%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : AGT036^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 07:44:39 AM UTC 2026
% Result : Theorem 0.34s 0.24s
% Output : Refutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 284 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 436 ( 44 ~; 23 |; 0 &; 329 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 9 con; 0-4 aty)
% ( 30 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 131 ( 94 ^; 37 !; 0 ?; 131 :)
% 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,
a1: $i > $i > $o ).
thf(func_def_33,type,
a2: $i > $i > $o ).
thf(func_def_34,type,
a3: $i > $i > $o ).
thf(func_def_35,type,
jan: mu ).
thf(func_def_36,type,
piotr: mu ).
thf(func_def_37,type,
cola: mu ).
thf(func_def_38,type,
pepsi: mu ).
thf(func_def_39,type,
beer: mu ).
thf(func_def_40,type,
likes: mu > mu > $i > $o ).
thf(func_def_41,type,
very_much_likes: mu > mu > $i > $o ).
thf(func_def_42,type,
possibly_likes: mu > mu > $i > $o ).
thf(func_def_43,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_44,type,
cond4s: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_50,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vIMP: $o > $o > $o ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_58,type,
vNOT: $o > $o ).
thf(func_def_59,type,
vOR: $o > $o > $o ).
thf(func_def_60,type,
sK0: $i > $i ).
thf(func_def_61,type,
sK1: mu > $i > mu > $i ).
thf(func_def_62,type,
sK2: mu > mu > $i > $i ).
thf(func_def_63,type,
sK3: mu > mu > $i > $i ).
thf(func_def_65,type,
sK5: $i > $i ).
thf(func_def_66,type,
sK6: $i > $i ).
thf(func_def_67,type,
sK7: $i > $i ).
thf(func_def_68,type,
sK8: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f17,axiom,
( mdia
= ( ^ [X0: $i > $i > $o,X1: $i > $o] : ( mnot @ ( mbox @ X0 @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mdia) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f33,axiom,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a1_2) ).
thf(f43,axiom,
mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_a3_3) ).
thf(f50,axiom,
msymmetric @ a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axioms_B_a1) ).
thf(f73,conjecture,
mvalid @ ( likes @ piotr @ pepsi ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f74,negated_conjecture,
~ ( mvalid @ ( likes @ piotr @ pepsi ) ),
inference(negated_conjecture,[status(cth)],[f73]) ).
thf(f85,plain,
~ ( mvalid @ ( likes @ piotr @ pepsi ) ),
inference(rectify,[],[f74]) ).
thf(f86,plain,
( ( mvalid @ ( likes @ piotr @ pepsi ) )
!= $true ),
inference(fool_elimination,[],[f85]) ).
thf(f120,plain,
mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ),
inference(rectify,[],[f43]) ).
thf(f121,plain,
( ( mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ) )
= $true ),
inference(fool_elimination,[],[f120]) ).
thf(f124,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f125,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f124]) ).
thf(f151,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f152,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f151]) ).
thf(f161,plain,
mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ),
inference(rectify,[],[f33]) ).
thf(f162,plain,
( ( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(fool_elimination,[],[f161]) ).
thf(f172,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f175,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f176,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f175]) ).
thf(f177,plain,
msymmetric @ a1,
inference(rectify,[],[f50]) ).
thf(f178,plain,
( ( msymmetric @ a1 )
= $true ),
inference(fool_elimination,[],[f177]) ).
thf(f196,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f197,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f196]) ).
thf(f210,plain,
( ( mvalid @ ( likes @ piotr @ pepsi ) )
!= $true ),
inference(flattening,[],[f86]) ).
thf(f214,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f223,plain,
( ( mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ) )
= $true ),
inference(cnf_transformation,[],[f121]) ).
thf(f231,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f197]) ).
thf(f249,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f152]) ).
thf(f252,plain,
( ( mvalid @ ( likes @ piotr @ pepsi ) )
!= $true ),
inference(cnf_transformation,[],[f210]) ).
thf(f261,plain,
( ( msymmetric @ a1 )
= $true ),
inference(cnf_transformation,[],[f178]) ).
thf(f263,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f176]) ).
thf(f276,plain,
( ( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ) )
= $true ),
inference(cnf_transformation,[],[f162]) ).
thf(f283,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] : ( mnot @ ( mbox @ Y0 @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f172]) ).
thf(f294,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f283,f231,f263,f231]) ).
