%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT334^8 : 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 : n017.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 07:48:48 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 380 ( 60 equ; 0 cnn)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 493 ( 7 ~; 13 |; 41 &; 400 @)
% ( 0 <=>; 12 =>; 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 : 40 ( 35 usr; 12 con; 0-4 aty)
% ( 6 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 102 ( 86 ^; 14 !; 2 ?; 102 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_20,type,
teach: $i > $i > mworld > $o ).
thf(func_def_21,type,
vOR: $o > $o > $o ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(func_def_33,type,
vIFF: $o > $o > $o ).
thf(func_def_34,type,
sK0: mworld > $i ).
thf(func_def_35,type,
sK1: mworld > $i ).
thf(func_def_36,type,
sK2: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f12,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def) ).
thf(f13,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/sandbox/benchmark/theBenchmark.p',db) ).
thf(f14,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f20,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f21,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[],[f12]) ).
thf(f23,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f24,plain,
( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f25,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f32,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f33,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f35,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f42,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f43,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(flattening,[],[f33]) ).
thf(f46,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f50,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f51,plain,
( $true
!= ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f52,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f56,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f61,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(definition_unfolding,[],[f51,f50,f53,f46]) ).
thf(f62,plain,
( $true
= ( ^ [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] :
( ( eiw_di @ Y2 @ Y1 )
& ( 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 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f56,f50,f53,f52,f52,f46,f52]) ).
thf(f63,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X1: mworld] :
( ( $true
= ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X1: mworld] :
( ( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f66]) ).
thf(f70,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f71,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) )
@ ( sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X1: mworld] :
( ( $true
= ( ( eiw_di @ ( sK1 @ X1 ) @ X1 )
& ( teach @ ( sK1 @ X1 ) @ cs @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X1: mworld] :
( ( $true
= ( teach @ ( sK1 @ X1 ) @ cs @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X1: mworld] :
( ( $true
= ( eiw_di @ ( sK1 @ X1 ) @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f77,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f78,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( teach @ Y0 @ cs @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( teach @ Y0 @ cs @ sK2 ) ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( mrel @ mactual @ sK2 )
= $true ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f82,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( teach @ Y0 @ cs @ sK2 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f83,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
& ( teach @ X1 @ cs @ sK2 ) )
= $false ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X1: $i] :
( ( ( teach @ X1 @ cs @ sK2 )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(and_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( ( eiw_di @ ( sK1 @ sK2 ) @ sK2 )
= $false )
| ( ( mrel @ mactual @ sK2 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f73,f84]) ).
thf(f87,plain,
( ( ( eiw_di @ ( sK1 @ sK2 ) @ sK2 )
= $false )
| ( ( mrel @ mactual @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f89,plain,
( ( $true = $false )
| ( ( eiw_di @ ( sK1 @ sK2 ) @ sK2 )
= $false ) ),
inference(forward_demodulation,[],[f87,f81]) ).
thf(f90,plain,
( ( eiw_di @ ( sK1 @ sK2 ) @ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f94,plain,
( ( $true = $false )
| ( ( mrel @ mactual @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f74,f90]) ).
thf(f95,plain,
( ( mrel @ mactual @ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f98,plain,
$true = $false,
inference(constrained_superposition,[],[f81,f95]) ).
thf(f99,plain,
$false,
inference(trivial_inequality_removal,[],[f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT334^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n017.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
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 18:23:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 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
% 0.07/0.27 % (709031)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.27 % (709037)lrs+10_16_si=on:nwc=1.5:random_seed=3978506653:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.07/0.27 % (709037) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-709031-709037"...
% 0.07/0.27 % (709037)...printing done.
% 0.07/0.27 % (709037)Refutation found. Thanks to Tanya!
% 0.07/0.27 % SZS status Theorem for theBenchmark
% 0.07/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.28 % (709037)------------------------------
% 0.07/0.28 % (709037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.28 % (709037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.28 % (709037)CaDiCaL version: 2.1.3
% 0.07/0.28 % (709037)Termination reason: Refutation
% 0.07/0.28 % (709037)Time elapsed: 0.004 s
% 0.07/0.28 % (709037)Peak memory usage: 12 MB
% 0.07/0.28 % (709037)Instructions burned: 10 (million)
% 0.07/0.28 % (709031)Success in time 0.034 s
% 0.07/0.28 % Vampire exiting
%------------------------------------------------------------------------------