%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PHI005^2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 Oct 7 10:36:10 AM UTC 2026
% Result : Theorem 0.40s 0.31s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 90 ( 75 unt; 0 typ; 25 def)
% Number of atoms : 345 ( 95 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 679 ( 122 ~; 72 |; 6 &; 458 @)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 149 ( 149 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 4 con; 0-4 aty)
% Number of variables : 246 ( 85 ^; 146 !; 15 ?; 246 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mu,type,
mu: $tType ).
thf(tp_essence,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(tp_god,type,
god: mu > $i > $o ).
thf(tp_mand,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mbox,type,
mbox: ( $i > $o ) > $i > $o ).
thf(tp_mbox_generic,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mdia,type,
mdia: ( $i > $o ) > $i > $o ).
thf(tp_mdia_generic,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_meq_ind,type,
meq_ind: mu > mu > $i > $o ).
thf(tp_mequiv,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mexists_ind,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mexists_indset,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mexists_prop,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mfalse,type,
mfalse: $i > $o ).
thf(tp_mforall_ind,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(tp_mforall_indset,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mforall_prop,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(tp_mimplied,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_mimplies,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_minvalid,type,
minvalid: ( $i > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( $i > $o ) > $i > $o ).
thf(tp_mor,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_msymmetric,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(tp_mtrue,type,
mtrue: $i > $o ).
thf(tp_mvalid,type,
mvalid: ( $i > $o ) > $o ).
thf(tp_mxor,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(tp_necessary_existence,type,
necessary_existence: mu > $i > $o ).
thf(tp_positive,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(tp_rel,type,
rel: $i > $i > $o ).
thf(tp_sK1_SY14,type,
sK1_SY14: $i ).
thf(tp_sK2_SY140,type,
sK2_SY140: $i ).
thf(tp_sK3_SY145,type,
sK3_SY145: $i > $i ).
thf(tp_sK4_SY159,type,
sK4_SY159: mu > $i > mu > $i > $o ).
thf(tp_sK5_SY165,type,
sK5_SY165: mu > mu > $i > $o ).
thf(tp_sK6_SY163,type,
sK6_SY163: $i > mu ).
thf(god,definition,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD1) ).
thf(mand,definition,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
& ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mbox_generic,definition,
( mbox_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ~ ( R @ W @ V )
| ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_generic) ).
thf(mdia,definition,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mdia_generic,definition,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( R @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_generic) ).
thf(meq_ind,definition,
( meq_ind
= ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meq_ind) ).
thf(mequiv,definition,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
<=> ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(mexists_ind,definition,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind) ).
thf(mexists_indset,definition,
( mexists_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
? [X: mu > $i > $o] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_indset) ).
thf(mexists_prop,definition,
( mexists_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
? [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_prop) ).
thf(mfalse,definition,
( mfalse
= ( ^ [W: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mfalse) ).
thf(mforall_ind,definition,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind) ).
thf(mforall_indset,definition,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_indset) ).
thf(mforall_prop,definition,
( mforall_prop
= ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
! [P: $i > $o] : ( Phi @ P @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop) ).
thf(mimplied,definition,
( mimplied
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Psi @ W )
=> ( Phi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplied) ).
thf(mimplies,definition,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(minvalid,definition,
( minvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minvalid) ).
thf(mnot,definition,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(msymmetric,definition,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric) ).
thf(mtrue,definition,
( mtrue
= ( ^ [W: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue) ).
thf(mvalid,definition,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid) ).
thf(mxor,definition,
( mxor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( ( Phi @ W )
& ~ ( Psi @ W ) )
| ( ~ ( Phi @ W )
& ( Psi @ W ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mxor) ).
thf(necessary_existence,definition,
( necessary_existence
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( essence @ Phi @ X )
@ ( mbox
@ ( mexists_ind
@ ^ [Y: mu] : ( Phi @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD3) ).
