%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO415^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:49:54 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 97 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 755 ( 138 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 1190 ( 248 ~; 161 |; 0 &; 711 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 5 con; 0-4 aty)
% ( 70 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 250 ( 209 ^; 41 !; 0 ?; 250 :)
% 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,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f33,axiom,
( mdia_k
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^1.ax',mdia_k) ).
thf(f34,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mbox_k @ ( mdia_k @ p ) ) @ ( mdia_k @ ( mbox_k @ ( mimplies @ p @ q ) ) ) ) @ ( mdia_k @ ( mdia_k @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_k @ ( mdia_k @ p ) ) @ ( mdia_k @ ( mbox_k @ ( mimplies @ p @ q ) ) ) ) @ ( mdia_k @ ( mdia_k @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f38,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
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(f89,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f90,plain,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_k @ ( mdia_k @ p ) ) @ ( mdia_k @ ( mbox_k @ ( mimplies @ p @ q ) ) ) ) @ ( mdia_k @ ( mdia_k @ q ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f91,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_k @ ( mdia_k @ p ) ) @ ( mdia_k @ ( mbox_k @ ( mimplies @ p @ q ) ) ) ) @ ( mdia_k @ ( mdia_k @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_k @ ( mdia_k @ p ) ) @ ( mdia_k @ ( mbox_k @ ( mimplies @ p @ q ) ) ) ) @ ( mdia_k @ ( mdia_k @ q ) ) ) )
!= $true ),
inference(flattening,[],[f91]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f96,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f97,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
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(f125,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f126,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_k @ ( mdia_k @ p ) ) @ ( mdia_k @ ( mbox_k @ ( mimplies @ p @ q ) ) ) ) @ ( mdia_k @ ( mdia_k @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f129,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f97,f95,f96,f95,f95]) ).
thf(f130,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,[],[f98,f96,f95]) ).
thf(f138,plain,
( mdia_k
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f125,f95,f124,f95]) ).
thf(f139,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 > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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
@ q ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f126,f120,f130,f129,f124,f138,f138,f124,f130,f138,f138]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( p @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( p @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f146]) ).
thf(f149,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK1 @ X1 ) )
| ~ ( p @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $false
= ( ~ ( p @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK1 @ X1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( p @ ( sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f161,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f162,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( $true
= ( rel_k @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f169,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( p @ Y0 )
| ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_k @ sK2 @ X1 )
| ~ ( p @ X1 )
| ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $false
= ( rel_k @ sK2 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f143]) ).
thf(f176,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ X1 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( q @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( ( rel_k @ X1 @ X2 )
= $false )
| ( $false
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK1 @ sK2 ) ) ) ),
inference(constrained_superposition,[],[f167,f160]) ).
thf(f189,plain,
( $true
= ( p @ ( sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f236,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $false
= ( q @ ( sK1 @ X0 ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f186,f159]) ).
thf(f237,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK1 @ sK2 ) ) )
| ( $false
= ( p @ ( sK1 @ sK2 ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(constrained_superposition,[],[f174,f159]) ).
thf(f238,plain,
( ( $true
= ( q @ ( sK1 @ sK2 ) ) )
| ( $false
= ( p @ ( sK1 @ sK2 ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f239,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $false
= ( q @ ( sK1 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f236]) ).
thf(f240,plain,
! [X0: $i] :
( ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $false
= ( q @ ( sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f246,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK1 @ sK2 ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(forward_demodulation,[],[f238,f189]) ).
thf(f247,plain,
( ( $true
= ( q @ ( sK1 @ sK2 ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f250,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK1 @ sK2 ) ) ) ),
inference(forward_demodulation,[],[f247,f167]) ).
thf(f251,plain,
( $true
= ( q @ ( sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f257,plain,
( ( $true = $false )
| ( $false
= ( q @ ( sK1 @ sK2 ) ) ) ),
inference(constrained_superposition,[],[f167,f240]) ).
thf(f260,plain,
( $false
= ( q @ ( sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f266,plain,
$true = $false,
inference(constrained_superposition,[],[f251,f260]) ).
thf(f267,plain,
$false,
inference(trivial_inequality_removal,[],[f266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO415^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n007.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:49:11 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.26 % (3633653)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (3633661)dis+10_1_sil=32000:sp=arity:random_seed=2309512916:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.26 % (3633659)% WARNING: option uhcvi not known.
% 0.10/0.26 % (3633661) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3633653-3633661"...
% 0.10/0.26 % (3633658)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3998247092_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.26 % (3633659)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3836047346:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.26 % (3633660)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3834243096:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.26 % (3633661)...printing done.
% 0.10/0.26 % (3633662)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3669993890:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.26 % (3633659)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (3633662)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (3633661)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (3633661)------------------------------
% 0.10/0.26 % (3633661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (3633661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (3633661)CaDiCaL version: 2.1.3
% 0.10/0.26 % (3633661)Termination reason: Refutation
% 0.10/0.26 % (3633661)Time elapsed: 0.007 s
% 0.10/0.26 % (3633661)Peak memory usage: 12 MB
% 0.10/0.26 % (3633661)Instructions burned: 22 (million)
% 0.10/0.26 % (3633653)Success in time 0.034 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------