thf(f303,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ Y0
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ a1
@ ( likes @ piotr @ beer ) ) ) ),
inference(definition_unfolding,[],[f223,f214,f294]) ).
thf(f316,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( likes @ piotr @ pepsi ) ) ),
inference(definition_unfolding,[],[f252,f214]) ).
thf(f322,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ a1 ) ),
inference(definition_unfolding,[],[f261,f249]) ).
thf(f330,plain,
( $true
= ( ^ [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 ) ) )
@ a1
@ ( likes @ piotr @ pepsi ) ) ) ),
inference(definition_unfolding,[],[f276,f214,f263]) ).
thf(f476,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ piotr @ pepsi @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f330]) ).
thf(f477,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ( likes @ piotr @ pepsi @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ( likes @ piotr @ pepsi @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f477]) ).
thf(f479,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ( likes @ piotr @ pepsi @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f478]) ).
thf(f480,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( a1 @ X1 @ X2 )
| ( likes @ piotr @ pepsi @ X2 ) ) ),
inference(beta-eta_normalization,[],[f479]) ).
thf(f481,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( a1 @ X1 @ X2 ) ) )
| ( $true
= ( likes @ piotr @ pepsi @ X2 ) ) ),
inference(or_proxy_clausification,[],[f480]) ).
thf(f482,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( likes @ piotr @ pepsi @ X2 ) )
| ( ( a1 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f481]) ).
thf(f524,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( a1 @ Y1 @ Y0 )
=> ( a1 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f525,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( a1 @ Y1 @ Y0 )
=> ( a1 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f524]) ).
thf(f526,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( a1 @ Y0 @ X1 )
=> ( a1 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f525]) ).
thf(f527,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( a1 @ Y0 @ X1 )
=> ( a1 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f526]) ).
thf(f528,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( a1 @ X2 @ X1 )
=> ( a1 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f527]) ).
thf(f529,plain,
! [X2: $i,X1: $i] :
( ( ( a1 @ X2 @ X1 )
= $false )
| ( $true
= ( a1 @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f528]) ).
thf(f550,plain,
( $true
!= ( !! @ $i @ ( likes @ piotr @ pepsi ) ) ),
inference(beta-eta_normalization,[],[f316]) ).
thf(f551,plain,
( ( likes @ piotr @ pepsi @ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f550]) ).
thf(f709,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ beer @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f710,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( a1 @ Y0 @ Y1 )
| ~ ( likes @ piotr @ beer @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f709]) ).
thf(f711,plain,
! [X1: $i] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ~ ( likes @ piotr @ beer @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f710]) ).
thf(f712,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ~ ( likes @ piotr @ beer @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f711]) ).
thf(f713,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( a1 @ X1 @ Y0 )
| ~ ( likes @ piotr @ beer @ Y0 ) )
@ ( sK8 @ X1 ) )
= $false ),
inference(sigma_proxy_clausification,[],[f712]) ).
thf(f714,plain,
! [X1: $i] :
( $false
= ( ~ ( a1 @ X1 @ ( sK8 @ X1 ) )
| ~ ( likes @ piotr @ beer @ ( sK8 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f713]) ).
thf(f716,plain,
! [X1: $i] :
( ( ~ ( a1 @ X1 @ ( sK8 @ X1 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f714]) ).
thf(f717,plain,
! [X1: $i] :
( $true
= ( a1 @ X1 @ ( sK8 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f716]) ).
thf(f788,plain,
! [X0: $i] :
( ( ( a1 @ X0 @ sK4 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f551,f482]) ).
thf(f794,plain,
! [X0: $i] :
( ( a1 @ X0 @ sK4 )
= $false ),
inference(trivial_inequality_removal,[],[f788]) ).
thf(f801,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( a1 @ sK4 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f529,f794]) ).
thf(f802,plain,
! [X0: $i] :
( ( a1 @ sK4 @ X0 )
= $false ),
inference(trivial_inequality_removal,[],[f801]) ).
thf(f808,plain,
$true = $false,
inference(constrained_superposition,[],[f717,f802]) ).
