%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO895^9 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 40 unt; 0 typ; 2 def)
% Number of atoms : 263 ( 50 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 297 ( 17 ~; 13 |; 13 &; 212 @)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 7 con; 0-4 aty)
% ( 13 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 75 ( 0 sgn 8 !; 0 ?; 75 :)
% 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 > mworld ).
thf(func_def_27,type,
sK1: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_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,conjecture,
mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f12,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f15,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f16,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f15]) ).
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(f29,plain,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f30,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) )
!= $true ),
inference(flattening,[],[f30]) ).
thf(f33,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f35,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f37,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f39,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f42,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ p ) @ ( mbox @ q ) ) @ ( mbox @ ( mand @ p @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f45,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [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] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [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 ) )
@ p
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f42,f33,f37,f35,f39,f39,f39,f35]) ).
thf(f46,plain,
( $true
!= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
& ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
& ( q @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f49,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f50,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f51,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( p @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f49]) ).
thf(f55,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
& ( q @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f47]) ).
thf(f58,plain,
( $false
= ( ( mrel @ mactual @ sK1 )
=> ( ( p @ sK1 )
& ( q @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
( $false
= ( ( p @ sK1 )
& ( q @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f61,plain,
( ( $false
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f59]) ).
thf(f63,definition,
( spl2_1
<=> ( $false
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f65,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f67,definition,
( spl2_2
<=> ( $false
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f69,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f70,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f61,f67,f63]) ).
thf(f82,plain,
( ( $true = $false )
| ( $true
= ( p @ sK1 ) ) ),
inference(constrained_superposition,[],[f60,f53]) ).
thf(f83,plain,
( $true
= ( p @ sK1 ) ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f90,plain,
( ( $true = $false )
| ( $true
= ( q @ sK1 ) ) ),
inference(constrained_superposition,[],[f56,f60]) ).
thf(f99,plain,
( $true
= ( q @ sK1 ) ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f103,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f99,f69]) ).
thf(f104,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f105,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f104]) ).
thf(f106,plain,
( ( $true = $false )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f65,f83]) ).
thf(f112,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f113,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f112]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f70]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f105]) ).
cnf(s5,plain,
~ spl2_1,
inference(sat_conversion,[],[f113]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f114,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO895^9 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:27:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.26 % (2801873)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (2801894)dis+10_1_sil=32000:sp=arity:random_seed=2206979044:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (2801894) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2801873-2801894"...
% 0.19/0.26 % (2801890)% WARNING: option uhcvi not known.
% 0.19/0.26 % (2801894)...printing done.
% 0.19/0.26 % (2801894)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (2801894)------------------------------
% 0.19/0.26 % (2801894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (2801894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (2801894)CaDiCaL version: 2.1.3
% 0.19/0.26 % (2801894)Termination reason: Refutation
% 0.19/0.26 % (2801894)Time elapsed: 0.003 s
% 0.19/0.26 % (2801894)Peak memory usage: 12 MB
% 0.19/0.26 % (2801894)Instructions burned: 7 (million)
% 0.19/0.26 % (2801873)Success in time 0.031 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------