thf(1,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA5) ).
thf(2,axiom,
msymmetric @ rel,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sym) ).
thf(3,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( god @ X ) @ ( essence @ god @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT2) ).
thf(4,axiom,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corC) ).
thf(5,conjecture,
( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT3) ).
thf(6,negated_conjecture,
( ( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [SY14: $i,SY25: $i] :
( ~ ( rel @ SY14 @ SY25 )
| ? [SY23: mu] :
! [SY24: mu > $i > $o] :
( ( positive @ SY24 @ SY25 )
=> ( SY24 @ SY23 @ SY25 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(8,plain,
( ( ! [SY33: $i] :
( positive
@ ^ [SY34: mu,SY42: $i] :
! [SY43: mu > $i > $o] :
( ( essence @ SY43 @ SY34 @ SY42 )
=> ! [SY55: $i] :
( ~ ( rel @ SY42 @ SY55 )
| ? [SY52: mu] : ( SY43 @ SY52 @ SY55 ) ) )
@ SY33 ) )
= $true ),
inference(unfold_def,[status(thm)],[1,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(9,plain,
( ( ! [SY63: $i,SY64: $i] :
( ( rel @ SY63 @ SY64 )
=> ( rel @ SY64 @ SY63 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(10,plain,
( ( ! [SY96: $i,SY97: mu] :
( ! [SY98: mu > $i > $o] :
( ( positive @ SY98 @ SY96 )
=> ( SY98 @ SY97 @ SY96 ) )
=> ( essence
@ ^ [SY84: mu,SY89: $i] :
! [SY90: mu > $i > $o] :
( ( positive @ SY90 @ SY89 )
=> ( SY90 @ SY84 @ SY89 ) )
@ SY97
@ SY96 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(11,plain,
( ( ! [SY122: $i] :
? [SY133: $i] :
( ( rel @ SY122 @ SY133 )
& ? [SY131: mu] :
! [SY132: mu > $i > $o] :
( ( positive @ SY132 @ SY133 )
=> ( SY132 @ SY131 @ SY133 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(12,plain,
( ( ! [SY140: $i] :
( ~ ( rel @ sK1_SY14 @ SY140 )
| ? [SY23: mu] :
! [SY24: mu > $i > $o] :
( ( positive @ SY24 @ SY140 )
=> ( SY24 @ SY23 @ SY140 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ~ ( rel @ sK1_SY14 @ sK2_SY140 )
| ? [SY143: mu] :
! [SY144: mu > $i > $o] :
( ( positive @ SY144 @ sK2_SY140 )
=> ( SY144 @ SY143 @ sK2_SY140 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ~ ( ~ ( rel @ sK1_SY14 @ sK2_SY140 )
| ? [SY143: mu] :
! [SY144: mu > $i > $o] :
( ( positive @ SY144 @ sK2_SY140 )
=> ( SY144 @ SY143 @ sK2_SY140 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [SY122: $i] :
? [SY133: $i] :
( ( rel @ SY122 @ SY133 )
& ? [SY131: mu] :
! [SY132: mu > $i > $o] :
( ( positive @ SY132 @ SY133 )
=> ( SY132 @ SY131 @ SY133 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SY96: $i,SY97: mu] :
( ! [SY98: mu > $i > $o] :
( ( positive @ SY98 @ SY96 )
=> ( SY98 @ SY97 @ SY96 ) )
=> ( essence
@ ^ [SY84: mu,SY89: $i] :
! [SY90: mu > $i > $o] :
( ( positive @ SY90 @ SY89 )
=> ( SY90 @ SY84 @ SY89 ) )
@ SY97
@ SY96 ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [SY63: $i,SY64: $i] :
( ( rel @ SY63 @ SY64 )
=> ( rel @ SY64 @ SY63 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(18,plain,
( ( ! [SY33: $i] :
( positive
@ ^ [SY34: mu,SY42: $i] :
! [SY43: mu > $i > $o] :
( ( essence @ SY43 @ SY34 @ SY42 )
=> ! [SY55: $i] :