thf(f812,plain,
$false,
inference(trivial_inequality_removal,[],[f808]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : AGT036^1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.15 % Computer : n012.cluster.edu
% 0.07/0.15 % Model : x86_64 x86_64
% 0.07/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.15 % Memory : 8046.5625MB
% 0.07/0.15 % OS : Linux 6.8.0-71-generic
% 0.07/0.15 % CPULimit : 300
% 0.07/0.15 % WCLimit : 300
% 0.07/0.15 % DateTime : Tue Sep 29 17:30:19 UTC 2026
% 0.07/0.15 % CPUTime :
% 0.07/0.15 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 Running higher-order theorem proving
% 0.07/0.19 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
% 0.34/0.24 % (424888)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.34/0.24 % (424897)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=117032818:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.34/0.24 % (424893)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=154540734:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.34/0.24 % (424894)lrs+10_16_si=on:nwc=1.5:random_seed=1778916439:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.34/0.24 % (424899)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.34/0.24 % (424899)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
% 0.34/0.24 % (424895)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2150945250:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.34/0.24 % (424896)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=2388346652: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)
% 0.34/0.24 % (424898)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1287602338:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.34/0.24 % (424895)Instruction limit reached!
% 0.34/0.24 % (424895)------------------------------
% 0.34/0.24 % (424895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.24 % (424895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.24 % (424895)CaDiCaL version: 2.1.3
% 0.34/0.24 % (424895)Termination reason: Instruction limit
% 0.34/0.24 % (424895)Termination phase: shuffling
% 0.34/0.24 % (424895)Time elapsed: 0.002 s
% 0.34/0.24 % (424895)Peak memory usage: 9 MB
% 0.34/0.24 % (424895)Instructions burned: 4 (million)
% 0.34/0.24 % (424899)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=3801688093:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.34/0.24 % (424897)Instruction limit reached!
% 0.34/0.24 % (424897)------------------------------
% 0.34/0.24 % (424897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.24 % (424897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.24 % (424897)CaDiCaL version: 2.1.3
% 0.34/0.24 % (424897)Termination reason: Instruction limit
% 0.34/0.24 % (424897)Termination phase: Saturation
% 0.34/0.24 % (424897)Time elapsed: 0.008 s
% 0.34/0.24 % (424897)Peak memory usage: 12 MB
% 0.34/0.24 % (424897)Instructions burned: 25 (million)
% 0.34/0.24 % (424894)Instruction limit reached!
% 0.34/0.24 % (424894)------------------------------
% 0.34/0.24 % (424894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.24 % (424894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.24 % (424894)CaDiCaL version: 2.1.3
% 0.34/0.24 % (424894)Termination reason: Instruction limit
% 0.34/0.24 % (424894)Termination phase: Property scanning
% 0.34/0.24 % (424894)Time elapsed: 0.008 s
% 0.34/0.24 % (424894)Peak memory usage: 10 MB
% 0.34/0.24 % (424894)Instructions burned: 19 (million)
% 0.34/0.24 % (424907)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=403959190:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.34/0.24 % (424909)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.34/0.24 % (424893) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-424888-424893"...
% 0.34/0.24 % (424899) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-424888-424899"...
% 0.34/0.24 % (424907)Instruction limit reached!
% 0.34/0.24 % (424907)------------------------------
% 0.34/0.24 % (424907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.24 % (424907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.24 % (424907)CaDiCaL version: 2.1.3
% 0.34/0.24 % (424907)Termination reason: Instruction limit
% 0.34/0.24 % (424907)Termination phase: Property scanning
% 0.34/0.24 % (424907)Time elapsed: 0.003 s
% 0.34/0.24 % (424907)Peak memory usage: 10 MB
% 0.34/0.24 % (424907)Instructions burned: 7 (million)
% 0.34/0.24 % (424909)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3786624230:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.34/0.24 % (424893)...printing done.
% 0.34/0.24 % (424908)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1697672965:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.34/0.24 % (424899)...printing done.
% 0.34/0.24 % (424893)Refutation found. Thanks to Tanya!
% 0.34/0.24 % SZS status Theorem for theBenchmark
% 0.34/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.34/0.25 % (424893)------------------------------
% 0.34/0.25 % (424893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.25 % (424893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.25 % (424893)CaDiCaL version: 2.1.3
% 0.34/0.25 % (424893)Termination reason: Refutation
% 0.34/0.25 % (424893)Time elapsed: 0.026 s
% 0.34/0.25 % (424893)Peak memory usage: 12 MB
% 0.34/0.25 % (424893)Instructions burned: 57 (million)
% 0.34/0.25 % (424888)Success in time 0.05 s
% 0.34/0.25 % Vampire exiting
%------------------------------------------------------------------------------