%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO574^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:50:26 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 67 unt; 0 typ; 2 def)
% Number of atoms : 553 ( 100 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 735 ( 134 ~; 100 |; 0 &; 455 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 56 usr; 7 con; 0-4 aty)
% ( 44 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 175 ( 0 sgn 24 !; 0 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: 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,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $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,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
p: $i > $o ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK0: $i > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( mdia_s4
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mdia_s4 @ ( mimplies @ p @ ( mbox_s4 @ q ) ) ) @ ( mimplies @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mimplies @ p @ ( mbox_s4 @ q ) ) ) @ ( mimplies @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f50,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f63,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f64,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f83,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f91,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f92,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f93,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f94,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f95,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f100,plain,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mimplies @ p @ ( mbox_s4 @ q ) ) ) @ ( mimplies @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mimplies @ p @ ( mbox_s4 @ q ) ) ) @ ( mimplies @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f100]) ).
thf(f102,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mimplies @ p @ ( mbox_s4 @ q ) ) ) @ ( mimplies @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ) )
!= $true ),
inference(flattening,[],[f101]) ).
thf(f107,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f114,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f123,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f133,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f137,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f138,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f139,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f142,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mimplies @ p @ ( mbox_s4 @ q ) ) ) @ ( mimplies @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f147,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f114,f108,f107]) ).
thf(f154,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f138,f107,f137,f107]) ).
thf(f155,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f139,f123]) ).
thf(f157,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f142,f133,f147,f154,f147,f137,f147,f137,f154]) ).
thf(f158,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( $false
= ( ~ ( ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( $true
= ( rel_s4 @ sK1 @ sK2 ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( $true
= ( ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f171,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( p @ sK2 ) ) ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( p @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f178,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f179,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f185,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ~ ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f199,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f200,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f203,definition,
( spl3_1
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f205,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f207,definition,
( spl3_2
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f208,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f207]) ).
thf(f209,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f176,f207,f203]) ).
thf(f211,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) ) ),
inference(constrained_superposition,[],[f169,f183]) ).
thf(f212,plain,
( $true
= ( p @ sK2 ) ),
inference(trivial_inequality_removal,[],[f211]) ).
thf(f230,plain,
( ( $true = $false )
| ( $false
= ( q @ sK2 ) ) ),
inference(constrained_superposition,[],[f169,f189]) ).
thf(f233,plain,
( $false
= ( q @ sK2 ) ),
inference(trivial_inequality_removal,[],[f230]) ).
thf(f290,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f208,f201]) ).
thf(f299,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f290]) ).
thf(f303,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(forward_demodulation,[],[f299,f233]) ).
thf(f304,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f305,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f304]) ).
thf(f336,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f205,f212]) ).
thf(f342,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f336]) ).
thf(f343,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f342]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f209]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f305]) ).
cnf(s5,plain,
~ spl3_1,
inference(sat_conversion,[],[f343]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f344,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO574^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n006.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 17:16:28 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.21/0.27 % (1044486)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (1044495)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3940650906:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.27 % (1044495)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.27 % (1044492)% WARNING: option uhcvi not known.
% 0.21/0.27 % (1044495) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1044486-1044495"...
% 0.21/0.27 % (1044493)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1688244976:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.27 % (1044491)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=658080409_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.27 % (1044492)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1850961974:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.27 % (1044494)dis+10_1_sil=32000:sp=arity:random_seed=105101224:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.27 % (1044496)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3870218414:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.27 % (1044495)...printing done.
% 0.21/0.27 % (1044497)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4077674820:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.27 % (1044495)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 % (1044495)------------------------------
% 0.21/0.27 % (1044495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (1044495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (1044495)CaDiCaL version: 2.1.3
% 0.21/0.27 % (1044495)Termination reason: Refutation
% 0.21/0.27 % (1044495)Time elapsed: 0.007 s
% 0.21/0.27 % (1044495)Peak memory usage: 13 MB
% 0.21/0.27 % (1044495)Instructions burned: 25 (million)
% 0.21/0.27 % (1044486)Success in time 0.037 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------