( ~ ( rel @ SY42 @ SY55 )
| ? [SY52: mu] : ( SY43 @ SY52 @ SY55 ) ) )
@ SY33 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(19,plain,
( ( ~ ( ~ ( rel @ sK1_SY14 @ sK2_SY140 )
| ? [SY143: mu] :
! [SY144: mu > $i > $o] :
( ( positive @ SY144 @ sK2_SY140 )
=> ( SY144 @ SY143 @ sK2_SY140 ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( rel @ SX0 @ SX1 )
| ~ ~ ! [SX2: mu] :
~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SX1 )
| ( SX3 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: mu] :
( ~ ! [SX2: mu > $i > $o] :
( ~ ( positive @ SX2 @ SX0 )
| ( SX2 @ SX1 @ SX0 ) )
| ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SX1
@ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(22,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel @ SX0 @ SX1 )
| ( rel @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(23,plain,
( ( ! [SX0: $i] :
( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( essence @ SX3 @ SX1 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[18,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(24,plain,
( ( ~ ( ~ ( rel @ sK1_SY14 @ sK2_SY140 )
| ~ ! [SX0: mu] :
~ ! [SX1: mu > $i > $o] :
( ~ ( positive @ SX1 @ sK2_SY140 )
| ( SX1 @ SX0 @ sK2_SY140 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19,god,mand,mbox,mbox_generic,mdia,mdia_generic,meq_ind,mequiv,mexists_ind,mexists_indset,mexists_prop,mfalse,mforall_ind,mforall_indset,mforall_prop,mimplied,mimplies,minvalid,mnot,mor,msymmetric,mtrue,mvalid,mxor,necessary_existence]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ! [SY145: $i] :
~ ~ ( ~ ( rel @ SV1 @ SY145 )
| ~ ~ ! [SX2: mu] :
~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SY145 )
| ( SX3 @ SX2 @ SY145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY148: mu] :
( ~ ! [SY149: mu > $i > $o] :
( ~ ( positive @ SY149 @ SV2 )
| ( SY149 @ SY148 @ SV2 ) )
| ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SY148
@ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY153: $i] :
( ~ ( rel @ SV3 @ SY153 )
| ( rel @ SY153 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV4: $i] :
( ( positive
@ ^ [SX1: mu,SX2: $i] :
! [SX3: mu > $i > $o] :
( ~ ( essence @ SX3 @ SX1 @ SX2 )
| ! [SX4: $i] :
( ~ ( rel @ SX2 @ SX4 )
| ~ ! [SX5: mu] :
~ ( SX3 @ SX5 @ SX4 ) ) )
@ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ( rel @ sK1_SY14 @ sK2_SY140 )
| ~ ! [SX0: mu] :
~ ! [SX1: mu > $i > $o] :
( ~ ( positive @ SX1 @ sK2_SY140 )
| ( SX1 @ SX0 @ sK2_SY140 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY145: $i] :
~ ~ ( ~ ( rel @ SV1 @ SY145 )
| ~ ~ ! [SX2: mu] :
~ ! [SX3: mu > $i > $o] :
( ~ ( positive @ SX3 @ SY145 )
| ( SX3 @ SX2 @ SY145 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV5: mu,SV2: $i] :
( ( ~ ! [SY159: mu > $i > $o] :
( ~ ( positive @ SY159 @ SV2 )
| ( SY159 @ SV5 @ SV2 ) )
| ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SV5
@ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( rel @ SV3 @ SV6 )
| ( rel @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( ~ ( rel @ sK1_SY14 @ sK2_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ! [SX0: mu] :
~ ! [SX1: mu > $i > $o] :
