%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO044^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:46:22 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 114 ( 18 ~; 10 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 48 usr; 5 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 45 ( 36 ^; 8 !; 1 ?; 45 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(f14,axiom,
( ( ^ [X0: $i] : $true )
= mtrue ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtrue) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] : ( mvalid @ ( mbox @ X0 @ mtrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] : ( mvalid @ ( mbox @ X0 @ mtrue ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f35,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f40,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f41,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f49,plain,
~ ! [X0: $i > $i > $o] : ( mvalid @ ( mbox @ X0 @ mtrue ) ),
inference(rectify,[],[f33]) ).
thf(f50,plain,
~ ! [X0: $i > $i > $o] :
( ( mvalid @ ( mbox @ X0 @ mtrue ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f82,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(fool_elimination,[],[f14]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( mvalid @ ( mbox @ X0 @ mtrue ) )
!= $true ),
inference(ennf_transformation,[],[f50]) ).
thf(f88,plain,
( $true
!= ( mvalid @ ( mbox @ sK0 @ mtrue ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f106,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f107,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f112,plain,
( $true
!= ( mvalid @ ( mbox @ sK0 @ mtrue ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f120,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f132,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ sK0
@ ^ [Y0: $i] : $true ) )
!= $true ),
inference(definition_unfolding,[],[f112,f106,f107,f120]) ).
thf(f133,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| $true ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| $true ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f133]) ).
thf(f135,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| $true ) )
= $false ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK1 @ Y0 )
| $true )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( ~ ( sK0 @ sK1 @ sK2 )
| $true )
= $false ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
$true = $false,
inference(or_proxy_clausification,[],[f137]) ).
thf(f141,plain,
$false,
inference(trivial_inequality_removal,[],[f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO044^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % 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 16:26:14 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 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
% 0.21/0.28 % (2701042)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (2701051)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=894837550:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (2701053)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (2701053)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.28 % (2701047)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1613182795:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (2701049)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2518406008:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (2701048)lrs+10_16_si=on:nwc=1.5:random_seed=2502019995:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (2701050)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3751794176:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.28 % (2701052)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1097060909:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (2701053)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=112345586:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (2701051)Instruction limit reached!
% 0.21/0.28 % (2701051)------------------------------
% 0.21/0.28 % (2701051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2701051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2701051)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2701051)Termination reason: Instruction limit
% 0.21/0.28 % (2701051)Termination phase: Saturation
% 0.21/0.28 % (2701051)Time elapsed: 0.008 s
% 0.21/0.28 % (2701051)Peak memory usage: 12 MB
% 0.21/0.28 % (2701051)Instructions burned: 26 (million)
% 0.21/0.28 % (2701049)Instruction limit reached!
% 0.21/0.28 % (2701049)------------------------------
% 0.21/0.28 % (2701049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2701049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2701049)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2701049)Termination reason: Instruction limit
% 0.21/0.28 % (2701049)Termination phase: Property scanning
% 0.21/0.28 % (2701049)Time elapsed: 0.002 s
% 0.21/0.28 % (2701049)Peak memory usage: 10 MB
% 0.21/0.28 % (2701049)Instructions burned: 4 (million)
% 0.21/0.28 % (2701047) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2701042-2701047"...
% 0.21/0.28 % (2701048) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2701042-2701048"...
% 0.21/0.28 % (2701052) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2701042-2701052"...
% 0.21/0.28 % (2701053) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2701042-2701053"...
% 0.21/0.28 % (2701047)...printing done.
% 0.21/0.28 % (2701048)...printing done.
% 0.21/0.28 % (2701052)...printing done.
% 0.21/0.28 % (2701047)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 % (2701047)------------------------------
% 0.21/0.28 % (2701047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2701047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2701047)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2701047)Termination reason: Refutation
% 0.21/0.28 % (2701047)Time elapsed: 0.005 s
% 0.21/0.28 % (2701047)Peak memory usage: 12 MB
% 0.21/0.28 % (2701047)Instructions burned: 8 (million)
% 0.21/0.28 % (2701042)Success in time 0.04 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------