( epso @ ( epsoo @ epso ) ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f14,f16]) ).
thf(f30,plain,
( $true
= ( epsoo @ epso @ ( epso @ ( epsoo @ epso ) ) ) ),
inference(trivial_inequality_removal,[],[f27]) ).
thf(f34,plain,
! [X1: $o] :
( ( $true != X1 )
| ( $true
= ( epso
@ ^ [Y0: $o] : Y0 ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f36,definition,
( spl0_1
<=> ! [X1: $o] : ( $true != X1 ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f37,plain,
( ! [X1: $o] : ( $true != X1 )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,definition,
( spl0_2
<=> ( $true
= ( epso
@ ^ [Y0: $o] : Y0 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
= ( epso
@ ^ [Y0: $o] : Y0 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f34,f39,f36]) ).
thf(f55,plain,
( ( $true
= ( epso @ ( epsoo @ epso ) ) )
| ( $true != $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f17,f41]) ).
thf(f56,plain,
( ( $true
= ( epso @ ( epsoo @ epso ) ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f59,plain,
( ( $true
= ( epsoo @ epso @ $true ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f30,f56]) ).
thf(f60,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f59,f15]) ).
thf(f61,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f60]) ).
thf(f62,plain,
( ( $true != $true )
| ~ spl0_1 ),
inference(imitation,[],[f37]) ).
thf(f65,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f66,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f65]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f61]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f66]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s3,s5]) ).
thf(f67,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n026.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 17:17:57 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.21/0.29 % (895871)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (895901)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3503113749:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (895903)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (895903)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
% 0.21/0.29 % (895899)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2896239667:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (895903)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=880771964:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (895896)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2431395057:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (895900)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=2495868383: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)
% 0.21/0.29 % (895899) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-895871-895899"...
% 0.21/0.29 % (895899)...printing done.
% 0.21/0.29 % (895896) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-895871-895896"...
% 0.21/0.29 % (895903)Refutation not found, incomplete strategy
% 0.21/0.29 % (895903)------------------------------
% 0.21/0.29 % (895903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (895903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (895903)CaDiCaL version: 2.1.3
% 0.21/0.29 % (895903)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (895903)Time elapsed: 0.003 s
% 0.21/0.29 % (895901)Instruction limit reached!
% 0.21/0.29 % (895901)------------------------------
% 0.21/0.29 % (895901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (895903)Peak memory usage: 12 MB
% 0.21/0.29 % (895903)Instructions burned: 4 (million)
% 0.21/0.29 % (895901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (895901)CaDiCaL version: 2.1.3
% 0.21/0.29 % (895901)Termination reason: Instruction limit
% 0.21/0.29 % (895901)Termination phase: Saturation
% 0.21/0.29 % (895901)Time elapsed: 0.010 s
% 0.21/0.29 % (895901)Peak memory usage: 11 MB
% 0.21/0.29 % (895901)Instructions burned: 27 (million)
% 0.21/0.29 % (895899)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (895899)------------------------------
% 0.21/0.29 % (895899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (895899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (895899)CaDiCaL version: 2.1.3
% 0.21/0.29 % (895899)Termination reason: Refutation
% 0.21/0.29 % (895899)Time elapsed: 0.004 s
% 0.21/0.29 % (895899)Peak memory usage: 13 MB
% 0.21/0.29 % (895899)Instructions burned: 4 (million)
% 0.21/0.29 % (895871)Success in time 0.042 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------