( ~ ( positive @ SX1 @ sK2_SY140 )
| ( SX1 @ SX0 @ sK2_SY140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ( rel @ SV1 @ ( sK3_SY145 @ SV1 ) )
| ~ ~ ! [SY163: mu] :
~ ! [SY164: mu > $i > $o] :
( ~ ( positive @ SY164 @ ( sK3_SY145 @ SV1 ) )
| ( SY164 @ SY163 @ ( sK3_SY145 @ SV1 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(36,plain,
! [SV5: mu,SV2: $i] :
( ( ( ~ ! [SY159: mu > $i > $o] :
( ~ ( positive @ SY159 @ SV2 )
| ( SY159 @ SV5 @ SV2 ) ) )
= $true )
| ( ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SV5
@ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( rel @ SV3 @ SV6 ) )
= $true )
| ( ( rel @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
( ( rel @ sK1_SY14 @ sK2_SY140 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(39,plain,
( ( ! [SX0: mu] :
~ ! [SX1: mu > $i > $o] :
( ~ ( positive @ SX1 @ sK2_SY140 )
| ( SX1 @ SX0 @ sK2_SY140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(40,plain,
! [SV1: $i] :
( ( ~ ( ~ ( rel @ SV1 @ ( sK3_SY145 @ SV1 ) )
| ~ ~ ! [SY163: mu] :
~ ! [SY164: mu > $i > $o] :
( ~ ( positive @ SY164 @ ( sK3_SY145 @ SV1 ) )
| ( SY164 @ SY163 @ ( sK3_SY145 @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV5: mu,SV2: $i] :
( ( ( ! [SY159: mu > $i > $o] :
( ~ ( positive @ SY159 @ SV2 )
| ( SY159 @ SV5 @ SV2 ) ) )
= $false )
| ( ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SV5
@ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV6: $i,SV3: $i] :
( ( ( rel @ SV3 @ SV6 )
= $false )
| ( ( rel @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV7: mu] :
( ( ~ ! [SY165: mu > $i > $o] :
( ~ ( positive @ SY165 @ sK2_SY140 )
| ( SY165 @ SV7 @ sK2_SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV1: $i] :
( ( ~ ( rel @ SV1 @ ( sK3_SY145 @ SV1 ) )
| ~ ~ ! [SY163: mu] :
~ ! [SY164: mu > $i > $o] :
( ~ ( positive @ SY164 @ ( sK3_SY145 @ SV1 ) )
| ( SY164 @ SY163 @ ( sK3_SY145 @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV2: $i,SV5: mu] :
( ( ( ~ ( positive @ ( sK4_SY159 @ SV5 @ SV2 ) @ SV2 )
| ( sK4_SY159 @ SV5 @ SV2 @ SV5 @ SV2 ) )
= $false )
| ( ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SV5
@ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(46,plain,
! [SV7: mu] :
( ( ! [SY165: mu > $i > $o] :
( ~ ( positive @ SY165 @ sK2_SY140 )
| ( SY165 @ SV7 @ sK2_SY140 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV1: $i] :
( ( ~ ( rel @ SV1 @ ( sK3_SY145 @ SV1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV1: $i] :
( ( ~ ~ ! [SY163: mu] :
~ ! [SY164: mu > $i > $o] :
( ~ ( positive @ SY164 @ ( sK3_SY145 @ SV1 ) )
| ( SY164 @ SY163 @ ( sK3_SY145 @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV2: $i,SV5: mu] :
( ( ( ~ ( positive @ ( sK4_SY159 @ SV5 @ SV2 ) @ SV2 ) )
= $false )
| ( ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SV5
@ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV2: $i,SV5: mu] :
( ( ( sK4_SY159 @ SV5 @ SV2 @ SV5 @ SV2 )
= $false )
| ( ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SV5
@ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV7: mu] :
( ( ~ ( positive @ ( sK5_SY165 @ SV7 ) @ sK2_SY140 )
| ( sK5_SY165 @ SV7 @ SV7 @ sK2_SY140 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(52,plain,
