%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO896^7 : 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 : 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 08:48:36 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 339 ( 71 equ; 0 cnn)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 397 ( 22 ~; 16 |; 17 &; 290 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 6 con; 0-4 aty)
% ( 10 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 106 ( 93 ^; 11 !; 2 ?; 106 :)
% 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,
vNOT: $o > $o ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
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_17,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vIMP: $o > $o > $o ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_21,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_25,type,
vIFF: $o > $o > $o ).
thf(func_def_26,type,
sK0: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f3,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
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,conjecture,
mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f10,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f11,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f14,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f16,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f19,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[],[f5]) ).
thf(f20,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f3]) ).
thf(f22,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
~ ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f24,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f28,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(flattening,[],[f24]) ).
thf(f29,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f31,plain,
( ( mlocal @ ( mimplies @ ( mand @ ( mbox @ ( mimplies @ p @ q ) ) @ ( mbox @ ( mimplies @ p @ ( mnot @ q ) ) ) ) @ ( mnot @ ( mdia @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f28]) ).
thf(f33,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f34,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f35,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f36,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f37,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f40,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] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [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 ) )
@ ( ^ [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
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ q ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f31,f33,f29,f37,f34,f29,f34,f29,f35,f35,f36]) ).
thf(f41,plain,
( ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) ) ) )
=> ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
( ( ~ ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f41]) ).
thf(f43,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) ) )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f41]) ).
thf(f44,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f45,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f46,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ~ ( q @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f47,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( p @ X1 )
=> ~ ( q @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X1: mworld] :
( ( ( ( p @ X1 )
=> ~ ( q @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X1: mworld] :
( ( ( p @ X1 )
= $false )
| ( ( ~ ( q @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( p @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( p @ Y0 )
=> ( q @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f52,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( p @ X1 )
=> ( q @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X1: mworld] :
( ( $true
= ( ( p @ X1 )
=> ( q @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( ( p @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f42]) ).
thf(f56,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( p @ Y0 ) )
@ sK0 )
= $true ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f57,plain,
( $true
= ( ( mrel @ mactual @ sK0 )
& ( p @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
( $true
= ( p @ sK0 ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f59,plain,
( $true
= ( mrel @ mactual @ sK0 ) ),
inference(and_proxy_clausification,[],[f57]) ).
thf(f60,plain,
( ( $false
= ( q @ sK0 ) )
| ( ( p @ sK0 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f50,f59]) ).
thf(f62,plain,
( ( $false
= ( q @ sK0 ) )
| ( ( p @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f60]) ).
thf(f64,plain,
( ( $false
= ( q @ sK0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f62,f58]) ).
thf(f65,plain,
( $false
= ( q @ sK0 ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f69,plain,
( ( ( p @ sK0 )
= $false )
| ( $true
= ( q @ sK0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f59,f54]) ).
thf(f70,plain,
( ( $true
= ( q @ sK0 ) )
| ( ( p @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f69]) ).
thf(f72,plain,
( ( ( p @ sK0 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f70,f65]) ).
thf(f73,plain,
( ( p @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f72]) ).
thf(f76,plain,
$true = $false,
inference(backward_demodulation,[],[f58,f73]) ).
thf(f77,plain,
$false,
inference(trivial_inequality_removal,[],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO896^7 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:21:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.27 % (632611)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (632621)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3467561544:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.27 % (632621) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-632611-632621"...
% 0.21/0.27 % (632621)...printing done.
% 0.21/0.27 % (632621)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (632621)------------------------------
% 0.21/0.27 % (632621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (632621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (632621)CaDiCaL version: 2.1.3
% 0.21/0.27 % (632621)Termination reason: Refutation
% 0.21/0.27 % (632621)Time elapsed: 0.003 s
% 0.21/0.27 % (632621)Peak memory usage: 13 MB
% 0.21/0.27 % (632621)Instructions burned: 7 (million)
% 0.21/0.27 % (632611)Success in time 0.029 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------