%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO897^6 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:50:34 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 200 ( 40 equ; 0 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 247 ( 7 ~; 5 |; 12 &; 190 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 6 con; 0-4 aty)
% ( 6 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 81 ( 60 ^; 19 !; 2 ?; 81 :)
% 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,
p: mworld > $o ).
thf(func_def_12,type,
q: mworld > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vOR: $o > $o > $o ).
thf(func_def_20,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
vIFF: $o > $o > $o ).
thf(func_def_22,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
sK0: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_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(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_def) ).
thf(f9,axiom,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).
thf(f10,conjecture,
mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f12,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f19,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f20,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f23,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f24,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f26,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[],[f9]) ).
thf(f28,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
~ ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f30,plain,
( ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f36,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f38,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f39,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f40,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[],[f28]) ).
thf(f41,plain,
( ( mlocal @ ( mimplies @ ( mdia @ p ) @ ( mimplies @ ( mbox @ q ) @ ( mdia @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,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 ) ) )
@ p )
@ ( ^ [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 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f41,f32,f36,f39,f36,f38,f39]) ).
thf(f45,plain,
( $true
!= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) ) )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( $false
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f52,plain,
( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f53,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f54,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X1: mworld] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f58,plain,
! [X1: mworld] :
( $false
= ( ( mrel @ mactual @ X1 )
& ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X1: mworld] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f69,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(constrained_superposition,[],[f56,f59]) ).
thf(f70,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f69]) ).
thf(f71,plain,
! [X0: mworld] :
( $false
= ( mrel @ mactual @ X0 ) ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f75,plain,
$true = $false,
inference(forward_demodulation,[],[f71,f40]) ).
thf(f76,plain,
$false,
inference(trivial_inequality_removal,[],[f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO897^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.18 % Computer : n003.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 17:27:59 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.22 Running first-order model finding
% 0.11/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.24 % (2801997)Will run a generic schedule for satisfiability detection.
% 0.11/0.24 % (2802014)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=404469974:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.24 % (2802014) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2801997-2802014"...
% 0.11/0.24 % (2802014)...printing done.
% 0.11/0.24 % (2802014)Refutation found. Thanks to Tanya!
% 0.11/0.24 % SZS status Theorem for theBenchmark
% 0.11/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.24 % (2802014)------------------------------
% 0.11/0.24 % (2802014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.24 % (2802014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.24 % (2802014)CaDiCaL version: 2.1.3
% 0.11/0.24 % (2802014)Termination reason: Refutation
% 0.11/0.24 % (2802014)Time elapsed: 0.002 s
% 0.11/0.24 % (2802014)Peak memory usage: 12 MB
% 0.11/0.24 % (2802014)Instructions burned: 5 (million)
% 0.11/0.24 % (2801997)Success in time 0.017 s
% 0.11/0.24 % Vampire exiting
%------------------------------------------------------------------------------