%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO892^15 : 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 : n016.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 08:48:35 AM UTC 2026
% Result : Theorem 0.25s 0.35s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 310 ( 67 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 412 ( 17 ~; 16 |; 20 &; 311 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 30 usr; 7 con; 0-4 aty)
% ( 11 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 113 ( 83 ^; 28 !; 2 ?; 113 :)
% 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_14,type,
f: $i > mworld > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vIFF: $o > $o > $o ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
sK0: mworld > $i ).
thf(func_def_29,type,
sK1: mworld > mworld ).
thf(func_def_30,type,
sK2: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_def) ).
thf(f11,axiom,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X0 )
& ( mrel @ X0 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(f12,axiom,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f14,conjecture,
( mlocal
@ ( mimplies
@ ( mdia
@ ( mforall_di
@ ^ [X0: $i] : ( f @ X0 ) ) )
@ ( mforall_di
@ ^ [X0: $i] : ( mdia @ ( f @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mdia
@ ( mforall_di
@ ^ [X0: $i] : ( f @ X0 ) ) )
@ ( mforall_di
@ ^ [X0: $i] : ( mdia @ ( f @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f16,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f17,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( eiw_di @ X2 @ X0 )
& ( mrel @ X0 @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ),
inference(rectify,[],[f11]) ).
thf(f18,plain,
! [X0: mworld,X2: $i,X1: mworld] :
( ( ( ( eiw_di @ X2 @ X0 )
= $true )
& ( ( mrel @ X0 @ X1 )
= $true ) )
=> ( ( eiw_di @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f17]) ).
thf(f23,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f24,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f27,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f28,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f31,plain,
~ ( mlocal
@ ( mimplies
@ ( mdia
@ ( mforall_di
@ ^ [X0: $i] : ( f @ X0 ) ) )
@ ( mforall_di
@ ^ [X1: $i] : ( mdia @ ( f @ X1 ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f32,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mdia
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[],[f12]) ).
thf(f36,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f43,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mdia
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f32]) ).
thf(f44,plain,
! [X0: mworld,X2: $i,X1: mworld] :
( ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f45,plain,
! [X0: mworld,X1: mworld,X2: $i] :
( ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true )
| ( ( eiw_di @ X2 @ X1 )
= $true ) ),
inference(flattening,[],[f44]) ).
thf(f48,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f49,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f51,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f53,plain,
! [X2: $i,X0: mworld,X1: mworld] :
( ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( eiw_di @ X2 @ X1 )
= $true )
| ( ( eiw_di @ X2 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f59,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mdia
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f61,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f64,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [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] : ( f @ Y0 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f59,f61,f51,f48,f49,f49,f48]) ).
thf(f65,plain,
( $true
!= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( f @ Y1 @ Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
& ( f @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
& ( f @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f65]) ).
thf(f68,plain,
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( f @ Y1 @ Y0 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( $true
= ( ( mrel @ mactual @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
=> ( f @ Y0 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
=> ( f @ Y0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( $true
= ( mrel @ mactual @ sK2 ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f72,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
=> ( f @ Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f70]) ).
thf(f73,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ sK2 )
=> ( f @ X1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X1: $i] :
( ( $true
= ( f @ X1 @ sK2 ) )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
& ( f @ Y0 @ Y1 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f76,plain,
( ( ( eiw_di @ sK3 @ mactual )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( f @ sK3 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( f @ sK3 @ Y0 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( $true
= ( eiw_di @ sK3 @ mactual ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f79,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( f @ sK3 @ Y0 ) )
@ X1 )
= $false ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f80,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
& ( f @ sK3 @ X1 ) )
= $false ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X1: mworld] :
( ( ( f @ sK3 @ X1 )
= $false )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f83,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ( ( eiw_di @ sK3 @ sK2 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f74,f81]) ).
thf(f84,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ( ( eiw_di @ sK3 @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f86,plain,
( ( ( eiw_di @ sK3 @ sK2 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f84,f71]) ).
thf(f87,plain,
( ( eiw_di @ sK3 @ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f90,plain,
! [X0: $i] :
( ( $true
!= ( eiw_di @ X0 @ mactual ) )
| ( $true
= ( eiw_di @ X0 @ sK2 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f53,f71]) ).
thf(f92,plain,
! [X0: $i] :
( ( $true
!= ( eiw_di @ X0 @ mactual ) )
| ( $true
= ( eiw_di @ X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f95,plain,
( ( $true != $true )
| ( $true
= ( eiw_di @ sK3 @ sK2 ) ) ),
inference(constrained_superposition,[],[f92,f78]) ).
thf(f97,plain,
( $true
= ( eiw_di @ sK3 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f98,plain,
$true = $false,
inference(forward_demodulation,[],[f97,f87]) ).
thf(f99,plain,
$false,
inference(trivial_inequality_removal,[],[f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO892^15 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n016.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:30:50 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running higher-order theorem proving
% 0.25/0.30 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
% 0.25/0.35 % (651669)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.35 % (651675)lrs+10_16_si=on:nwc=1.5:random_seed=2819730149:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.35 % (651675) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-651669-651675"...
% 0.25/0.35 % (651675)...printing done.
% 0.25/0.35 % (651675)Refutation found. Thanks to Tanya!
% 0.25/0.35 % SZS status Theorem for theBenchmark
% 0.25/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.35 % (651675)------------------------------
% 0.25/0.35 % (651675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.35 % (651675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.35 % (651675)CaDiCaL version: 2.1.3
% 0.25/0.35 % (651675)Termination reason: Refutation
% 0.25/0.35 % (651675)Time elapsed: 0.006 s
% 0.25/0.35 % (651675)Peak memory usage: 12 MB
% 0.25/0.35 % (651675)Instructions burned: 8 (million)
% 0.25/0.35 % (651669)Success in time 0.03 s
% 0.25/0.35 % Vampire exiting
%------------------------------------------------------------------------------