%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT333^3 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 07:48:47 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 40 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 368 ( 7 ~; 3 |; 19 &; 308 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 34 usr; 11 con; 0-4 aty)
% ( 8 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 96 ( 82 ^; 12 !; 2 ?; 96 :)
% 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_19,type,
teach: $i > $i > mworld > $o ).
thf(func_def_22,type,
vIFF: $o > $o > $o ).
thf(func_def_23,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vOR: $o > $o > $o ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
sK0: mworld > mworld ).
thf(func_def_34,type,
sK1: $i > mworld ).
thf(func_def_35,type,
sK2: mworld > $i ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f11,axiom,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f12,axiom,
( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',db) ).
thf(f13,conjecture,
( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( teach @ john @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',query) ).
thf(f14,negated_conjecture,
~ ( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( teach @ john @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
thf(f21,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f22,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
~ ( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( teach @ john @ X0 ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f26,plain,
( $true
!= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f29,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f32,plain,
( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f33,plain,
( ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f35,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f38,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f39,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( $true
!= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) ) ),
inference(flattening,[],[f26]) ).
thf(f47,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f48,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f49,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f50,plain,
( ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f52,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f53,plain,
( $true
!= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f57,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( teach @ john @ math )
@ ( ^ [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] : ( teach @ Y0 @ cs ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( teach @ mary @ psych )
@ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f50,f47,f49,f48,f48,f52,f48]) ).
thf(f58,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [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 ) ) )
@ ( teach @ john @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f53,f47,f52,f49]) ).
thf(f59,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( teach @ john @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f58]) ).
thf(f60,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( teach @ john @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X1: $i] :
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( teach @ john @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( teach @ john @ X1 @ Y0 ) )
@ ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X1: $i] :
( ( ( mrel @ mactual @ ( sK1 @ X1 ) )
=> ( teach @ john @ X1 @ ( sK1 @ X1 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X1: $i] :
( $false
= ( teach @ john @ X1 @ ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( mrel @ mactual @ ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( teach @ Y1 @ cs @ Y0 ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f67,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( teach @ Y1 @ cs @ Y0 ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] : ( teach @ Y0 @ cs @ X1 ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X1: mworld] :
( ( ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] : ( teach @ Y0 @ cs @ X1 ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f71,plain,
! [X1: mworld] :
( ( $true
= ( teach @ john @ math @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f78,plain,
( ( $false = $true )
| ( $false
= ( mrel @ mactual @ ( sK1 @ math ) ) ) ),
inference(constrained_superposition,[],[f71,f64]) ).
thf(f80,plain,
( $false
= ( mrel @ mactual @ ( sK1 @ math ) ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f82,plain,
$false = $true,
inference(forward_demodulation,[],[f80,f65]) ).
thf(f83,plain,
$false,
inference(trivial_inequality_removal,[],[f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT333^3 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 18:31:19 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.30 % (3919001)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (3919006)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2625619030:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (3919006) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3919001-3919006"...
% 0.22/0.30 % (3919006)...printing done.
% 0.22/0.30 % (3919006)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (3919006)------------------------------
% 0.22/0.30 % (3919006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3919006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3919006)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3919006)Termination reason: Refutation
% 0.22/0.30 % (3919006)Time elapsed: 0.003 s
% 0.22/0.30 % (3919006)Peak memory usage: 12 MB
% 0.22/0.30 % (3919006)Instructions burned: 7 (million)
% 0.22/0.30 % (3919001)Success in time 0.037 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------