%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL706^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 08:15:06 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 78 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 470 ( 102 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 727 ( 61 ~; 73 |; 15 &; 507 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 112 ( 112 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 50 usr; 6 con; 0-4 aty)
% ( 48 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 209 ( 155 ^; 51 !; 3 ?; 209 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sK1: $i > $i > $i ).
thf(func_def_50,type,
sK3: $i > $o ).
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(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
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(f25,axiom,
( mweakly_dense
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( X0 @ X1 @ X2 )
=> ? [X3: $i] :
( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mweakly_dense) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( mweakly_dense @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( mweakly_dense @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f36,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f37,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f39,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f48,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f54,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f71,plain,
( mweakly_dense
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ? [X4: $i] :
( ( X0 @ X4 @ X2 )
& ( X0 @ X1 @ X4 ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f72,plain,
( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f77,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f78,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f85,plain,
~ ! [X0: $i > $i > $o] :
( ( mweakly_dense @ X0 )
=> ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( ( mweakly_dense @ X0 )
= $true )
=> ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mbox @ X0 @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) )
& ( ( mweakly_dense @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ Y0 ) ) ) ) )
& ( $true
= ( mweakly_dense @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f87]) ).
thf(f91,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f92,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f94,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f99,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f104,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f113,plain,
( mweakly_dense
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f120,plain,
( $true
= ( mweakly_dense @ sK0 ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f121,plain,
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ ( mbox @ sK0 @ Y0 ) ) @ ( mbox @ sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f125,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,[],[f94,f92,f91]) ).
thf(f133,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ sK0
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f116,f99,f125,f104,f104,f104]) ).
thf(f134,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f120,f113]) ).
thf(f135,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X2 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK0 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f140,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK0 @ Y0 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
@ ( sK1 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) )
& ( sK0 @ ( sK1 @ X1 @ X2 ) @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ ( sK1 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ ( sK1 @ X1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f146,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( sK0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( $false
= ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( sK0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ sK2 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f152,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( sK0 @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( $true
= ( ~ ( sK0 @ sK2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( sK0 @ sK2 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( sK0 @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X2 )
| ( sK3 @ X2 ) ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK3 @ X2 ) )
| ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK2 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( sK0 @ sK2 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f162,plain,
( $false
= ( ~ ( sK0 @ sK2 @ sK4 )
| ( sK3 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( $false
= ( sK3 @ sK4 ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( ~ ( sK0 @ sK2 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( $true
= ( sK0 @ sK2 @ sK4 ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f203,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 @ ( sK1 @ X0 @ X1 ) ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f160,f143]) ).
thf(f204,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK2 @ ( sK1 @ X0 @ X1 ) ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f203]) ).
thf(f214,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) )
| ( $false
= ( sK0 @ sK2 @ X0 ) ) ),
inference(constrained_superposition,[],[f144,f204]) ).
thf(f215,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f214]) ).
thf(f216,plain,
! [X0: $i] :
( ( $false
= ( sK0 @ sK2 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f224,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK4 ) ) ),
inference(constrained_superposition,[],[f165,f216]) ).
thf(f225,plain,
( $true
= ( sK3 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f224]) ).
thf(f230,plain,
$true = $false,
inference(forward_demodulation,[],[f225,f163]) ).
thf(f231,plain,
$false,
inference(trivial_inequality_removal,[],[f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL706^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n006.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 09:44:40 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.25 % (490549)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (490558)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3839050131:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (490558)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (490558) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-490549-490558"...
% 0.08/0.25 % (490558)...printing done.
% 0.08/0.25 % (490558)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (490558)------------------------------
% 0.08/0.25 % (490558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (490558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (490558)CaDiCaL version: 2.1.3
% 0.08/0.25 % (490558)Termination reason: Refutation
% 0.08/0.25 % (490558)Time elapsed: 0.005 s
% 0.08/0.25 % (490558)Peak memory usage: 12 MB
% 0.08/0.25 % (490558)Instructions burned: 17 (million)
% 0.08/0.25 % (490549)Success in time 0.033 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------