%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO886^6 : TPTP v9.3.1. Released v8.1.0.
% 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 08:48:34 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 186 ( 38 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 261 ( 7 ~; 2 |; 0 &; 209 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 6 con; 0-4 aty)
% ( 21 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 94 ( 82 ^; 12 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
f: $i > mworld > $o ).
thf(func_def_14,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vIMP: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vIFF: $o > $o > $o ).
thf(func_def_27,type,
sK0: mworld > mworld ).
thf(func_def_28,type,
sK1: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f10,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f12,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( f @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f13,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( f @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f18,plain,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( f @ X1 ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f19,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f24,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f25,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f31,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f32,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f33,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f34,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f37,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f39,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f40,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f42,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f47,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f53,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f47,f42,f46,f40,f39,f39,f40]) ).
thf(f54,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( f @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: mworld,X1: $i] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( f @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: mworld,X1: $i] :
( $true
= ( ( mrel @ mactual @ X2 )
=> ( f @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: mworld,X1: $i] :
( ( $true
= ( f @ X1 @ X2 ) )
| ( $false
= ( mrel @ mactual @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f63,plain,
( $false
= ( ( mrel @ mactual @ sK1 )
=> ( !! @ $i
@ ^ [Y0: $i] : ( f @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( f @ Y0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( ^ [Y0: $i] : ( f @ Y0 @ sK1 )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( $false
= ( f @ sK2 @ sK1 ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK1 ) ) ),
inference(constrained_superposition,[],[f61,f67]) ).
thf(f70,plain,
( $false
= ( mrel @ mactual @ sK1 ) ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f73,plain,
$true = $false,
inference(constrained_superposition,[],[f65,f70]) ).
thf(f74,plain,
$false,
inference(trivial_inequality_removal,[],[f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO886^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.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 17:27:57 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.29 % (909527)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (909535)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=869838580: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)
% 0.22/0.29 % (909538)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (909538)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
% 0.22/0.29 % (909536)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=112263739:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (909532)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3701009546:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (909533)lrs+10_16_si=on:nwc=1.5:random_seed=2915930772:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (909534)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=971129681:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (909537)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1636520199:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (909534)Refutation not found, incomplete strategy
% 0.22/0.29 % (909534)------------------------------
% 0.22/0.29 % (909534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (909534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (909534)CaDiCaL version: 2.1.3
% 0.22/0.29 % (909534)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.29 % (909534)Time elapsed: 0.002 s
% 0.22/0.29 % (909534)Peak memory usage: 12 MB
% 0.22/0.29 % (909534)Instructions burned: 3 (million)
% 0.22/0.29 % (909538)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=3295140494:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (909533) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-909527-909533"...
% 0.22/0.29 % (909532) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-909527-909532"...
% 0.22/0.29 % (909534)------------------------------
% 0.22/0.29 % (909534)------------------------------
% 0.22/0.29 % (909537) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-909527-909537"...
% 0.22/0.29 % (909532)...printing done.
% 0.22/0.29 % (909533)...printing done.
% 0.22/0.29 % (909535) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-909527-909535"...
% 0.22/0.29 % (909537)...printing done.
% 0.22/0.29 % (909533)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (909533)------------------------------
% 0.22/0.29 % (909533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (909533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (909533)CaDiCaL version: 2.1.3
% 0.22/0.29 % (909533)Termination reason: Refutation
% 0.22/0.29 % (909533)Time elapsed: 0.004 s
% 0.22/0.29 % (909533)Peak memory usage: 12 MB
% 0.22/0.29 % (909533)Instructions burned: 5 (million)
% 0.22/0.29 % (909527)Success in time 0.039 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------