%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO902^8 : 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 : n006.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 08:48:37 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 327 ( 70 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 433 ( 7 ~; 20 |; 33 &; 324 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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)
% ( 8 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 107 ( 81 ^; 24 !; 2 ?; 107 :)
% 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,
vIMP: $o > $o > $o ).
thf(func_def_13,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vIFF: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
sK0: mworld ).
thf(func_def_26,type,
sK1: mworld > mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
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,
( ( ^ [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,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,conjecture,
mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f11,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f12,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f15,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f23,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f24,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f23]) ).
thf(f29,plain,
~ ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f30,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f29]) ).
thf(f31,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) )
!= $true ),
inference(flattening,[],[f30]) ).
thf(f32,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f36,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f37,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f24]) ).
thf(f38,plain,
( ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f40,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f41,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
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 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ 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 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f38,f36,f40,f32,f41,f32,f32,f32]) ).
thf(f45,plain,
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( p @ Y2 ) ) ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( p @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( p @ Y1 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( p @ Y2 ) ) ) ) ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f48,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( p @ Y2 ) ) ) ) ) )
@ sK0 )
= $true ),
inference(sigma_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( $true
= ( ( mrel @ mactual @ sK0 )
& ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( p @ Y1 ) ) ) ) )
= $true ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( mrel @ mactual @ sK0 )
= $true ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f52,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( p @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f53,plain,
! [X1: mworld] :
( ( ( mrel @ sK0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( p @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( p @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( p @ Y0 ) )
@ ( sK1 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( ( ( mrel @ X1 @ ( sK1 @ X1 ) )
& ( p @ ( sK1 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ sK0 @ X1 ) )
| ( ( p @ ( sK1 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X1: mworld] :
( ( ( mrel @ X1 @ ( sK1 @ X1 ) )
= $true )
| ( $false
= ( mrel @ sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f56]) ).
thf(f59,plain,
! [X1: mworld] :
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
& ( p @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f60,plain,
! [X1: mworld] :
( $false
= ( ( mrel @ mactual @ X1 )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X1: mworld] :
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( p @ Y0 ) ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( p @ Y0 ) )
@ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( ( mrel @ X1 @ X2 )
& ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( mrel @ X1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) ) ),
inference(and_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( $false = $true )
| ( ( p @ ( sK1 @ sK0 ) )
= $true ) ),
inference(constrained_superposition,[],[f37,f57]) ).
thf(f67,plain,
( ( p @ ( sK1 @ sK0 ) )
= $true ),
inference(trivial_inequality_removal,[],[f66]) ).
thf(f84,plain,
! [X0: mworld] :
( ( $false
= ( p @ ( sK1 @ X0 ) ) )
| ( ( mrel @ sK0 @ X0 )
= $false )
| ( $false = $true )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(constrained_superposition,[],[f58,f64]) ).
thf(f87,plain,
! [X0: mworld] :
( ( ( mrel @ sK0 @ X0 )
= $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( p @ ( sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f127,plain,
( ( $false = $true )
| ( ( mrel @ mactual @ sK0 )
= $false )
| ( $false
= ( p @ ( sK1 @ sK0 ) ) ) ),
inference(constrained_superposition,[],[f87,f37]) ).
thf(f131,plain,
( ( $false
= ( p @ ( sK1 @ sK0 ) ) )
| ( ( mrel @ mactual @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f135,plain,
( ( ( mrel @ mactual @ sK0 )
= $false )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f131,f67]) ).
thf(f136,plain,
( ( mrel @ mactual @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f135]) ).
thf(f147,plain,
$false = $true,
inference(constrained_superposition,[],[f136,f51]) ).
thf(f149,plain,
$false,
inference(trivial_inequality_removal,[],[f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO902^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n006.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:26:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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 % (1050669)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (1050675)lrs+10_16_si=on:nwc=1.5:random_seed=4150255715:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (1050675) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1050669-1050675"...
% 0.21/0.27 % (1050675)...printing done.
% 0.21/0.27 % (1050675)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 % (1050675)------------------------------
% 0.21/0.27 % (1050675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1050675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1050675)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1050675)Termination reason: Refutation
% 0.21/0.27 % (1050675)Time elapsed: 0.004 s
% 0.21/0.27 % (1050675)Peak memory usage: 12 MB
% 0.21/0.27 % (1050675)Instructions burned: 10 (million)
% 0.21/0.27 % (1050669)Success in time 0.032 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------