! [SV1: $i] :
( ( rel @ SV1 @ ( sK3_SY145 @ SV1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV1: $i] :
( ( ~ ! [SY163: mu] :
~ ! [SY164: mu > $i > $o] :
( ~ ( positive @ SY164 @ ( sK3_SY145 @ SV1 ) )
| ( SY164 @ SY163 @ ( sK3_SY145 @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
! [SV2: $i,SV5: mu] :
( ( ( positive @ ( sK4_SY159 @ SV5 @ SV2 ) @ SV2 )
= $true )
| ( ( essence
@ ^ [SX2: mu,SX3: $i] :
! [SX4: mu > $i > $o] :
( ~ ( positive @ SX4 @ SX3 )
| ( SX4 @ SX2 @ SX3 ) )
@ SV5
@ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV7: mu] :
( ( ~ ( positive @ ( sK5_SY165 @ SV7 ) @ sK2_SY140 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV7: mu] :
( ( sK5_SY165 @ SV7 @ SV7 @ sK2_SY140 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV1: $i] :
( ( ! [SY163: mu] :
~ ! [SY164: mu > $i > $o] :
( ~ ( positive @ SY164 @ ( sK3_SY145 @ SV1 ) )
| ( SY164 @ SY163 @ ( sK3_SY145 @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV7: mu] :
( ( positive @ ( sK5_SY165 @ SV7 ) @ sK2_SY140 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV1: $i] :
( ( ~ ! [SY166: mu > $i > $o] :
( ~ ( positive @ SY166 @ ( sK3_SY145 @ SV1 ) )
| ( SY166 @ ( sK6_SY163 @ SV1 ) @ ( sK3_SY145 @ SV1 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(60,plain,
! [SV1: $i] :
( ( ! [SY166: mu > $i > $o] :
( ~ ( positive @ SY166 @ ( sK3_SY145 @ SV1 ) )
| ( SY166 @ ( sK6_SY163 @ SV1 ) @ ( sK3_SY145 @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(61,plain,
! [SV1: $i,SV8: mu > $i > $o] :
( ( ~ ( positive @ SV8 @ ( sK3_SY145 @ SV1 ) )
| ( SV8 @ ( sK6_SY163 @ SV1 ) @ ( sK3_SY145 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(62,plain,
! [SV1: $i,SV8: mu > $i > $o] :
( ( ( ~ ( positive @ SV8 @ ( sK3_SY145 @ SV1 ) ) )
= $true )
| ( ( SV8 @ ( sK6_SY163 @ SV1 ) @ ( sK3_SY145 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(63,plain,
! [SV1: $i,SV8: mu > $i > $o] :
( ( ( positive @ SV8 @ ( sK3_SY145 @ SV1 ) )
= $false )
| ( ( SV8 @ ( sK6_SY163 @ SV1 ) @ ( sK3_SY145 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(64,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,63,58,56,54,52,50,42,38]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI005^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n003.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 Oct 6 13:51:54 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.31
% 0.40/0.31 No.of.Axioms: 4
% 0.40/0.31
% 0.40/0.31 Length.of.Defs: 4048
% 0.40/0.31
% 0.40/0.31 Contains.Choice.Funs: false
% 0.40/0.31 ...
% 0.40/0.31
% 0.40/0.31 ********************************
% 0.40/0.31 * All subproblems solved! *
% 0.40/0.31 ********************************
% 0.40/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.40/0.31
% 0.40/0.31 %**** Beginning of derivation protocol ****
% 0.40/0.31 % SZS output start CNFRefutation
% See solution above
% 0.40/0.31
% 0.40/0.31 %**** End of derivation protocol ****
% 0.40/0.31 %**** no. of clauses in derivation: 65 ****
% 0.40/0.31 %**** clause counter: 64 ****
% 0.40/0.31
% 0.40/0.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------