%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO431^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 08:49:57 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 11
% Syntax : Number of formulae : 107 ( 72 unt; 0 typ; 2 def)
% Number of atoms : 686 ( 113 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 1201 ( 269 ~; 136 |; 0 &; 694 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 59 ( 55 usr; 8 con; 0-4 aty)
% ( 90 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 238 ( 0 sgn 34 !; 0 ?; 238 :)
% 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_b: $i > $i > $o ).
thf(func_def_33,type,
mbox_b: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_b: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $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(func_def_54,type,
sK3: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
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_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',mbox_b) ).
thf(f33,axiom,
( mdia_b
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',mdia_b) ).
thf(f35,axiom,
msymmetric @ rel_b,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
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,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f63,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f64,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f81,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f89,plain,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f94,plain,
msymmetric @ rel_b,
inference(rectify,[],[f35]) ).
thf(f95,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
~ ( mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f97]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f103,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f117,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f126,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f130,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f131,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f133,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f134,plain,
( ( mvalid @ ( mnot @ ( mdia_b @ ( mand @ ( mdia_b @ ( mbox_b @ ( mdia_b @ p ) ) ) @ ( mbox_b @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f137,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,[],[f103,f101,f102,f101,f101]) ).
thf(f146,plain,
( mdia_b
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f131,f101,f130,f101]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_b ) ),
inference(definition_unfolding,[],[f133,f117]) ).
thf(f149,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f134,f126,f101,f146,f137,f146,f130,f146,f130,f101]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ~ ( p @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ~ ( p @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( $false
= ( ~ ( rel_b @ sK0 @ sK1 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f160,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f161,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( $false
= ( ~ ( rel_b @ sK1 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( $false
= ( ~ ( rel_b @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( $true
= ( rel_b @ sK1 @ sK2 ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f172,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_b @ sK2 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_b @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK3 @ X1 ) )
| ~ ( p @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( rel_b @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $false
= ( ~ ( p @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( rel_b @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( rel_b @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_b @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( rel_b @ sK2 @ X1 ) )
| ( $true
= ( p @ ( sK3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f183,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f184,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_b @ sK1 @ X1 )
| ~ ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f190,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_b @ X2 @ X1 )
=> ( rel_b @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_b @ X2 @ X1 ) )
| ( ( rel_b @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f250,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ X0 @ sK2 ) )
| ( $true
= ( p @ ( sK3 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f194,f182]) ).
thf(f251,plain,
! [X0: $i] :
( ( $false
= ( rel_b @ X0 @ sK2 ) )
| ( $true
= ( p @ ( sK3 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f256,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK2 @ sK1 ) )
| ( $false
= ( p @ ( sK3 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f181,f188]) ).
thf(f263,plain,
( ( $false
= ( rel_b @ sK2 @ sK1 ) )
| ( $false
= ( p @ ( sK3 @ sK1 ) ) ) ),
inference(trivial_inequality_removal,[],[f256]) ).
thf(f267,definition,
( spl4_1
<=> ( $false
= ( rel_b @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f269,plain,
( ( $false
= ( rel_b @ sK2 @ sK1 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f271,definition,
( spl4_2
<=> ( $false
= ( p @ ( sK3 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f273,plain,
( ( $false
= ( p @ ( sK3 @ sK1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f277,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f263,f267,f271]) ).
thf(f282,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK3 @ sK1 ) ) ) ),
inference(constrained_superposition,[],[f251,f170]) ).
thf(f291,plain,
( $true
= ( p @ ( sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f297,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f291,f273]) ).
thf(f298,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f299,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f298]) ).
thf(f304,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK1 @ sK2 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f194,f269]) ).
thf(f305,plain,
( ( $false
= ( rel_b @ sK1 @ sK2 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f308,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f305,f170]) ).
thf(f314,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f315,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f314]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f277]) ).
cnf(s4,plain,
~ spl4_2,
inference(sat_conversion,[],[f299]) ).
cnf(s6,plain,
~ spl4_1,
inference(sat_conversion,[],[f315]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s4,s6]) ).
thf(f316,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO431^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n015.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:54:48 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.18/0.27 % (3791925)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (3791934)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4174317703:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.27 % (3791934)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % (3791931)% WARNING: option uhcvi not known.
% 0.18/0.27 % (3791934) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3791925-3791934"...
% 0.18/0.27 % (3791932)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=263190253:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.27 % (3791930)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3058155482_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (3791931)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1223402083:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (3791934)...printing done.
% 0.18/0.27 % (3791931)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.27 % Exception at run slice level
% 0.18/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.27 % (3791931)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.27 % (3791933)dis+10_1_sil=32000:sp=arity:random_seed=1778951704:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (3791934)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (3791934)------------------------------
% 0.18/0.27 % (3791934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (3791934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (3791934)CaDiCaL version: 2.1.3
% 0.18/0.27 % (3791934)Termination reason: Refutation
% 0.18/0.27 % (3791934)Time elapsed: 0.007 s
% 0.18/0.27 % (3791934)Peak memory usage: 13 MB
% 0.18/0.27 % (3791934)Instructions burned: 24 (million)
% 0.18/0.27 % (3791925)Success in time 0.05 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------