%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL719^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:15:08 AM UTC 2026
% Result : Theorem 0.04s 0.16s
% Output : Refutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 122 ( 25 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 129 ( 17 ~; 10 |; 1 &; 85 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 51 usr; 5 con; 0-4 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 29 ^; 5 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
phi: $i > $o ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f34,conjecture,
( ( mvalid @ phi )
=> ( mvalid @ ( mbox_k @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f35,negated_conjecture,
~ ( ( mvalid @ phi )
=> ( mvalid @ ( mbox_k @ phi ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f79,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f80,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f87,plain,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f88,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f90,plain,
~ ( ( mvalid @ phi )
=> ( mvalid @ ( mbox_k @ phi ) ) ),
inference(rectify,[],[f35]) ).
thf(f91,plain,
~ ( ( ( mvalid @ phi )
= $true )
=> ( ( mvalid @ ( mbox_k @ phi ) )
= $true ) ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ( ( mvalid @ ( mbox_k @ phi ) )
!= $true )
& ( ( mvalid @ phi )
= $true ) ),
inference(ennf_transformation,[],[f91]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f124,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f126,plain,
( ( mvalid @ phi )
= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f127,plain,
( ( mvalid @ ( mbox_k @ phi ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f140,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi ) ) ),
inference(definition_unfolding,[],[f127,f120,f124]) ).
thf(f141,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ phi ) ),
inference(definition_unfolding,[],[f126,f120]) ).
thf(f142,plain,
( $true
= ( !! @ $i @ phi ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( $true
= ( phi @ X1 ) ),
inference(pi_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f145,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( phi @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( phi @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ( phi @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( $false
= ( phi @ sK1 ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f161,plain,
$true = $false,
inference(constrained_superposition,[],[f143,f149]) ).
thf(f162,plain,
$false,
inference(trivial_inequality_removal,[],[f161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL719^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.04/0.11 % CPULimit : 300
% 0.04/0.11 % WCLimit : 300
% 0.04/0.11 % DateTime : Tue Sep 29 09:54:19 UTC 2026
% 0.04/0.12 % CPUTime :
% 0.04/0.12 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.04/0.13 Running first-order model finding
% 0.04/0.13 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
% 0.04/0.16 % (4076783)Will run a generic schedule for satisfiability detection.
% 0.04/0.16 % (4076789)% WARNING: option uhcvi not known.
% 0.04/0.16 % (4076789)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1534318625:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.04/0.16 % (4076791)dis+10_1_sil=32000:sp=arity:random_seed=3998236900:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.04/0.16 % (4076790)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=590607285:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.04/0.16 % (4076788)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3998435409_2999 on theBenchmark for (2999ds/0Mi)
% 0.04/0.16 % (4076794)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=922854883:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.04/0.16 % (4076789)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.04/0.16 % Exception at run slice level% (4076789)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.04/0.16
% 0.04/0.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.04/0.16 % (4076791) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4076783-4076791"...
% 0.04/0.16 % (4076790) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4076783-4076790"...
% 0.04/0.16 % (4076789) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4076783-4076789"...
% 0.04/0.16 % (4076794) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4076783-4076794"...
% 0.04/0.16 % (4076790)...printing done.
% 0.04/0.16 % (4076791)...printing done.
% 0.04/0.16 % (4076789)...printing done.
% 0.04/0.16 % (4076794)...printing done.
% 0.04/0.16 % (4076793)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=291926265:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.04/0.16 % (4076789)Refutation found. Thanks to Tanya!
% 0.04/0.16 % SZS status Theorem for theBenchmark
% 0.04/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.04/0.17 % (4076789)------------------------------
% 0.04/0.17 % (4076789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.04/0.17 % (4076789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.04/0.17 % (4076789)CaDiCaL version: 2.1.3
% 0.04/0.17 % (4076789)Termination reason: Refutation
% 0.04/0.17 % (4076789)Time elapsed: 0.003 s
% 0.04/0.17 % (4076789)Peak memory usage: 12 MB
% 0.04/0.17 % (4076789)Instructions burned: 8 (million)
% 0.04/0.17 % (4076783)Success in time 0.026 s
% 0.04/0.17 % Vampire exiting
%------------------------------------------------------------------------------