%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO886^6 : 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 : n019.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 08:50:32 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 186 ( 38 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 261 ( 7 ~; 2 |; 0 &; 209 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 6 con; 0-4 aty)
% ( 21 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 96 ( 82 ^; 14 !; 0 ?; 96 :)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
f: $i > mworld > $o ).
thf(func_def_14,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_16,type,
vNOT: $o > $o ).
thf(func_def_17,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vAND: $o > $o > $o ).
thf(func_def_19,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
vIMP: $o > $o > $o ).
thf(func_def_22,type,
vIFF: $o > $o > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
sK0: mworld > mworld ).
thf(func_def_28,type,
sK1: 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(f10,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f12,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( f @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f13,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X0: $i] : ( f @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f14,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f21,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f22,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f26,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f31,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f32,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f35,plain,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [X0: $i] : ( mbox @ ( f @ X0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( f @ X1 ) ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f36,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[],[f36]) ).
thf(f39,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f45,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f48,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f50,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [Y0: $i] : ( mbox @ ( f @ Y0 ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f53,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( f @ Y0 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f50,f39,f43,f48,f45,f45,f48]) ).
thf(f54,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f57,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( f @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( f @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f59,plain,
! [X2: mworld,X1: $i] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( f @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: mworld,X1: $i] :
( $true
= ( ( mrel @ mactual @ X2 )
=> ( f @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( $true
= ( f @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] : ( f @ Y1 @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f55]) ).
thf(f63,plain,
( $false
= ( ( mrel @ mactual @ sK1 )
=> ( !! @ $i
@ ^ [Y0: $i] : ( f @ Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( f @ Y0 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( $true
= ( mrel @ mactual @ sK1 ) ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( $false
= ( ^ [Y0: $i] : ( f @ Y0 @ sK1 )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f64]) ).
thf(f67,plain,
( $false
= ( f @ sK2 @ sK1 ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f79,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( f @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f65,f61]) ).
thf(f80,plain,
! [X0: $i] :
( $true
= ( f @ X0 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f79]) ).
thf(f88,plain,
$true = $false,
inference(constrained_superposition,[],[f67,f80]) ).
thf(f89,plain,
$false,
inference(trivial_inequality_removal,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO886^6 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n019.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 17:25:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.28 % (1110600)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (1110618)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2189520195:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (1110618)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (1110618) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1110600-1110618"...
% 0.21/0.28 % (1110618)...printing done.
% 0.21/0.28 % (1110614)% WARNING: option uhcvi not known.
% 0.21/0.28 % (1110618)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1110618)------------------------------
% 0.21/0.28 % (1110618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1110618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1110618)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1110618)Termination reason: Refutation
% 0.21/0.28 % (1110618)Time elapsed: 0.003 s
% 0.21/0.28 % (1110618)Peak memory usage: 12 MB
% 0.21/0.28 % (1110618)Instructions burned: 6 (million)
% 0.21/0.28 % (1110600)Success in time 0.038 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------